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# voronoipotato/Fsharp_4_1_spec.md Last active Jun 14, 2019

Note: This documentation is the specification of version 4.1 of the F# language, released in 2015-16.

Note: thi does not yet incorporate the RFCs for F# 4.1, see

https://github.com/fsharp/fslang-design/tree/master/FSharp-4.1

https://github.com/fsharp/fslang-design/tree/master/FSharp-4.1b

Discrepancies may exist between this specification and the 4.1 implementation. Some of these are noted as comments in this document. If you find further discrepancies please contact us and we will gladly address the issue in future releases of this specification. The F# team is always grateful for feedback on this specification, and on both the design and implementation of F#. You can submit feedback by opening issues, comments and pull requests at https://github.com/fsharp/fsfoundation/tree/gh-pages/specs/language-spec.

The latest version of this specification can be found at fsharp.org. Many thanks to the F# user community for their helpful feedback on the document so far.

Certain parts of this specification refer to the C# 4.0, Unicode, and IEEE specifications.

Authors: Don Syme, with assistance from Anar Alimov, Keith Battocchi, Jomo Fisher, Michael Hale, Jack Hu, Luke Hoban, Tao Liu, Dmitry Lomov, James Margetson, Brian McNamara, Joe Pamer, Penny Orwick, Daniel Quirk, Kevin Ransom, Chris Smith, Matteo Taveggia, Donna Malayeri, Wonseok Chae, Uladzimir Matsveyeu, Lincoln Atkinson, and others.

Notice

© 2005-2016 various contributors. Made available under the Creative Commons CC-by 4.0 licence.

Product and company names mentioned herein may be the trademarks of their respective owners.

• Initial updates for F# 4.1, May 2018

• Updates for F# 4.0, January 2016

• Updates for F# 3.1 and type providers, January 2016

• Edits to change version numbers for F# 3.1, May 2014

• Initial updates for F# 3.1, June 2013 (see online description of language updates)

• Updated to F# 3.0, September 2012

• Updated with formatting changes, April 2012

• Updated with grammar summary, December 2011

• Updated with glossary, index, and style corrections, February 2011

• Updated with glossary, index, and style corrections, August 2010

1. Introduction 11

1.1 A First Program 11

1.1.1 Lightweight Syntax 11

1.1.2 Making Data Simple 12

1.1.3 Making Types Simple 13

1.1.4 Functional Programming 13

1.1.5 Imperative Programming 15

1.1.6 .NET Interoperability and CLI Fidelity 15

1.1.7 Parallel and Asynchronous Programming 15

1.1.8 Strong Typing for Floating-Point Code 16

1.1.9 Object-Oriented Programming and Code Organization 17

1.1.10 Information-rich Programming 18

1.2 Notational Conventions in This Specification 19

2. Program Structure 21

3. Lexical Analysis 23

3.1 Whitespace 23

3.3 Conditional Compilation 24

3.4 Identifiers and Keywords 24

3.5 Strings and Characters 26

3.6 Symbolic Keywords 27

3.7 Symbolic Operators 28

3.8 Numeric Literals 28

3.8.1 Post-filtering of Adjacent Prefix Tokens 29

3.8.2 Post-filtering of Integers Followed by Adjacent “..” 30

3.8.3 Reserved Numeric Literal Forms 30

3.8.4 Shebang 30

3.9 Line Directives 30

3.10 Hidden Tokens 30

3.11 Identifier Replacements 31

4. Basic Grammar Elements 33

4.1 Operator Names 33

4.2 Long Identifiers 35

4.3 Constants 35

4.4 Operators and Precedence 36

4.4.1 Categorization of Symbolic Operators 36

4.4.2 Precedence of Symbolic Operators and Pattern/Expression Constructs 37

5. Types and Type Constraints 39

5.1 Checking Syntactic Types 40

5.1.1 Named Types 41

5.1.2 Variable Types 41

5.1.3 Tuple Types 42

5.1.4 Array Types 42

5.1.5 Constrained Types 42

5.2 Type Constraints 43

5.2.1 Subtype Constraints 43

5.2.2 Nullness Constraints 44

5.2.3 Member Constraints 44

5.2.4 Default Constructor Constraints 45

5.2.5 Value Type Constraints 45

5.2.6 Reference Type Constraints 45

5.2.7 Enumeration Constraints 46

5.2.8 Delegate Constraints 46

5.2.9 Unmanaged Constraints 46

5.2.10 Equality and Comparison Constraints 47

5.3 Type Parameter Definitions 47

5.4 Logical Properties of Types 48

5.4.1 Characteristics of Type Definitions 48

5.4.2 Expanding Abbreviations and Inference Equations 49

5.4.3 Type Variables and Definition Sites 50

5.4.4 Base Type of a Type 51

5.4.5 Interfaces Types of a Type 51

5.4.6 Type Equivalence 51

5.4.7 Subtyping and Coercion 52

5.4.8 Nullness 52

5.4.9 Default Initialization 53

5.4.10 Dynamic Conversion Between Types 53

6. Expressions 55

6.1 Some Checking and Inference Terminology 57

6.2 Elaboration and Elaborated Expressions 58

6.3 Data Expressions 59

6.3.1 Simple Constant Expressions 60

6.3.2 Tuple Expressions 61

6.3.3 List Expressions 62

6.3.4 Array Expressions 62

6.3.5 Record Expressions 62

6.3.6 Copy-and-update Record Expressions 64

6.3.7 Function Expressions 65

6.3.8 Object Expressions 65

6.3.9 Delayed Expressions 67

6.3.10 Computation Expressions 67

6.3.11 Sequence Expressions 79

6.3.12 Range Expressions 80

6.3.13 Lists via Sequence Expressions 80

6.3.14 Arrays Sequence Expressions 81

6.3.15 Null Expressions 81

6.3.16 'printf' Formats 81

6.4 Application Expressions 82

6.4.1 Basic Application Expressions 82

6.4.2 Object Construction Expressions 84

6.4.3 Operator Expressions 85

6.4.4 Dynamic Operator Expressions 86

6.4.6 Lookup Expressions 87

6.4.7 Slice Expressions 88

6.4.8 Member Constraint Invocation Expressions 89

6.4.9 Assignment Expressions 90

6.5 Control Flow Expressions 91

6.5.1 Parenthesized and Block Expressions 91

6.5.2 Sequential Execution Expressions 91

6.5.3 Conditional Expressions 92

6.5.4 Shortcut Operator Expressions 92

6.5.5 Pattern-Matching Expressions and Functions 93

6.5.6 Sequence Iteration Expressions 93

6.5.7 Simple for-Loop Expressions 94

6.5.8 While Expressions 95

6.5.9 Try-with Expressions 95

6.5.10 Reraise Expressions 95

6.5.11 Try-finally Expressions 96

6.5.12 Assertion Expressions 96

6.6 Definition Expressions 96

6.6.1 Value Definition Expressions 97

6.6.2 Function Definition Expressions 98

6.6.3 Recursive Definition Expressions 99

6.6.4 Deterministic Disposal Expressions 99

6.7 Type-Related Expressions 100

6.7.1 Type-Annotated Expressions 100

6.7.2 Static Coercion Expressions 100

6.7.3 Dynamic Type-Test Expressions 100

6.7.4 Dynamic Coercion Expressions 101

6.8 Quoted Expressions 101

6.8.1 Strongly Typed Quoted Expressions 102

6.8.2 Weakly Typed Quoted Expressions 102

6.8.3 Expression Splices 103

6.9 Evaluation of Elaborated Forms 104

6.9.1 Values and Execution Context 104

6.9.2 Parallel Execution and Memory Model 105

6.9.3 Zero Values 106

6.9.4 Taking the Address of an Elaborated Expression 106

6.9.5 Evaluating Value References 107

6.9.6 Evaluating Function Applications 107

6.9.7 Evaluating Method Applications 107

6.9.8 Evaluating Union Cases 108

6.9.9 Evaluating Field Lookups 108

6.9.10 Evaluating Array Expressions 108

6.9.11 Evaluating Record Expressions 108

6.9.12 Evaluating Function Expressions 108

6.9.13 Evaluating Object Expressions 109

6.9.14 Evaluating Definition Expressions 109

6.9.15 Evaluating Integer For Loops 109

6.9.16 Evaluating While Loops 109

6.9.17 Evaluating Static Coercion Expressions 109

6.9.18 Evaluating Dynamic Type-Test Expressions 110

6.9.19 Evaluating Dynamic Coercion Expressions 110

6.9.20 Evaluating Sequential Execution Expressions 111

6.9.21 Evaluating Try-with Expressions 111

6.9.22 Evaluating Try-finally Expressions 111

6.9.24 Values with Underspecified Object Identity and Type Identity 112

7. Patterns 115

7.1 Simple Constant Patterns 116

7.2 Named Patterns 116

7.2.1 Union Case Patterns 117

7.2.2 Literal Patterns 118

7.2.3 Active Patterns 118

7.3 “As” Patterns 120

7.4 Wildcard Patterns 120

7.5 Disjunctive Patterns 121

7.6 Conjunctive Patterns 121

7.7 List Patterns 121

7.8 Type-Annotated Patterns 122

7.9 Dynamic Type-Test Patterns 122

7.10 Record Patterns 123

7.11 Array Patterns 123

7.12 Null Patterns 124

7.13 Guarded Pattern Rules 124

8. Type Definitions 125

8.1 Type Definition Group Checking and Elaboration 128

8.2 Type Kind Inference 131

8.3 Type Abbreviations 132

8.4 Record Type Definitions 133

8.4.1 Members in Record Types 134

8.4.2 Name Resolution and Record Field Labels 134

8.4.3 Structural Hashing, Equality, and Comparison for Record Types 134

8.4.4 With/End in Record Type Definitions 134

8.4.5 CLIMutable Attributes 134

8.5 Union Type Definitions 135

8.5.1 Members in Union Types 136

8.5.2 Structural Hashing, Equality, and Comparison for Union Types 136

8.5.3 With/End in Union Type Definitions 136

8.5.4 Compiled Form of Union Types for Use from Other CLI Languages 137

8.6 Class Type Definitions 137

8.6.1 Primary Constructors in Classes 138

8.6.2 Members in Classes 142

8.6.3 Additional Object Constructors in Classes 142

8.6.4 Additional Fields in Classes 143

8.7 Interface Type Definitions 144

8.8 Struct Type Definitions 145

8.9 Enum Type Definitions 147

8.10 Delegate Type Definitions 148

8.11 Exception Definitions 148

8.12 Type Extensions 149

8.12.1 Imported CLI C# Extensions Members 151

8.13 Members 152

8.13.1 Property Members 153

8.13.2 Auto-implemented Properties 154

8.13.3 Method Members 155

8.13.4 Curried Method Members 155

8.13.5 Named Arguments to Method Members 156

8.13.6 Optional Arguments to Method Members 157

8.13.7 Type-directed Conversions at Member Invocations 159

8.13.9 Naming Restrictions for Members 162

8.13.10 Members Represented as Events 162

8.13.11 Members Represented as Static Members 163

8.14 Abstract Members and Interface Implementations 164

8.14.1 Abstract Members 164

8.14.2 Members that Implement Abstract Members 165

8.14.3 Interface Implementations 167

8.15 Equality, Hashing, and Comparison 169

8.15.1 Equality Attributes 170

8.15.2 Comparison Attributes 170

8.15.3 Behavior of the Generated Object.Equals Implementation 172

8.15.4 Behavior of the Generated CompareTo Implementations 172

8.15.5 Behavior of the Generated GetHashCode Implementations 173

8.15.6 Behavior of Hash, =, and Compare 173

9. Units Of Measure 175

9.1 Measures 176

9.2 Constants Annotated by Measures 177

9.3 Relations on Measures 177

9.3.1 Constraint Solving 178

9.3.2 Generalization of Measure Variables 179

9.4 Measure Definitions 179

9.5 Measure Parameter Definitions 179

9.6 Measure Parameter Erasure 180

9.7 Type Definitions with Measures in the F# Core Library 180

9.8 Restrictions 181

10. Namespaces and Modules 183

10.1 Namespace Declaration Groups 183

10.2 Module Definitions 185

10.2.1 Function and Value Definitions in Modules 186

10.2.2 Literal Definitions in Modules 187

10.2.3 Type Function Definitions in Modules 188

10.2.4 Active Pattern Definitions in Modules 189

10.2.5 “do” statements in Modules 189

10.3 Import Declarations 190

10.4 Module Abbreviations 190

10.5 Accessibility Annotations 191

11. Namespace and Module Signatures 193

11.1 Signature Elements 194

11.1.1 Value Signatures 194

11.1.2 Type Definition and Member Signatures 195

11.2 Signature Conformance 195

11.2.1 Signature Conformance for Functions and Values 196

11.2.2 Signature Conformance for Members 197

12. Program Structure and Execution 199

12.1 Implementation Files 200

12.2 Signature Files 201

12.3 Script Files 202

12.4 Compiler Directives 202

12.5 Program Execution 204

12.5.1 Execution of Static Initializers 204

12.5.2 Explicit Entry Point 207

13. Custom Attributes and Reflection 209

13.1 Custom Attributes 209

13.1.1 Custom Attributes and Signatures 211

13.2 Reflected Forms of Declaration Elements 211

14. Inference Procedures 213

14.1 Name Resolution 213

14.1.1 Name Environments 213

14.1.2 Name Resolution in Module and Namespace Paths 214

14.1.3 Opening Modules and Namespace Declaration Groups 214

14.1.4 Name Resolution in Expressions 215

14.1.5 Name Resolution for Members 218

14.1.6 Name Resolution in Patterns 219

14.1.7 Name Resolution for Types 220

14.1.8 Name Resolution for Type Variables 221

14.1.9 Field Label Resolution 221

14.2 Resolving Application Expressions 221

14.2.1 Unqualified Lookup 222

14.2.2 Item-Qualified Lookup 223

14.2.3 Expression-Qualified Lookup 224

14.3 Function Application Resolution 226

14.4 Method Application Resolution 226

14.4.1 Additional Propagation of Known Type Information in F# 3.1 232

14.4.2 Conditional Compilation of Member Calls 232

14.4.3 Implicit Insertion of Flexibility for Uses of Functions and Members 233

14.5 Constraint Solving 234

14.5.1 Solving Equational Constraints 235

14.5.2 Solving Subtype Constraints 235

14.5.3 Solving Nullness, Struct, and Other Simple Constraints 236

14.5.4 Solving Member Constraints 236

14.5.5 Over-constrained User Type Annotations 237

14.6 Checking and Elaborating Function, Value, and Member Definitions 238

14.6.1 Ambiguities in Function and Value Definitions 238

14.6.2 Mutable Value Definitions 239

14.6.3 Processing Value Definitions 239

14.6.4 Processing Function Definitions 239

14.6.5 Processing Recursive Groups of Definitions 240

14.6.6 Recursive Safety Analysis 241

14.6.7 Generalization 243

14.6.8 Condensation of Generalized Types 245

14.7 Dispatch Slot Inference 247

14.8 Dispatch Slot Checking 248

14.9 Byref Safety Analysis 249

14.10 Arity Inference 250

14.11 Additional Constraints on CLI Methods 252

15. Lexical Filtering 253

15.1 Lightweight Syntax 253

15.1.1 Basic Lightweight Syntax Rules by Example 253

15.1.2 Inserted Tokens 254

15.1.3 Grammar Rules Including Inserted Tokens 254

15.1.4 Offside Lines 255

15.1.5 The Pre-Parse Stack 256

15.1.6 Full List of Offside Contexts 256

15.1.7 Balancing Rules 257

15.1.8 Offside Tokens, Token Insertions, and Closing Contexts 258

15.1.9 Exceptions to the Offside Rules 259

15.1.10 Permitted Undentations 261

15.2 High Precedence Application 262

15.3 Lexical Analysis of Type Applications 263

16. Provided Types 265

16.1 Static Parameters 266

16.1.1 Mangling of Static Parameter Values 266

16.2 Provided Namespace 267

16.3 Provided Type Definitions 267

16.3.1 Generated v. Erased Types 267

16.3.2 Type References 268

16.3.3 Static Parameters 268

16.3.4 Kind 268

16.3.5 Inheritance 269

16.3.6 Members 269

16.3.7 Attributes 270

16.3.8 Accessibility 270

16.3.9 Elaborated Code 270

16.3.10 Further Restrictions 271

17. Special Attributes and Types 272

17.1 Custom Attributes Recognized by F# 272

17.2 Custom Attributes Emitted by F# 277

17.3 Custom Attributes Not Recognized by F# 278

17.4 Exceptions Thrown by F# Language Primitives 278

18. The F# Library FSharp.Core.dll 281

18.1 Basic Types (FSharp.Core) 281

18.1.1 Basic Type Abbreviations 281

18.1.2 Basic Types that Accept Unit of Measure Annotations 281

18.1.3 The nativeptr<_> Type 282

18.2 Basic Operators and Functions (FSharp.Core.Operators) 282

18.2.1 Basic Arithmetic Operators 282

18.2.2 Generic Equality and Comparison Operators 283

18.2.3 Bitwise Operators 283

18.2.4 Math Operators 283

18.2.5 Function Pipelining and Composition Operators 284

18.2.6 Object Transformation Operators 284

18.2.7 Pair Operators 284

18.2.8 Exception Operators 284

18.2.9 Input/Output Handles 284

18.3 Checked Arithmetic Operators 285

18.4 List and Option Types 286

18.4.1 The List Type 286

18.4.2 The Option Type 286

18.5 Lazy Computations (Lazy) 286

18.6 Asynchronous Computations (Async) 286

18.7 Query Expressions 287

18.8 Agents (MailboxProcessor) 287

18.9 Event Types 287

18.10 Immutable Collection Types (Map, Set) 287

18.11 Text Formatting (Printf) 287

18.12 Reflection 287

18.13 Quotations 287

18.14 Native Pointer Operations 287

18.14.1 Stack Allocation 288

19. Features for ML Compatibility 289

19.1 Conditional Compilation for ML Compatibility 289

19.2 Extra Syntactic Forms for ML Compatibility 289

19.3 Extra Operators 290

19.4 File Extensions and Lexical Matters 291

Appendix A: F# Grammar Summary 292

References 313

Glossary 314

Index 326

# Introduction

F# is a scalable, succinct, type-safe, type-inferred, efficiently executing functional/imperative/object-oriented programming language. It aims to be the premier typed functional programming language for the .NET framework and other implementations of the Ecma 335 Common Language Infrastructure (CLI) specification. F# was partly inspired by the OCaml language and shares some common core constructs with it.

## A First Program

Over the next few sections, we will look at some small F# programs, describing some important aspects of F# along the way. As an introduction to F#, consider the following program:

let numbers = [ 1 .. 10 ]

let square x = x * x

let squares = List.map square numbers

printfn "N^2 = %A" squares

To explore this program, you can:

• Compile it as a project in a development environment such as Visual Studio.

• Manually invoke the F# command line compiler fsc.exe.

• Use F# Interactive, the dynamic compiler that is part of the F# distribution.

### Lightweight Syntax

The F# language uses simplified, indentation-aware syntactic constructs known as lightweight syntax. The lines of the sample program in the previous section form a sequence of declarations and are aligned on the same column. For example, the two lines in the following code are two separate declarations:

let squares = List.map square numbers

printfn "N^2 = %A" squares

Lightweight syntax applies to all the major constructs of the F# syntax. In the next example, the code is incorrectly aligned. The declaration starts in the first line and continues to the second and subsequent lines, so those lines must be indented to the same column under the first line:

let computeDerivative f x =

let p1 = f (x - 0.05)

let p2 = f (x + 0.05)

(p2 - p1) / 0.1

The following shows the correct alignment:

let computeDerivative f x =

let p1 = f (x - 0.05)

let p2 = f (x + 0.05)

(p2 - p1) / 0.1

The use of lightweight syntax is the default for all F# code in files with the extension .fs, .fsx, .fsi, or .fsscript.

### Making Data Simple

The first line in our sample simply declares a list of numbers from one through ten.

let numbers = [1 .. 10]

An F# list is an immutable linked list, which is a type of data used extensively in functional programming. Some operators that are related to lists include :: to add an item to the front of a list and @ to concatenate two lists. If we try these operators in F# Interactive, we see the following results:

> let vowels = ['e'; 'i'; 'o'; 'u'];;

val vowels: char list = ['e'; 'i'; 'o'; 'u']

> ['a'] @ vowels;;

val it: char list = ['a'; 'e'; 'i'; 'o'; 'u']

> vowels @ ['y'];;

val it: char list = ['e'; 'i'; 'o'; 'u'; 'y']

Note that double semicolons delimit lines in F# Interactive, and that F# Interactive prefaces the result with val to indicate that the result is an immutable value, rather than a variable.

F# supports several other highly effective techniques to simplify the process of modeling and manipulating data such as tuples, options, records, unions, and sequence expressions. A tuple is an ordered collection of values that is treated as an atomic unit. In many languages, if you want to pass around a group of related values as a single entity, you need to create a named type, such as a class or record, to store these values. A tuple allows you to keep things organized by grouping related values together, without introducing a new type.

To define a tuple, you separate the individual components with commas.

> let tuple = (1, false, "text");;

val tuple : int * bool * string = (1, false, "text")

> let getNumberInfo (x : int) = (x, x.ToString(), x * x);;

val getNumberInfo : int -> int * string * int

> getNumberInfo 42;;

val it : int * string * int = (42, "42", 1764)

A key concept in F# is immutability. Tuples and lists are some of the many types in F# that are immutable, and indeed most things in F# are immutable by default. Immutability means that once a value is created and given a name, the value associated with the name cannot be changed. Immutability has several benefits. Most notably, it prevents many classes of bugs, and immutable data is inherently thread-safe, which makes the process of parallelizing code simpler.

### Making Types Simple

The next line of the sample program defines a function called square, which squares its input.

let square x = x * x

Most statically-typed languages require that you specify type information for a function declaration. However, F# typically infers this type information for you. This process is referred to as type inference.

From the function signature, F# knows that square takes a single parameter named x and that the function returns x * x. The last thing evaluated in an F# function body is the return value; hence there is no “return” keyword here. Many primitive types support the multiplication (*) operator (such as byte, uint64, and double); however, for arithmetic operations, F# infers the type int (a signed 32-bit integer) by default.

Although F# can typically infer types on your behalf, occasionally you must provide explicit type annotations in F# code. For example, the following code uses a type annotation for one of the parameters to tell the compiler the type of the input.

> let concat (x : string) y = x + y;;

val concat : string -> string -> string

Because x is stated to be of type string, and the only version of the + operator that accepts a left-hand argument of type string also takes a string as the right-hand argument, the F# compiler infers that the parameter y must also be a string. Thus, the result of x + y is the concatenation of the strings. Without the type annotation, the F# compiler would not have known which version of the + operator was intended and would have assumed int data by default.

The process of type inference also applies automatic generalization to declarations. This automatically makes code generic when possible, which means the code can be used on many types of data. For example, the following code defines a function that returns a new tuple in which the two values are swapped:

> let swap (x, y) = (y, x);;

val swap : 'a * 'b -> 'b * 'a

> swap (1, 2);;

val it : int * int = (2, 1)

> swap ("you", true);;

val it : bool * string = (true,"you")

Here the function swap is generic, and 'a and 'b represent type variables, which are placeholders for types in generic code. Type inference and automatic generalization greatly simplify the process of writing reusable code fragments.

### Functional Programming

Continuing with the sample, we have a list of integers named numbers, and the square function, and we want to create a new list in which each item is the result of a call to our function. This is called mapping our function over each item in the list. The F# library function List.map does just that:

let squares = List.map square numbers

Consider another example:

> List.map (fun x -> x % 2 = 0) [1 .. 5];;

val it : bool list

= [false; true; false; true; false]

The code (fun x -> x % 2 = 0) defines an anonymous function, called a function expression, that takes a single parameter x and returns the result x % 2 = 0, which is a Boolean value that indicates whether x is even. The -> symbol separates the argument list (x) from the function body (x % 2 = 0).

Both of these examples pass a function as a parameter to another function—the first parameter to List.map is itself another function. Using functions as function values is a hallmark of functional programming.

Another tool for data transformation and analysis is pattern matching. This powerful switch construct allows you to branch control flow and to bind new values. For example, we can match an F# list against a sequence of list elements.

let checkList alist =

match alist with

| [] -> 0

| [a] -> 1

| [a; b] -> 2

| [a; b; c] -> 3

| _ -> failwith "List is too big!"

In this example, alist is compared with each potentially matching pattern of elements. When alist matches a pattern, the result expression is evaluated and is returned as the value of the match expression. Here, the ‑> operator separates a pattern from the result that a match returns.

Pattern matching can also be used as a control construct—for example, by using a pattern that performs a dynamic type test:

let getType (x : obj) =

match x with

| :? string -> "x is a string"

| :? int -> "x is an int"

| :? System.Exception -> "x is an exception"

The :? operator returns true if the value matches the specified type, so if x is a string, getType returns “x is a string”.

Function values can also be combined with the pipeline operator, |>. For example, given these functions:

let square x = x * x

let toStr (x : int) = x.ToString()

let reverse (x : string) = new System.String(Array.rev (x.ToCharArray()))

We can use the functions as values in a pipeline:

> let result = 32 |> square |> toStr |> reverse;;

val it : string = "4201"

Pipelining demonstrates one way in which F# supports compositionality, a key concept in functional programming. The pipeline operator simplifies the process of writing compositional code where the result of one function is passed into the next.

### Imperative Programming

The next line of the sample program prints text in the console window.

printfn "N^2 = %A" squares

The F# library function printfn is a simple and type-safe way to print text in the console window. Consider this example, which prints an integer, a floating-point number, and a string:

> printfn "%d * %f = %s" 5 0.75 ((5.0 * 0.75).ToString());;

5 * 0.750000 = 3.75

val it : unit = ()

The format specifiers %d, %f, and %s are placeholders for integers, floats, and strings. The %A format can be used to print arbitrary data types (including lists).

The printfn function is an example of imperative programming, which means calling functions for their side effects. Other commonly used imperative programming techniques include arrays and dictionaries (also called hash tables). F# programs typically use a mixture of functional and imperative techniques.

### .NET Interoperability and CLI Fidelity

The Common Language Infrastructure (CLI) function System.Console.ReadKey to pause the program before the console window closes.

Because F# is built on top of CLI implementations, you can call any CLI library from F#. Furthermore, other CLI languages can easily use any F# components.

### Parallel and Asynchronous Programming

F# is both a parallel and a reactive language. During execution, F# programs can have multiple parallel active evaluations and multiple pending reactions, such as callbacks and agents that wait to react to events and messages.

One way to write parallel and reactive F# programs is to use F# async expressions. For example, the code below is similar to the original program in §1.1 except that it computes the Fibonacci function (using a technique that will take some time) and schedules the computation of the numbers in parallel:

let rec fib x = if x < 2 then 1 else fib(x-1) + fib(x-2)

let fibs =

Async.Parallel [ for i in 0..40 -> async { return fib(i) } ]

|> Async.RunSynchronously

printfn "The Fibonacci numbers are %A" fibs

The preceding code sample shows multiple, parallel, CPU-bound computations.

F# is also a reactive language. The following example requests multiple web pages in parallel, reacts to the responses for each request, and finally returns the collected results.

open System

open System.IO

open System.Net

let http url =

async { let req = WebRequest.Create(Uri url)

use! resp = req.AsyncGetResponse()

use stream = resp.GetResponseStream()

return contents }

let htmlOfSites =

Async.Parallel [for site in sites -> http site ]

|> Async.RunSynchronously

By using asynchronous workflows together with other CLI libraries, F# programs can implement parallel tasks, parallel I/O operations, and message-receiving agents.

### Strong Typing for Floating-Point Code

F# applies type checking and type inference to floating-point-intensive domains through units of measure inference and checking. This feature allows you to type-check programs that manipulate floating-point numbers that represent physical and abstract quantities in a stronger way than other typed languages, without losing any performance in your compiled code. You can think of this feature as providing a type system for floating-point code.

Consider the following example:

[<Measure>] type kg

[<Measure>] type m

[<Measure>] type s

let gravityOnEarth = 9.81<m/s^2>

let heightOfTowerOfPisa = 55.86<m>

let speedOfImpact = sqrt(2.0 * gravityOnEarth * heightOfTowerOfPisa)

The Measure attribute tells F# that kg, s, and m are not really types in the usual sense of the word, but are used to build units of measure. Here speedOfImpact is inferred to have type float<m/s>.

### Object-Oriented Programming and Code Organization

The sample program shown at the start of this chapter is a script. Although scripts are excellent for rapid prototyping, they are not suitable for larger software components. F# supports the transition from scripting to structured code through several techniques.

The most important of these is object-oriented programming through the use of class type definitions, interface type definitions, and object expressions. Object-oriented programming is a primary application programming interface (API) design technique for controlling the complexity of large software projects. For example, here is a class definition for an encoder/decoder object.

open System

/// Build an encoder/decoder object that maps characters to an

/// encoding and back. The encoding is specified by a sequence

/// of character pairs, for example, [('a','Z'); ('Z','a')]

type CharMapEncoder(symbols: seq<char*char>) =

let swap (x, y) = (y, x)

/// An immutable tree map for the encoding

let fwd = symbols |> Map.ofSeq

/// An immutable tree map for the decoding

let bwd = symbols |> Seq.map swap |> Map.ofSeq

let encode (s:string) =

String [| for c in s -> if fwd.ContainsKey(c) then fwd.[c] else c |]

let decode (s:string) =

String [| for c in s -> if bwd.ContainsKey(c) then bwd.[c] else c |]

/// Encode the input string

member x.Encode(s) = encode s

/// Decode the given string

member x.Decode(s) = decode s

You can instantiate an object of this type as follows:

let rot13 (c:char) =

char(int 'a' + ((int c - int 'a' + 13) % 26))

let encoder =

CharMapEncoder( [for c in 'a'..'z' -> (c, rot13 c)])

And use the object as follows:

> "F# is fun!" |> encoder.Encode ;;

val it : string = "F# vf sha!"

> "F# is fun!" |> encoder.Encode |> encoder.Decode ;;

val it : String = "F# is fun!"

An interface type can encapsulate a family of object types:

open System

type IEncoding =

abstract Encode : string -> string

abstract Decode : string -> string

In this example, IEncoding is an interface type that includes both Encode and Decode object types.

Both object expressions and type definitions can implement interface types. For example, here is an object expression that implements the IEncoding interface type:

let nullEncoder =

{ new IEncoding with

member x.Encode(s) = s

member x.Decode(s) = s }

Modules are a simple way to encapsulate code during rapid prototyping when you do not want to spend the time to design a strict object-oriented type hierarchy. In the following example, we place a portion of our original script in a module.

module ApplicationLogic =

let numbers n = [1 .. n]

let square x = x * x

let squares n = numbers n |> List.map square

printfn "Squares up to 5 = %A" (ApplicationLogic.squares 5)

printfn "Squares up to 10 = %A" (ApplicationLogic.squares 10)

Modules are also used in the F# library design to associate extra functionality with types. For example, List.map is a function in a module.

Other mechanisms aimed at supporting software engineering include signatures, which can be used to give explicit types to components, and namespaces, which serve as a way of organizing the name hierarchies for larger APIs.

### Information-rich Programming

F# Information-rich programming addresses the trend toward greater availability of data, services, and information. The key to information-rich programming is to eliminate barriers to working with diverse information sources that are available on the Internet and in modern enterprise environments. Type providers and query expressions are a significant part of F# support for information-rich programming.

The F# Type Provider mechanism allows you to seamlessly incorporate, in a strongly typed manner, data and services from external sources. A type provider presents your program with new types and methods that are typically based on the schemas of external information sources. For example, an F# type provider for Structured Query Language (SQL) supplies types and methods that allow programmers to work directly with the tables of any SQL database:

// Add References to FSharp.Data.TypeProviders, System.Data, and System.Data.Linq

type schema = SqlDataConnection<"Data Source=localhost;Integrated Security=SSPI;">

let db = schema.GetDataContext()

The type provider connects to the database automatically and uses this for IntelliSense and type information.

Query expressions (added in F# 3.0) add the established power of query-based programming against SQL, Open Data Protocol (OData), and other structured or relational data sources. Query expressions provide support for Language-Integrated Query (LINQ) in F#, and several query operators enable you to construct more complex queries. For example, we can create a query to filter the customers in the data source:

let countOfCustomers =

query { for customer in db.Customers do

where (customer.LastName.StartsWith("N"))

select (customer.FirstName, customer.LastName) }

Now it is easier than ever to access many important data sources—including enterprise, web, and cloud—by using a set of built-in type providers for SQL databases and web data protocols. Where necessary, you can create your own custom type providers or reference type providers that others have created. For example, assume your organization has a data service that provides a large and growing number of named data sets, each with its own stable data schema. You may choose to create a type provider that reads the schemas and presents the latest available data sets to the programmer in a strongly typed way.

## Notational Conventions in This Specification

This specification describes the F# language by using a mixture of informal and semiformal techniques. All examples in this specification use lightweight syntax, unless otherwise specified.

Regular expressions are given in the usual notation, as shown in the table:

Notation Meaning
regexp+ One or more occurrences
regexp* Zero or more occurrences
regexp? Zero or one occurrences
[ char - char ] Range of ASCII characters
[ ^ char - char ] Any characters except those in the range

Unicode character classes are referred to by their abbreviation as used in CLI libraries for regular expressions—for example, \Lu refers to any uppercase letter. The following characters are referred to using the indicated notation:

Character Name Notation
\b backspace ASCII/UTF-8/UTF-16/UTF-32 code 08
\n newline ASCII/UTF-8/UTF-16/UTF-32 code 10
\r return ASCII/UTF-8/UTF-16/UTF-32 code 13
\t tab ASCII/UTF-8/UTF-16/UTF-32 code 09

Strings of characters that are clearly not a regular expression are written verbatim. Therefore, the following string

abstract

matches precisely the characters abstract.

Where appropriate, apostrophes and quotation marks enclose symbols that are used in the specification of the grammar itself, such as '<' and '|'. For example, the following regular expression matches (+) or (-):

'(' (+|-) ')'

This regular expression matches precisely the characters #if:

"#if"

Regular expressions are typically used to specify tokens.

token token-name = regexp

In the grammar rules, the notation element-nameopt indicates an optional element. The notation ... indicates repetition of the preceding non-terminal construct and the separator token. For example, expr ',' ... ',' expr means a sequence of one or more expr elements separated by commas.

# Program Structure

The inputs to the F# compiler or the F# Interactive dynamic compiler consist of:

• Source code files, with extensions .fs, .fsi, .fsx, or .fsscript.
• Files with extension .fs must conform to grammar element implementation-file in §12.1.

• Files with extension .fsi must conform to grammar element signature-file in §12.2.

• Files with extension .fsx or .fsscript must conform to grammar element script-file in §12.3.

• Script fragments (for F# Interactive). These must conform to grammar element script-fragment. Script fragments can be separated by ;; tokens.

• Assembly references that are specified by command line arguments or interactive directives.

• Compilation parameters that are specified by command line arguments or interactive directives.

• Compiler directives such as #time.

The COMPILED compilation symbol is defined for input that the F# compiler has processed. The INTERACTIVE compilation symbol is defined for input that F# Interactive has processed.

Processing the source code portions of these inputs consists of the following steps:

1. Decoding. Each file and source code fragment is decoded into a stream of Unicode characters, as described in the C# specification, sections 2.3 and 2.4. The command-line options may specify a code page for this process.

2. Tokenization. The stream of Unicode characters is broken into a token stream by the lexical analysis described in §3.

3. Lexical Filtering. The token stream is filtered by a state machine that implements the rules described in §15. Those rules describe how additional (artificial) tokens are inserted into the token stream and how some existing tokens are replaced with others to create an augmented token stream.

4. Parsing. The augmented token stream is parsed according to the grammar specification in this document.

5. Importing. The imported assembly references are resolved to F# or CLI assembly specifications, which are then imported. From the F# perspective, this results in the pre-definition of numerous namespace declaration groups (§12.1), types and type provider instances. The namespace declaration groups are then combined to form an initial name resolution environment (§14.1).

6. Checking. The results of parsing are checked one by one. Checking involves such procedures as Name Resolution (§14.1), Constraint Solving (§14.5), and Generalization (§14.6.7), as well as the application of other rules described in this specification.

Type inference uses variables to represent unknowns in the type inference problem. The various checking processes maintain tables of context information including a name resolution environment and a set of current inference constraints. After the processing of a file or program fragment is complete, all such variables have been either generalized or resolved and the type inference environment is discarded.

7. Elaboration. One result of checking is an elaborated program fragment that contains elaborated declarations, expressions, and types. For most constructs, such as constants, control flow, and data expressions, the elaborated form is simple. Elaborated forms are used for evaluation, CLI reflection, and the F# expression trees that are returned by quoted expressions (§6.8).

8. Execution. Elaborated program fragments that are successfully checked are added to a collection of available program fragments. Each fragment has a static initializer. Static initializers are executed as described in (§12.5).

# Lexical Analysis

Lexical analysis converts an input stream of Unicode characters into a stream of tokens by iteratively processing the stream. If more than one token can match a sequence of characters in the source file, lexical processing always forms the longest possible lexical element. Some tokens, such as block-comment-start, are discarded after processing as described later in this section.

## Whitespace

Whitespace consists of spaces and newline characters.

regexp whitespace = ' '+

regexp newline = '\n' | '\r' '\n'

token whitespace-or-newline = whitespace | newline

Whitespace tokens whitespace-or-newline are discarded from the returned token stream.

Block comments are delimited by (* and *) and may be nested. Single-line comments begin with two backslashes (//) and extend to the end of the line.

token block-comment-start = "(*"

token block-comment-end = "*)"

token end-of-line-comment = "//" [^'\n' '\r']*

When the input stream matches a block-comment-start token, the subsequent text is tokenized recursively against the tokens that are described in §3 until a block-comment-end token is found. The intermediate tokens are discarded.

For example, comments can be nested, and strings that are embedded within comments are tokenized by the rules for string, verbatim-string, and triple-quoted string. In particular, strings that are embedded in comments are tokenized in their entirety, without considering closing *) marks. As a result of this rule, the following is a valid comment:

(* Here's a code snippet: let s = "*)" *)

However, the following construct, which was valid in F# 2.0, now produces a syntax error because a closing comment token *) followed by a triple-quoted mark is parsed as part of a string:

(* """ *)

For the purposes of this specification, comment tokens are discarded from the returned lexical stream. In practice, XML documentation tokens are end-of-line-comments that begin with ///. The delimiters are retained and are associated with the remaining elements to generate XML documentation.

## Conditional Compilation

The lexical preprocessing directives #if ident**/#else/#endif** delimit conditional compilation sections. The following describes the grammar for such sections:

token if-directive = "#if" whitespace if-expression-text

token else-directive = "#else"

token endif-directive = "#endif"

if-expression-term =

ident-text

'(' if-expression ')'

if-expression-neg =

if-expression-term

'!' if-expression-term

if-expression-and =

if-expression-neg

if-expression-and && if-expression-and

if-expression-or =

if-expression-and

if-expression-or || if-expression-or

if-expression = if-expression-or

A preprocessing directive always occupies a separate line of source code and always begins with a # character followed immediately by a preprocessing directive name, with no intervening whitespace. However, whitespace can appear before the # character. A source line that contains the #if, #else, or #endif directive can end with whitespace and a single-line comment. Multiple-line comments are not permitted on source lines that contain preprocessing directives.

If an if-directive token is matched during tokenization, text is recursively tokenized until a corresponding else-directive or endif-directive. If the evaluation of the associated if-expression-text when parsed as an if-expression is true in the compilation environment defines (where each ident-text is evaluataed according to the values given by command line options such as –define), the token stream includes the tokens between the if-directive and the corresponding else-directive or endif-directive. Otherwise, the tokens are discarded. The converse applies to the text between any corresponding else-directive and the endif-directive.

• In skipped text, #if ident**/#else/#endif** sections can be nested.

• Strings and comments are not treated as special

## Identifiers and Keywords

Identifiers follow the specification in this section.

regexp digit-char = [0-9]

regexp letter-char = '\Lu' | '\Ll' | '\Lt' | '\Lm' | '\Lo' | '\Nl'

regexp connecting-char = '\Pc'

regexp combining-char = '\Mn' | '\Mc'

regexp formatting-char = '\Cf'

regexp ident-start-char =

| letter-char

| _

regexp ident-char =

| letter-char

| digit-char

| connecting-char

| combining-char

| formatting-char

| '

| _

regexp ident-text = ident-start-char ident-char*****

token ident =

| ident-text For example, myName1

|  ( [^'' '\n' '\r' '\t'] | '' [^ '' '\n' '\r' '\t'] )+ 

For example, value.with odd#name

Any sequence of characters that is enclosed in double-backtick marks ( ), excluding newlines, tabs, and double-backtick pairs themselves, is treated as an identifier. Note that when an identifier is used for the name of a types, union type case, module, or namespace, the following characters are not allowed even inside double-backtick marks:

‘.', '+', '$', '&', '[', ']', '/', '\\', '*', '\"', '' All input files are currently assumed to be encoded as UTF-8. See the C# specification for a list of the Unicode characters that are accepted for the Unicode character classes \Lu, \Li, \Lt, \Lm, \Lo, \Nl, \Pc, \Mn, \Mc, and \Cf. The following identifiers are treated as keywords of the F# language: token ident-keyword = abstract and as assert base begin class default delegate do done downcast downto elif else end exception extern false finally for fun function global if in inherit inline interface internal lazy let match member module mutable namespace new null of open or override private public rec return sig static struct then to true try type upcast use val void when while with yield The following identifiers are reserved for future use: token reserved-ident-keyword = atomic break checked component const constraint constructor continue eager fixed fori functor include measure method mixin object parallel params process protected pure recursive sealed tailcall trait virtual volatile A future revision of the F# language may promote any of these identifiers to be full keywords. The following token forms are reserved, except when they are part of a symbolic keyword (§3.6). token reserved-ident-formats = | ident-text ( '!' | '#') In the remainder of this specification, we refer to the token that is generated for a keyword simply by using the text of the keyword itself. ## Strings and Characters String literals may be specified for two types: • Unicode strings, type string = System.String • Unsigned byte arrays, type byte[] = bytearray Literals may also be specified by using C#-like verbatim forms that interpret \ as a literal character rather than an escape sequence. In a UTF-8-encoded file, you can directly embed the following in a string in the same way as in C#: • Unicode characters, such as “\u0041bc • Identifiers, as described in the previous section, such as “abc • Trigraph specifications of Unicode characters, such as “\067” which represents “C” regexp escape-char = '\' ["\'ntbrafv] regexp non-escape-chars = '\' [^"\'ntbrafv] regexp simple-char-char = | (any char except '\n' '\t' '\r' '\b' '\a' '\f' '\v' ' \ ") regexp unicodegraph-short = '\' 'u' hexdigit hexdigit hexdigit hexdigit regexp unicodegraph-long = '\' 'U' hexdigit hexdigit hexdigit hexdigit hexdigit hexdigit hexdigit hexdigit regexp trigraph = '\' digit-char digit-char digit-char regexp char-char = | simple-char-char | escape-char | trigraph | unicodegraph-short regexp string-char = | simple-string-char | escape-char | non-escape-chars | trigraph | unicodegraph-short | unicodegraph-long | newline regexp string-elem = | string-char | '\' newline whitespace***** string-elem token char = ' char-char ' token string = " string-char*** "** regexp verbatim-string-char = | simple-string-char | non-escape-chars | newline | \ | "" token verbatim-string = @" verbatim-string-char*** "** token bytechar = ' simple-or-escape-char 'B token bytearray = " string-char*** "B** token verbatim-bytearray = @" verbatim-string-char*** "B** token simple-or-escape-char = escape-char | simple-char token simple-char = any char except newline,return,tab,backspace,',\," token triple-quoted-string = """ simple-or-escape-char* """ To translate a string token to a string value, the F# parser concatenates all the Unicode characters for the string-char elements within the string. Strings may include \n as a newline character. However, if a line ends with \, the newline character and any leading whitespace elements on the subsequent line are ignored. Thus, the following gives s the value "abcdef": let s = "abc\ def" Without the backslash, the resulting string includes the newline and whitespace characters. For example: let s = "abc def" In this case, s has the value "abc*\010* def" where \010 is the embedded control character for \n, which has Unicode UTF-16 value 10. Verbatim strings may be specified by using the @ symbol preceding the string as in C#. For example, the following assigns the value "abc\def" to s. let s = @"abc\def" String-like and character-like literals can also be specified for unsigned byte arrays (type byte[]). These tokens cannot contain Unicode characters that have surrogate-pair UTF-16 encodings or UTF-16 encodings greater than 127. A triple-quoted string is specified by using three quotation marks (""") to ensure that a string that includes one or more escaped strings is interpreted verbatim. For example, a triple-quoted string can be used to embed XML blobs: let catalog = """ <?xml version="1.0"?> <catalog> <book id="book"> <author>Author</author> <title>F#</title> <genre>Computer</genre> <price>44.95</price> <publish_date>2012-10-01</publish_date> <description>An in-depth look at creating applications in F#</description> </book> </catalog> """ ## Symbolic Keywords The following symbolic or partially symbolic character sequences are treated as keywords: token symbolic-keyword = let! use! do! yield! return! | -> <- . : ( ) [ ] [< >] [| |] { } ' # :?> :? :> .. :: := ;; ; = _ ? ?? (*) <@ @> <@@ @@> The following symbols are reserved for future use: token reserved-symbolic-sequence = ~  ## Symbolic Operators User-defined and library-defined symbolic operators are sequences of characters as shown below, except where the sequence of characters is a symbolic keyword (§3.6). regexp first-op-char = !%&*+-./<=>@^|~ regexp op-char = first-op-char | ? token quote-op-left = | <@ <@@ token quote-op-right = | @> @@> token symbolic-op = | ? | ?<- | first-op-char op-char***** | quote-op-left | quote-op-right For example, &&& and ||| are valid symbolic operators. Only the operators ? and ?<- may start with ?. The quote-op-left and quote-op-right operators are used in quoted expressions (§6.8). For details about the associativity and precedence of symbolic operators in expression forms, see §4.4. ## Numeric Literals The lexical specification of numeric literals is as follows: regexp digit = [0-9] regexp hexdigit = digit | [A-F] | [a-f] regexp octaldigit = [0-7] regexp bitdigit = [0-1] regexp int = | digit**+ For example, 34** regexp xint = | 0 (x|X) hexdigit**+ For example, 0x22** | 0 (o|O) octaldigit**+ For example, 0o42** | 0 (b|B) bitdigit**+ For example, 0b10010** token sbyte **= (**int|xint) 'y' For example, 34y token byte **= (**int|xint) *'*uy' For example, 34uy token int16 **= (**int|xint) *'*s' For example, 34s token uint16 **= (**int|xint) *'*us' For example, 34us token int32 **= (**int|xint) *'*l' For example, 34l token uint32 **= (**int|xint) *'*ul' For example, 34ul **| (**int|xint) *'*u' For example, 34u token nativeint **= (**int|xint) *'*n' For example, 34n token unativeint **= (**int|xint) *'*un' For example, 34un token int64 **= (**int|xint) *'*L' For example, 34L token uint64 **= (**int|xint) *'*UL' For example, 34UL | **(**int|xint) *'*uL' For example, 34uL token ieee32 = | float [Ff] For example, 3.0F or 3.0f | xint 'lf' For example, 0x00000000lf token ieee64 = | float For example, 3.0 | xint 'LF' For example, 0x0000000000000000LF token bignum = int ('Q' | *'*R' | 'Z' | 'I' | 'N' | 'G') For example, 34742626263193832612536171N token decimal = (float|int) [Mm] token float = digit**+ .** digit***** digit**+ (.** digit*** )? (e|E) (+|-)?** digit**+** ### Post-filtering of Adjacent Prefix Tokens Negative integers are specified using the token; for example, -3. The token steam is post-filtered according to the following rules: • If the token stream contains the adjacent tokens token: If token is a constant numeric literal, the pair of tokens is merged. For example, adjacent tokens - and 3 becomes the single token “-3”. Otherwise, the tokens remain separate. However the “-” token is marked as an ADJACENT_PREFIX_OP token. This rule does not apply to the sequence token1 - token2, if all three tokens are adjacent and token1 is a terminating token from expression forms that have lower precedence than the grammar production expr = MINUS expr. For example, the and b tokens in the following sequence are not merged if all three tokens are adjacent: a**-**b • Otherwise, the usual grammar rules apply to the uses of and +, with an addition for ADJACENT_PREFIX_OP: expr = expr MINUS expr | MINUS expr | ADJACENT_PREFIX_OP expr ### Post-filtering of Integers Followed by Adjacent “..” Tokens of the form token intdotdot = int.. such as 34.. are post-filtered to two tokens: one int and one symbolic-keyword, “..”. This rule allows “..” to immediately follow an integer. This construction is used in expressions of the form **[for x in 1..2 -> x • x ]. Without this rule, the longest-match rule would consider this sequence to be a floating-point number followed by a “.**”. ### Reserved Numeric Literal Forms The following token forms are reserved for future numeric literal formats: token reserved-literal-formats = | (xint | ieee32 | ieee64) ident-char+ ### Shebang A shebang (#!) directive may exist at the beginning of F# source files. Such a line is treated as a comment. This allows F# scripts to be compatible with the Unix convention whereby a script indicates the interpreter to use by providing the path to that interpreter on the first line, following the #! directive. #!/bin/usr/env fsharpi --exec ## Line Directives Line directives adjust the source code filenames and line numbers that are reported in error messages, recorded in debugging symbols, and propagated to quoted expressions. F# supports the following line directives: token line-directive = # int** #** int string** #** int verbatim-string #line int** #line** int string** #line** int verbatim-string A line directive applies to the line that immediately follows the directive. If no line directive is present, the first line of a file is numbered 1. ## Hidden Tokens Some hidden tokens are inserted by lexical filtering (§15) or are used to replace existing tokens. See §15 for a full specification and for the augmented grammar rules that take these into account. ## Identifier Replacements The following table lists identifiers that are automatically replaced by expressions. Identifier Replacement __SOURCE_DIRECTORY__ A literal verbatim string that specifies the name of the directory that contains the current file. For example: C:\source The name of the current file is derived from the most recent line directive in the file. If no line directive has appeared, the name is derived from the name that was specificed to the command-line compiler in combination with System.IO.Path.GetFullPath. In F# Interactive, the name stdin is used. When F# Interactive is used from tools such as Visual Studio, a line directive is implicitly added before the interactive execution of each script fragment. __SOURCE_FILE__ A literal verbatim string that contains the name of the current file. For example: file.fs __LINE__ A literal string that specifies the line number in the source file, after taking into account adjustments from line directives. # Basic Grammar Elements This section defines grammar elements that are used repeatedly in later sections. ## Operator Names Several places in the grammar refer to an ident-or-op rather than an ident: ident-or-op := | ident | ( op-name ) | (*) op-name := | symbolic-op | range-op-name | active-pattern-op-name range-op-name := | .. | .. .. active-pattern-op-name := | | ident | ... | ident | | | ident | ... | ident | _ | In operator definitions, the operator name is placed in parentheses. For example: let (+++) x y = (x, y) This example defines the binary operator +++. The text (+++) is an ident-or-op that acts as an identifier with associated text +++. Likewise, for active pattern definitions (§7), the active pattern case names are placed in parentheses, as in the following example: let (|A|B|C|) x = if x < 0 then A elif x = 0 then B else C Because an ident-or-op acts as an identifier, such names can be used in expressions. For example: List.map ((+) 1) [ 1; 2; 3 ] The three character token **(*)**defines the * operator: let (*) x y = (x + y) To define other operators that begin with *, whitespace must follow the opening parenthesis; otherwise (* is interpreted as the start of a comment: let ( *+* ) x y = (x + y) Symbolic operators and some symbolic keywords have a compiled name that is visible in the compiled form of F# programs. The compiled names are shown below. [] op_Nil :: op_ColonColon + op_Addition - op_Subtraction * op_Multiply / op_Division ** op_Exponentiation @ op_Append ^ op_Concatenate % op_Modulus &&& op_BitwiseAnd ||| op_BitwiseOr ^^^ op_ExclusiveOr <<< op_LeftShift ~~~ op_LogicalNot >>> op_RightShift ~+ op_UnaryPlus ~- op_UnaryNegation = op_Equality <> op_Inequality <= op_LessThanOrEqual >= op_GreaterThanOrEqual < op_LessThan > op_GreaterThan ? op_Dynamic ?<- op_DynamicAssignment |> op_PipeRight ||> op_PipeRight2 |||> op_PipeRight3 <| op_PipeLeft <|| op_PipeLeft2 <||| op_PipeLeft3 ! op_Dereference >> op_ComposeRight << op_ComposeLeft <@ @> op_Quotation <@@ @@> op_QuotationUntyped ~% op_Splice ~%% op_SpliceUntyped ~& op_AddressOf ~&& op_IntegerAddressOf || op_BooleanOr && op_BooleanAnd += op_AdditionAssignment -= op_SubtractionAssignment *= op_MultiplyAssignment /= op_DivisionAssignment .. op_Range .. .. op_RangeStep Compiled names for other symbolic operators are op_N1...Nn where N1 to Nn are the names for the characters as shown in the table below. For example, the symbolic identifier <* has the compiled name op_LessMultiply: > Greater < Less + Plus - Minus * Multiply = Equals ~ Twiddle % Percent . Dot & Amp | Bar @ At # Hash ^ Hat ! Bang ? Qmark / Divide . Dot : Colon ( LParen , Comma ) RParen [ LBrack ] RBrack ## Long Identifiers Long identifiers long-ident are sequences of identifiers that are separated by ‘.’ and optional whitespace. Long identifiers long-ident-or-op are long identifiers that may terminate with an operator name. long-ident := ident '.' ... '.' ident long-ident-or-op := | long-ident '.' ident-or-op | ident-or-op ## Constants The constants in the following table may be used in patterns and expressions. The individual lexical formats for the different constants are defined in §3. const := | sbyte | int16 | int32 | int64 -- 8, 16, 32 and 64-bit signed integers | byte | uint16 | uint32 | int -- 32-bit signed integer | uint64 -- 8, 16, 32 and 64-bit unsigned integers | ieee32 -- 32-bit number of type "float32" | ieee64 -- 64-bit number of type "float" | bignum -- User or library-defined integral literal type | char -- Unicode character of type "char" | string -- String of type "string" (System.String) | verbatim-string -- String of type "string" (System.String) | triple-quoted-string -- String of type "string" (System.String) | bytestring -- String of type "byte[]" | verbatim-bytearray -- String of type "byte[]" | bytechar -- Char of type "byte" | false | true -- Boolean constant of type "bool" | '(' ')' -- unit constant of type "unit" ## Operators and Precedence ### Categorization of Symbolic Operators The following symbolic-op tokens can be used to form prefix and infix expressions. The marker OP represents all symbolic-op tokens that begin with the indicated prefix, except for tokens that appear elsewhere in the table. infix-or-prefix-op := +, -, +., -., %, &, && prefix-op := infix-or-prefix-op ~ ~~ ~~~ (and any repetitions of ~) !OP (except !=) infix-op := infix-or-prefix-op -OP +OP || <OP >OP = |OP &OP ^OP *OP /OP %OP != (or any of these preceded by one or more ‘.’) := ::$

or

?

The operators +, -, +., -., %, %%, &, && can be used as both prefix and infix operators. When these operators are used as prefix operators, the tilde character is prepended internally to generate the operator name so that the parser can distinguish such usage from an infix use of the operator. For example, -x is parsed as an application of the operator ~- to the identifier x. This generated name is also used in definitions for these prefix operators. Consequently, the definitions of the following prefix operators include the ~ character:

// To completely redefine the prefix + operator:

let (~+) x = x

// To completely redefine the infix + operator to be addition modulo-7

let (+) a b = (a + b) % 7

// To define the operator on a type:

type C(n:int) =

let n = n % 7

member x.N = n

static member (~+) (x:C) = x

static member (~-) (x:C) = C(-n)

static member (+) (x1:C,x2:C) = C(x1.N+x2.N)

static member (-) (x1:C,x2:C) = C(x1.N-x2.N)

The**::** operator is special. It represents the union case for the addition of an element to the head of an immutable linked list, and cannot be redefined, although it may be used to form infix expressions. It always accepts arguments in tupled form—as do all union cases—rather than in curried form.

### Precedence of Symbolic Operators and Pattern/Expression Constructs

Rules of precedence control the order of evaluation for ambiguous expression and pattern constructs. Higher precedence items are evaluated before lower precedence items.

The following table shows the order of precedence, from highest to lowest, and indicates whether the operator or expression is associated with the token to its left or right. The OP marker represents the symbolic-op tokens that begin with the specified prefix, except those listed elsewhere in the table. For example, +OP represents any token that begins with a plus sign, unless the token appears elsewhere in the table.

f<types> Left High-precedence type application; see §15.3
f(x) Left High-precedence application; see §15.2
. Left
prefix-op Left Applies to prefix uses of these symbols
"| rule" Right Pattern matching rules
"f x"
"lazy x"
"assert x"
Left
**OP Right
*OP /OP %OP Left
-OP +OP Left Applies to infix uses of these symbols
:? Not associative
:: Right
^OP Right
!=OP <OP >OP = |OP &OP $Left :> :?> Right & && Left or || Left , Not associative := Right -> Right if Not associative function, fun, match, try Not associative let Not associative ; Right | Left when Right as Right If ambiguous grammar rules (such as the rules from §6) involve tokens in the table, a construct that appears earlier in the table has higher precedence than a construct that appears later in the table. The associativity indicates whether the operator or construct applies to the item to the left or the right of the operator. For example, consider the following token stream: a + b * c In this expression, the expr infix-op expr rule for b * c takes precedence over the expr infix-op expr rule for a + b, because the * operator has higher precedence than the + operator. Thus, this expression can be pictured as follows: a + b * c rather than a + b * c Likewise, given the tokens a * b * c the left associativity of * means we can picture the resolution of the ambiguity as: a * b * c In the preceding table, leading . characters are ignored when determining precedence for infix operators. For example, .* has the same precedence as *. This rule ensures that operators such as .*, which is frequently used for pointwise-operation on matrices, have the expected precedence. The table entries marked as “High-precedence application” and “High-precedence type application” are the result of the augmentation of the lexical token stream, as described in §15.2 and §15.3. # Types and Type Constraints The notion of type is central to both the static checking of F# programs and to dynamic type tests and reflection at runtime. The word is used with four distinct but related meanings: • Type definitions, such as the actual CLI or F# definitions of System.String or FSharp.Collections.Map<_,_>. • Syntactic types, such as the text option<_> that might occur in a program text. Syntactic types are converted to static types during the process of type checking and inference. • Static types, which result from type checking and inference, either by the translation of syntactic types that appear in the source text, or by the application of constraints that are related to particular language constructs. For example, option<int> is the fully processed static type that is inferred for an expression Some(1+1). Static types may contain type variables as described later in this section. • Runtime types, which are objects of type System.Type and represent some or all of the information that type definitions and static types convey at runtime. The obj.GetType() method, which is available on all F# values, provides access to the runtime type of an object. An object’s runtime type is related to the static type of the identifiers and expressions that correspond to the object. Runtime types may be tested by built-in language operators such as :? and :?>, the expression form downcast expr, and pattern matching type tests. Runtime types of objects do not contain type variables. Runtime types that System.Reflection reports may contain type variables that are represented by System.Type values. The following describes the syntactic forms of types as they appear in programs: type := ( type ) type -> type -- function type type * ... * type -- tuple type typar -- variable type long-ident -- named type, such as int long-ident**<type-args> -- named type, such as list<int>** long-ident**< > -- named type, such as IEnumerable< >** type long-ident -- named type, such as int list type**[ , ... , ] -- array type** type typar-defns -- type with constraints typar :> type -- variable type with subtype constraint **#**type -- anonymous type with subtype constraint type-args := type-arg**, ...,** type-arg type-arg := type -- type argument measure -- unit of measure argument static-parameter -- static parameter atomic-type := type : one of #type typar ( type ) long-ident long-ident**<type-args>** typar := _ -- anonymous variable type **'**ident -- type variable **^**ident -- static head-type type variable constraint := typar :> type -- coercion constraint typar : null -- nullness constraint static-typars **: (**member-sig ) -- member "trait" constraint typar : (new : unit -> 'T) -- CLI default constructor constraint typar : struct -- CLI non-Nullable struct typar : not struct -- CLI reference type typar : enum<type> -- enum decomposition constraint typar : unmanaged -- unmanaged constraint typar : delegate<type, type> -- delegate decomposition constraint typar : equality typar : comparison typar-defn := attributesopt typar typar-defns := < typar-defn, ..., typar-defn typar-constraintsopt > typar-constraints := when constraint and ... and constraint static-typars := **^**ident **(^**ident or ... or ^ident) member-sig := <see Section 10> In a type instantiation, the type name and the opening angle bracket must be syntactically adjacent with no intervening whitespace, as determined by lexical filtering (§15). Specifically: array<int> and not array < int > ## Checking Syntactic Types Syntactic types are checked and converted to static types as they are encountered. Static types are a specification device used to describe • The process of type checking and inference. • The connection between syntactic types and the execution of F# programs. Every expression in an F# program is given a unique inferred static type, possibly involving one or more explicit or implicit generic parameters. For the remainder of this specification we use the same syntax to represent syntactic types and static types. For example int32 * int32 is used to represent the syntactic type that appears in source code and the static type that is used during checking and type inference. The conversion from syntactic types to static types happens in the context of a name resolution environment (§14.1), a floating type variable environment, which is a mapping from names to type variables, and a type inference environment (§14.5). The phrase “fresh type” means a static type that is formed from a fresh type inference variable. Type inference variables are either solved or generalized by type inference (§14.5). During conversion and throughout the checking of types, expressions, declarations, and entire files, a set of current inference constraints is maintained. That is, each static type is processed under input constraints Χ, and results in output constraints Χ’. Type inference variables and constraints are progressively simplified and eliminated based on these equations through constraint solving (§14.5). ### Named Types Named types have several forms, as listed in the following table. Form Description long-ident<ty1,…,tyn> Named type with one or more suffixed type arguments. long-ident Named type with no type arguments type long-ident Named type with one type argument; processed the same as long-ident<type> ty1 -> ty2 A function type, where: • ty1 is the domain of the function values associated with the type • ty2 is the range. In compiled code it is represented by the named type FSharp.Core.FastFunc<ty1,ty2>. Named types are converted to static types as follows: • Name Resolution for Types (§14.1) resolves long-ident to a type definition with formal generic parameters <typar1,…, typar*n***> and formal constraints C. The number of type arguments n is used during the name resolution process to distinguish between similarly named types that take different numbers of type arguments. • Fresh type inference variables <ty'1,…,ty'n> are generated for each formal type parameter. The formal constraints C are added to the current inference constraints for the new type inference variables; and constraints tyi = *ty'i*** are added to the current inference constraints. ### Variable Types A type of the form 'ident is a variable type. For example, the following are all variable types: 'a 'T 'Key During checking, Name Resolution (§14.1) is applied to the identifier. • If name resolution succeeds, the result is a variable type that refers to an existing declared type parameter. • If name resolution fails, the current floating type variable environment is consulted, although only in the context of a syntactic type that is embedded in an expression or pattern. If the type variable name is assigned a type in that environment, F# uses that mapping. Otherwise, a fresh type inference variable is created (see §14.5) and added to both the type inference environment and the floating type variable environment. A type of the form _ is an anonymous variable type. A fresh type inference variable is created and added to the type inference environment (see §14.5) for such a type. A type of the form ^ident is a statically resolved type variable. A fresh type inference variable is created and added to the type inference environment (see §14.5). This type variable is tagged with an attribute that indicates that it can be generalized only at inline definitions (see §14.6.7). The same restriction on generalization applies to any type variables that are contained in any type that is equated with the ^ident type in a type inference equation. Note: this specification generally uses uppercase identifiers such as 'T or 'Key for user-declared generic type parameters, and uses lowercase identifiers such as 'a or 'b for compiler-inferred generic parameters. ### Tuple Types A tuple type has the following form: ty*1*** * ... * ty*n*** The elaborated form of a tuple type is shorthand for a use of the family of F# library types System.Tuple<_,...,_>. See §6.3.2 for the details of this encoding. When considered as static types, tuple types are distinct from their encoded form. However, the encoded form of tuple types is visible in the F# type system through runtime types. For example, typeof<int * int> is equivalent to typeof<System.Tuple<int,int>>. ### Array Types Array types have the following forms: ty**[]** ty**[ , ... , ]** A type of the form ty**[]** is a single-dimensional array type, and a type of the form ty**[ , ... , ]** is a multidimensional array type. For example, int[,,] is an array of integers of rank 3. Except where specified otherwise in this document, these array types are treated as named types, as if they are an instantiation of a fictitious type definition System.Arrayn*<ty>* where n corresponds to the rank of the array type. Note: The type int[][,] in F# is the same as the type int[,][] in C# although the dimensions are swapped. This ensures consistency with other postfix type names in F# such as int list list. F# supports multidimensional array types only up to rank 4. ### Constrained Types A type with constraints has the following form: type when constraints During checking, type is first checked and converted to a static type, then constraints are checked and added to the current inference constraints. The various forms of constraints are described in§5.2. A type of the form typar :> type is a type variable with a subtype constraint and is equivalent to typar when typar :> type. A type of the form **#**type is an anonymous type with a subtype constraint and is equivalent to 'a when 'a :> type, where 'a is a fresh type inference variable. ## Type Constraints A type constraint limits the types that can be used to create an instance of a type parameter or type variable. F# supports the following type constraints: • Subtype constraints • Nullness constraints • Member constraints • Default constructor constraints • Value type constraints • Reference type constraints • Enumeration constraints • Delegate constraints • Unmanaged constraints • Equality and comparison constraints ### Subtype Constraints An explicit subtype constraint has the following form: typar :> type During checking, typar is first checked as a variable type, type is checked as a type, and the constraint is added to the current inference constraints. Subtype constraints affect type coercion as specified in §5.4.7. Note that subtype constraints also result implicitly from: • Expressions of the form expr :> type. • Patterns of the form pattern :> type. • The use of generic values, types, and members with constraints. • The implicit use of subsumption when using values and members (§14.4.3). A type variable cannot be constrained by two distinct instantiations of the same named type. If two such constraints arise during constraint solving, the type instantiations are constrained to be equal. For example, during type inference, if a type variable is constrained by both IA<int> and IA<string>, an error occurs when the type instantiations are constrained to be equal. This limitation is specifically necessary to simplify type inference, reduce the size of types shown to users, and help ensure the reporting of useful error messages. ### Nullness Constraints An explicit nullness constraint has the following form: typar**: null** During checking, typar is checked as a variable type and the constraint is added to the current inference constraints. The conditions that govern when a type satisfies a nullness constraint are specified in §5.4.8. In addition: • The typar must be a statically resolved type variable of the form ^ident. This limitation ensures that the constraint is resolved at compile time, and means that generic code may not use this constraint unless that code is marked inline (§14.6.7). Note: Nullness constraints are primarily for use during type checking and are used relatively rarely in F# code. Nullness constraints also arise from expressions of the form null. ### Member Constraints An explicit member constraint has the following form: (typar or ... or typar) : (member-sig) For example, the F# library defines the + operator with the following signature: val inline (+) : ^a -> ^b -> ^c when (^a or ^b) : (static member (+) : ^a * ^b -> ^c) This definition indicates that each use of the + operator results in a constraint on the types that correspond to parameters ^a, ^b, and ^c. If these are named types, then either the named type for ^a or the named type for ^b must support a static member called + that has the given signature. In addition: • Each typar must be a statically resolved type variable (§5.1.2) in the form ^ident. This ensures that the constraint is resolved at compile time against a corresponding named type. It also means that generic code cannot use this constraint unless that code is marked inline (§14.6.7). • The member-sig cannot be generic; that is, it cannot include explicit type parameter definitions. • The conditions that govern when a type satisfies a member constraint are specified in §14.5.4 . Note: Member constraints are primarily used to define overloaded functions in the F# library and are used relatively rarely in F# code. Uses of overloaded operators do not result in generalized code unless definitions are marked as inline. For example, the function let f x = x + x results in a function f that can be used only to add one type of value, such as int or float. The exact type is determined by later constraints. A type variable may not be involved in the support set of more than one member constraint that has the same name, staticness, argument arity, and support set (§14.5.4). If it is, the argument and return types in the two member constraints are themselves constrained to be equal. This limitation is specifically necessary to simplify type inference, reduce the size of types shown to users, and ensure the reporting of useful error messages. ### Default Constructor Constraints An explicit default constructor constraint has the following form: typar : (new : unit -> 'T) During constraint solving (§14.5), the constraint type : (new : unit -> 'T) is met if type has a parameterless object constructor. Note: This constraint form exists primarily to provide the full set of constraints that CLI implementations allow. It is rarely used in F# programming. ### Value Type Constraints An explicit value type constraint has the following form: typar : struct During constraint solving (§14.5), the constraint type : struct is met if type is a value type other than the CLI type System.Nullable<_>. Note: This constraint form exists primarily to provide the full set of constraints that CLI implementations allow. It is rarely used in F# programming. The restriction on System.Nullable is inherited from C# and other CLI languages, which give this type a special syntactic status. In F#, the type option<_> is similar to some uses of System.Nullable<_>. For various technical reasons the two types cannot be equated, notably because types such as System.Nullable<System.Nullable<_>> and System.Nullable<string> are not valid CLI types. ### Reference Type Constraints An explicit reference type constraint has the following form: typar : not struct During constraint solving (§14.5), the constraint type : not struct is met if type is a reference type. Note: This constraint form exists primarily to provide the full set of constraints that CLI implementations allow. It is rarely used in F# programming. ### Enumeration Constraints An explicit enumeration constraint has the following form: typar : enum<underlying-type> During constraint solving (§14.5), the constraint type : enum<underlying-type> is met if type is a CLI or F# enumeration type that has constant literal values of type underlying-type. Note: This constraint form exists primarily to allow the definition of library functions such as enum. It is rarely used directly in F# programming. The enum constraint does not imply anything about subtypes. For example, an enum constraint does not imply that the type is a subtype of System.Enum. ### Delegate Constraints An explicit delegate constraint has the following form: typar : delegate<tupled-arg-type, return-type**>** During constraint solving (§14.5), the constraint type : delegate<tupled-arg-type, return-types**>** is met if type is a delegate type D with declaration type D = delegate of object * arg1 * ... * argN and tupled-arg-type = arg1 * ... * argN. That is, the delegate must match the CLI design pattern where the sender object is the first argument to the event. Note: This constraint form exists primarily to allow the definition of certain F# library functions that are related to event programming. It is rarely used directly in F# programming. The delegate constraint does not imply anything about subtypes. In particular, a ‘delegate’ constraint does not imply that the type is a subtype of System.Delegate. The delegate constraint applies only to delegate types that follow the usual form for CLI event handlers, where the first argument is a “sender” object. The reason is that the purpose of the constraint is to simplify the presentation of CLI event handlers to the F# programmer. ### Unmanaged Constraints An unmanaged constraint has the following form: typar : unmanaged During constraint solving (§14.5), the constraint type : unmanaged is met if type is unmanaged as specified below: • Types sbyte**,** byte**,** char**,** nativeint**,** unativeint**,** float32**,** float**,** int16**,** uint16**,** int32**,** uint32**,** int64**,** uint64**,** decimal are unmanaged*.* • Type nativeptr<type> is unmanaged*.* • A non-generic struct type whose fields are all unmanaged types is unmanaged*.* ### Equality and Comparison Constraints Equality constraints and comparison constraints have the following forms, respectively: typar : equality typar : comparison During constraint solving (§14.5), the constraint type : equality is met if both of the following conditions are true: • The type is a named type, and the type definition does not have, and is not inferred to have, the NoEquality attribute. • The type has equality dependencies ty*1, ..., tyn, each of which satisfies tyi*** : equality. The constraint type : comparison is a comparison constraint. Such a constraint is met if all the following conditions hold: • If the type is a named type, then the type definition does not have, and is not inferred to have, the NoComparison attribute, and the type definition implements System.IComparable or is an array type or is System.IntPtr or is System.UIntPtr. • If the type has comparison dependencies ty*1, ..., tyn, then each of these must satisfy tyi*** : comparison An equality constraint is a relatively weak constraint, because with two exceptions, all CLI types satisfy this constraint. The exceptions are F# types that are annotated with the NoEquality attribute and structural types that are inferred to have the NoEquality attribute. The reason is that in other CLI languages, such as C#, it possible to use reference equality on all reference types. A comparison constraint is a stronger constraint, because it usually implies that a type must implement System.IComparable. ## Type Parameter Definitions Type parameter definitions can occur in the following locations: • Value definitions in modules • Member definitions • Type definitions • Corresponding specifications in signatures For example, the following defines the type parameter ‘T in a function definition: let id<'T> (x:'T) = x Likewise, in a type definition: type Funcs<'T1,'T2> = { Forward: 'T1 -> 'T2; Backward : 'T2 -> 'T2 } Likewise, in a signature file: val id<'T> : 'T -> 'T Explicit type parameter definitions can include explicit constraint declarations. For example: let dispose2<'T when 'T :> System.IDisposable> (x: 'T, y: 'T) = x.Dispose() y.Dispose() The constraint in this example requires that 'T be a type that supports the IDisposable interface. However, in most circumstances, declarations that imply subtype constraints on arguments can be written more concisely: let throw (x: Exception) = raise x Multiple explicit constraint declarations use and: let multipleConstraints<'T when 'T :> System.IDisposable and 'T :> System.IComparable > (x: 'T, y: 'T) = if x.CompareTo(y) < 0 then x.Dispose() else y.Dispose() Explicit type parameter definitions can declare custom attributes on type parameter definitions (§13.1). ## Logical Properties of Types During type checking and elaboration, syntactic types and constraints are processed into a reduced form composed of: • Named types op**<types>**, where each op consists of a specific type definition, an operator to form function types, an operator to form array types of a specific rank, or an operator to form specific *n-*tuple types. • Type variables **'**ident. ### Characteristics of Type Definitions Type definitions include CLI type definitions such as System.String and types that are defined in F# code (§8). The following terms are used to describe type definitions: • Type definitions may be generic, with one or more type parameters; for example, System.Collections.Generic.Dictionary<'Key,'Value>. • The generic parameters of type definitions may have associated formal type constraints. • Type definitions may have custom attributes (§13.1), some of which are relevant to checking and inference. • Type definitions may be type abbreviations (§8.3). These are eliminated for the purposes of checking and inference (see §5.4.2). • Type definitions have a kind which is one of the following: • Class • Interface • Delegate • Struct • Record • Union • Enum • Measure • Abstract The kind is determined at the point of declaration by Type Kind Inference (§8.2) if it is not specified explicitly as part of the type definition. The kind of a type refers to the kind of its outermost named type definition, after expanding abbreviations. For example, a type is a class type if it is a named type C<types> where C is of kind class. Thus, System.Collections.Generic.List<int> is a class type. • Type definitions may be sealed. Record, union, function, tuple, struct, delegate, enum, and array types are all sealed, as are class types that are marked with the SealedAttribute attribute. • Type definitions may have zero or one base type declarations. Each base type declaration represents an additional type that is supported by any values that are formed using the type definition. Furthermore, some aspects of the base type are used to form the implementation of the type definition. • Type definitions may have one or more interface declarations. These represent additional encapsulated types that are supported by values that are formed using the type. Class, interface, delegate, function, tuple, record, and union types are all reference type definitions. A type is a reference type if its outermost named type definition is a reference type, after expanding type definitions. Struct types are value types. ### Expanding Abbreviations and Inference Equations Two static types are considered equivalent and indistinguishable if they are equivalent after taking into account both of the following: • The inference equations that are inferred from the current inference constraints (§14.5). • The expansion of type abbreviations (§8.3). For example, static types may refer to type abbreviations such as int, which is an abbreviation for System.Int32and is declared by the F# library: type int = System.Int32 This means that the types int32 and System.Int32 are considered equivalent, as are System.Int32 -> int and int -> System.Int32. Likewise, consider the process of checking this function: let checkString (x:string) y = (x = y), y.Contains("Hello") During checking, fresh type inference variables are created for values x and y; let’s call them ty1 and ty2. Checking imposes the constraints ty1 = string and ty1 = ty2. The second constraint results from the use of the generic = operator. As a result of constraint solving, ty2 = string is inferred, and thus the type of y is string. All relations on static types are considered after the elimination of all equational inference constraints and type abbreviations. For example, we say int is a struct type because System.Int32 is a struct type. Note: Implementations of F# should attempt to preserve type abbreviations when reporting types and errors to users. This typically means that type abbreviations should be preserved in the logical structure of types throughout the checking process. ### Type Variables and Definition Sites Static types may be type variables. During type inference, static types may be partial, in that they contain type inference variables that have not been solved or generalized. Type variables may also refer to explicit type parameter definitions, in which case the type variable is said to be rigid and have a definition site. For example, in the following, the definition site of the type parameter 'T is the type definition of C: type C<'T> = 'T * 'T Type variables that do not have a binding site are inference variables. If an expression is composed of multiple sub-expressions, the resulting constraint set is normally the union of the constraints that result from checking all the sub-expressions. However, for some constructs (notably function, value and member definitions), the checking process applies generalization (§14.6.7). Consequently, some intermediate inference variables and constraints are factored out of the intermediate constraint sets and new implicit definition site(s) are assigned for these variables. For example, given the following declaration, the type inference variable that is associated with the value x is generalized and has an implicit definition site at the definition of function id: let id x = x Occasionally in this specification we use a more fully annotated representation of inferred and generalized type information. For example: let id***<'a>*** x***'a*** = x***'a*** Here, 'a represents a generic type parameter that is inferred by applying type inference and generalization to the original source code (§14.6.7), and the annotation represents the definition site of the type variable. ### Base Type of a Type The base type for the static types is shown in the table. These types are defined in the CLI specifications and corresponding implementation documentation. Static Type Base Type Abstract types System.Object All array types System.Array Class types The declared base type of the type definition if the type has one; otherwise, System.Object. For generic types C<type-inst>, substitute the formal generic parameters of C for type-inst. Delegate types System.MulticastDelegate Enum types System.Enum Exception types System.Exception Interface types System.Object Record types System.Object Struct types System.ValueType Union types System.Object Variable types System.Object ### Interfaces Types of a Type The interface types of a named type C<type-inst> are defined by the transitive closure of the interface declarations of C and the interface types of the base type of C, where formal generic parameters are substituted for the actual type instantiation type-inst. The interface types for single dimensional array types ty**[]** include the transitive closure that starts from the interface System.Collections.Generic.IList<ty>, which includes System.Collections.Generic.ICollection<ty> and System.Collections.Generic.IEnumerable<ty>. ### Type Equivalence Two static types ty1 and ty2 are definitely equivalent (with respect to a set of current inference constraints) if either of the following is true: • ty1 has form op**<ty11, ..., ty1n>, ty2 has form op**<ty21, ..., ty2n> and each ty*1i*** is definitely equivalent to ty*2i*** for all 1 <= i <= n. —OR— • ty1 and ty2 are both variable types, and they both refer to the same definition site or are the same type inference variable. This means that the addition of new constraints may make types definitely equivalent where previously they were not. For example, given Χ = { 'a = int }, we have list<int> = list<'a>. Two static types ty1 and ty2 are feasibly equivalent if ty1 and ty2 may become definitely equivalent if further constraints are added to the current inference constraints. Thus list<int> and list<'a> are feasibly equivalent for the empty constraint set. ### Subtyping and Coercion A static type ty2 coerces to static type ty1 (with respect to a set of current inference constraints X), if ty1 is in the transitive closure of the base types and interface types of ty2. Static coercion is written with the :> symbol: ty2 :> ty1, Variable types 'T coerce to all types ty if the current inference constraints include a constraint of the form 'T :> ty2, and ty is in the inclusive transitive closure of the base and interface types of ty2. A static type ty2 feasibly coerces to static type ty1 if ty2 coerces to ty*1*** may hold through the addition of further constraints to the current inference constraints. The result of adding constraints is defined in Constraint Solving (§14.5). ### Nullness The design of F# aims to greatly reduce the use of null literals in common programming tasks, because they generally result in error-prone code. However: • The use of some null literals is required for interoperation with CLI libraries. • The appearance of null values during execution cannot be completely precluded for technical reasons related to the CLI and CLI libraries. As a result, F# types differ in their treatment of the null literal and null values. All named types and type definitions fall into one of the following categories: • Types with the null literal. These types have null as an “extra” value. The following types are in this category: • All CLI reference types that are defined in other CLI languages. • All types that are defined in F# and annotated with the AllowNullLiteral attribute. For example, System.String and other CLI reference types satisfy this constraint, and these types permit the direct use of the null literal. • Types with null as an abnormal value. These types do not permit the null literal, but do have null as an abnormal value. The following types are in this category: • All F# list, record, tuple, function, class, and interface types. • All F# union types except those that have null as a normal value, as discussed in the next bullet point. For types in this category, the use of the null literal is not directly allowed. However, strictly speaking, it is possible to generate a null value for these types by using certain functions such as Unchecked.defaultof<type>. For these types, null is considered an abnormal value. Operations differ in their use and treatment of null values; for details about evaluation of expressions that might include null values, see §6.9. • Types with null as a representation value. These types do not permit the null literal but use the null value as a representation. For these types, the use of the null literal is not directly permitted. However, one or all of the “normal” values of the type is represented by the null value. The following types are in this category: • The unit type. The null value is used to represent all values of this type. • Any union type that has the FSharp.Core.CompilationRepresentation(CompilationRepresentationFlags.UseNullAsTrueValue) attribute flag and a single null union case. The null value represents this case. In particular, null represents None in the F# option<_> type. • Types without null. These types do not permit the null literal and do not have the null value. All value types are in this category, including primitive integers, floating-point numbers, and any value of a CLI or F# struct type. A static type ty satisfies a nullness constraint ty : null if it: • Has an outermost named type that has the null literal. • Is a variable type with a typar : null constraint. ### Default Initialization Related to nullness is the default initialization of values of some types to zero values. This technique is common in some programming languages, but the design of F# deliberately de-emphasizes it. However, default initialization is allowed in some circumstances: • Checked default initialization may be used when a type is known to have a valid and “safe” default zero value. For example, the types of fields that are labeled with DefaultValue(true) are checked to ensure that they allow default initialization. • CLI libraries sometimes perform unchecked default initialization, as do the F# library primitives Unchecked.defaultof<_> and Array.zeroCreate. The following types permit default initialization: • Any type that satisfies the nullness constraint. • Primitive value types. • Struct types whose field types all permit default initialization. ### Dynamic Conversion Between Types A runtime type vty dynamically converts to a static type ty if any of the following are true: • vty coerces to ty. • vty is **int32[]**and ty is uint32[](or conversely). Likewise for sbyte[]/byte[], int16[]/uint16[], int64[]/uint64[], and nativeint[]/unativeint[]. • vty is enum**[]** where enum has underlying type underlying, and ty is underlying**[]** (or conversely), or the (un)signed equivalent of underlying**[]** by the immediately preceding rule. • vty is elemty*1[], ty is elemty2[], elemty1*** is a reference type, and elemty*1*** converts to elemty*2***. • ty is System.Nullable<vty>. Note that this specification does not define the full algebra of the conversions of runtime types to static types because the information that is available in runtime types is implementation dependent. However, the specification does state the conditions under which objects are guaranteed to have a runtime type that is compatible with a particular static type. Note: This specification covers the additional rules of CLI dynamic conversions, all of which apply to F# types. For example: let x = box [| System.DayOfWeek.Monday |] let y = x :? int32[] printf "%b" y // true In the previous code, the type System.DayOfWeek.Monday[] does not statically coerce to int32[], but the expression x :? int32[] evaluates to true. let x = box [| 1 |] let y = x :? uint32 [] printf "%b" y // true In the previous code, the type int32[] does not statically coerce to uint32[], but the expression x :? uint32 [] evaluates to true. let x = box [| "" |] let y = x :? obj [] printf "%b" y // true In the previous code, the type string[] does not statically coerce to obj[], but the expression **x :? obj []**evaluates to true. let x = box 1 let y = x :? System.Nullable<int32> printf "%b" y // true In the previous code, the type int32 does not coerce to System.Nullable<int32>, but the expression x :? System.Nullable<int32> evaluates to true. # Expressions The expression forms and related elements are as follows: expr := const -- a constant value ( expr ) -- block expression begin expr end -- block expression long-ident-or-op -- lookup expression expr '.' long-ident-or-op -- dot lookup expression expr expr -- application expression expr**(expr) -- high precedence application** expr**<types> -- type application expression** expr infix-op expr -- infix application expression prefix-op expr -- prefix application expression expr**.[expr] -- indexed lookup expression** expr**.[slice-ranges] -- slice expression** expr <- expr -- assignment expression expr , ... , expr -- tuple expression new type expr -- simple object expression { new base-call object-members interface-impls } -- object expression { field-initializers } -- record expression { expr with field-initializers } -- record cloning expression [ expr ; ... ; expr ] -- list expression [| expr ; ... ; expr |] -- array expression expr { comp-or-range-expr } -- computation expression [ comp-or-range-expr**] -- computed list expression** [| comp-or-range-expr |] -- computed array expression lazy expr -- delayed expression null -- the "null" value for a reference type expr : type -- type annotation expr :> type -- static upcast coercion expr :? type -- dynamic type test expr :?> type -- dynamic downcast coercion upcast expr -- static upcast expression downcast expr -- dynamic downcast expression let function-defn in expr –- function definition expression let value-defn in expr –- value definition expression let rec function-or-value-defns in expr -- recursive definition expression use ident = expr in expr –- deterministic disposal expression fun argument-pats -> expr -- function expression function rules -- matching function expression expr ; expr -- sequential execution expression match expr with rules -- match expression try expr with rules -- try/with expression try expr finally expr -- try/finally expression if expr then expr elif-branches*opt*** else-branchopt -- conditional expression while expr do expr done -- while loop for ident = expr to expr do expr done -- simple for loop for pat in expr**-**or-range-expr do expr done -- enumerable for loop assert expr -- assert expression <@ expr @> -- quoted expression <@@ expr @@> -- quoted expression **%**expr -- expression splice %%expr -- weakly typed expression splice (static-typars : (member-sig) expr) -– static member invocation Expressions are defined in terms of patterns and other entities that are discussed later in this specification. The following constructs are also used: exprs := expr ',' ... ',' expr expr-or-range-expr := expr range-expr elif-branches := elif-branch ... elif-branch elif-branch := elif expr then expr else-branch := else expr function-or-value-defn := function-defn value-defn function-defn := inlineopt** access*opt*** ident-or-op typar-defns*opt*** argument-pats return-type*opt*** = expr value-defn := mutableopt** access*opt*** pat typar-defns*opt*** return-type*opt*** = expr return-type := : type function-or-value-defns := function-or-value-defn and ... and function-or-value-defn argument-pats**:=** atomic-pat ... atomic-pat field-initializer := long-ident = expr -- field initialization field-initializers := field-initializer ; ... ; field-initializer object-construction := type expr -- construction expression type -- interface construction expression base-call := object-construction -- anonymous base construction object-construction as ident -- named base construction interface-impls := interface-impl ... interface-impl interface-impl := interface type object-members*opt*** -- interface implementation object-members := with member-defns end member-defns := member-defn ... member-defn Computation and range expressions are defined in terms of the following productions: comp-or-range-expr := comp-expr short-comp-expr range-expr comp-expr := let! pat = expr in comp-expr -- binding computation let pat = expr in comp-expr **do! ** expr in comp-expr **-- sequential computation do ** expr in comp-expr use! pat = expr in comp-expr -- auto cleanup computation use pat = expr in comp-expr yield! expr -- yield computation yield expr -- yield result return! expr -- return computation return expr -- return result if expr **then comp-**expr -- control flow or imperative action if expr then expr else comp-expr match expr with pat -> comp-expr | … | pat -> comp-expr **try comp-**expr with pat -> comp-expr | … | pat -> comp-expr **try comp-**expr finally expr while expr **do comp-**expr done for ident = expr to expr **do comp-**expr done for pat in expr**-**or-range-expr **do comp-**expr done **comp-**expr **; comp-**expr expr short-comp-expr := for pat in expr-or-range-expr -> expr -- yield result range-expr := expr .. expr -- range sequence expr .. expr .. expr -- range sequence with skip slice-ranges := slice-range , , slice-range** ** slice-range := expr -- slice of one element of dimension expr**.. -- slice from index to end** **..**expr -- slice from start to index expr**..**expr -- slice from index to index '*' -- slice from start to end ## Some Checking and Inference Terminology The rules applied to check individual expressions are described in the following subsections. Where necessary, these sections reference specific inference procedures such as Name Resolution (§14.1) and Constraint Solving (§14.5). All expressions are assigned a static type through type checking and inference. During type checking, each expression is checked with respect to an initial type. The initial type establishes some of the information available to resolve method overloading and other language constructs. We also use the following terminology: • The phrase “the type ty*1*** is asserted to be equal to the type ty*2” or simply “ty1* = ty*2*** is asserted” indicates that the constraint “ty*1*** = ty*2***” is added to the current inference constraints. • The phrase “ty*1*** is asserted to be a subtype of ty*2” or simply “ty1* :> ty*2*** is asserted” indicates that the constraint ty*1*** :> ty*2*** is added to the current inference constraints. • The phrase “type ty is known to ...” indicates that the initial type satisfies the given property given the current inference constraints. • The phrase “the expression expr has type ty” means the initial type of the expression is asserted to be equal to ty. Additionally: • The addition of constraints to the type inference constraint set fails if it causes an inconsistent set of constraints (§14.5). In this case either an error is reported or, if we are only attempting to assert the condition, the state of the inference procedure is left unchanged and the test fails. ## Elaboration and Elaborated Expressions Checking an expression generates an elaborated expression in a simpler, reduced language that effectively contains a fully resolved and annotated form of the expression. The elaborated expression provides more explicit information than the source form. For example, the elaborated form of System.Console.WriteLine("Hello") indicates exactly which overloaded method definition the call has resolved to. Elaborated forms are underlined in this specification, for example, let x = 1 in x + x. Except for this extra resolution information, elaborated forms are syntactically a subset of syntactic expressions, and in some cases (such as constants) the elaborated form is the same as the source form. This specification uses the following elaborated forms: • Constants • Resolved value references: path • Lambda expressions: (fun ident -> expr**)** • Primitive object expressions • Data expressions (tuples, union cases, array creation, record creation) • Default initialization expressions • Local definitions of values: let ident = expr in expr • Local definitions of functions: let rec ident = expr and ... and ident = expr in expr • Applications of methods and functions (with static overloading resolved) • Dynamic type coercions: expr :?> type • Dynamic type tests: expr :? type • For-loops: for ident in ident to ident do expr done • While-loops: while expr do expr done • Sequencing: expr**;** expr • Try-with: try expr with expr • Try-finally: try expr finally expr • The constructs required for the elaboration of pattern matching (§7). • Null tests • Switches on integers and other types • Switches on union cases • Switches on the runtime types of objects The following constructs are used in the elaborated forms of expressions that make direct assignments to local variables and arrays and generate “byref” pointer values. The operations are loosely named after their corresponding primitive constructs in the CLI. • Assigning to a byref-pointer: expr <-stobj expr • Generating a byref-pointer by taking the address of a mutable value: &path. • Generating a byref-pointer by taking the address of a record field: &(expr.field) • Generating a byref-pointer by taking the address of an array element: &(expr.[expr]) Elaborated expressions form the basis for evaluation (see §6.9) and for the expression trees that quoted expressions return(see §6.8). By convention, when describing the process of elaborating compound expressions, we omit the process of recursively elaborating sub-expressions. ## Data Expressions This section describes the following data expressions: • Simple constant expressions • Tuple expressions • List expressions • Array expressions • Record expressions • Copy-and-update record expressions • Function expressions • Object expressions • Delayed expressions • Computation expressions • Sequence expressions • Range expressions • Lists via sequence expressions • Arrays via sequence expressions • Null expressions • 'printf' formats ### Simple Constant Expressions Simple constant expressions are numeric, string, Boolean and unit constants. For example: 3y // sbyte 32uy // byte 17s // int16 18us // uint16 86 // int/int32 99u // uint32 99999999L // int64 10328273UL // uint64 1. // float/double 1.01 // float/double 1.01e10 // float/double 1.0f // float32/single 1.01f // float32/single 1.01e10f // float32/single 99999999n // nativeint (System.IntPtr) 10328273un // unativeint (System.UIntPtr) 99999999I // bigint (System.Numerics.BigInteger or user-specified) 'a' // char (System.Char) "3" // string (String) "c:\\home" // string (System.String) @"c:\home" // string (Verbatim Unicode, System.String) "ASCII"B // byte[] () // unit (FSharp.Core.Unit) false // bool (System.Boolean) true // bool (System.Boolean) Simple constant expressions have the corresponding simple type and elaborate to the corresponding simple constant value. Integer literals with the suffixes Q, R, Z, I, N, G are processed using the following syntactic translation: xxxx<suffix> For xxxx = 0 NumericLiteral<suffix>.FromZero() For xxxx = 1 NumericLiteral<suffix>.FromOne() For xxxx in the Int32 range NumericLiteral<suffix>.FromInt32(xxxx) For xxxx in the Int64 range NumericLiteral<suffix>.FromInt64(xxxx) For other numbers NumericLiteral<suffix>.FromString("xxxx") For example, defining a module NumericLiteralZ as below enables the use of the literal form 32Z to generate a sequence of 32 ‘Z’ characters. No literal syntax is available for numbers outside the range of 32-bit integers. module NumericLiteralZ = let FromZero() = "" let FromOne() = "Z" let FromInt32 n = String.replicate n "Z" F# compilers may optimize on the assumption that calls to numeric literal functions always terminate, are idempotent, and do not have observable side effects. ### Tuple Expressions An expression of the form expr1, ..., exprn is a tuple expression. For example: let three = (1,2,"3") let blastoff = (10,9,8,7,6,5,4,3,2,1,0) The expression has the type (ty1 * ... * ty*n) for fresh types ty1* ty*n***, and each individual expression ei is checked using initial type tyi. Tuple types and expressions are translated into applications of a family of F# library types named System.Tuple. Tuple types ty*1*** * ... * ty*n*** are translated as follows: • For n <= 7 the elaborated form is Tuple<ty1,...,tyn>. • For larger n, tuple types are shorthand for applications of the additional F# library type System.Tuple<_> as follows: • For n = 8 the elaborated form is Tuple<ty1,...,ty7,Tuple<ty8>>. • For 9 <= n the elaborated form is Tuple<ty1,...,ty7,tyB> where ty*B*** is the converted form of the type (ty8 *...* ty*n***). Tuple expressions (expr1,...,exprn) are translated as follows: • For n <= 7 the elaborated form new Tuple<ty1,…,tyn>(expr1,...,exprn). • For n = 8 the elaborated form new Tuple<ty1,…,ty7,Tuple<ty8>>(expr1,...,expr7, new Tuple<ty8>(expr8). • For 9 <= n the elaborated form new Tuple<ty1,...ty7,ty8n>(expr1,..., expr7, new ty**8n(e8n)** where ty8n is the type (ty8*...* tyn) and expr8n is the elaborated form of the expression expr8,...,* expr*n. When considered as static types, tuple types are distinct from their encoded form. However, the encoded form of tuple values and types is visible in the F# type system through runtime types. For example, typeof<int * int> is equivalent to typeof<System.Tuple<int,int>>, and (1,2) has the runtime type System.Tuple<int,int>. Likewise, (1,2,3,4,5,6,7,8,9) has the runtime type Tuple<int,int,int,int,int,int,int,Tuple<int,int>>. Note: The above encoding is invertible and the substitution of types for type variables preserves this inversion. This means, among other things, that the F# reflection library can correctly report tuple types based on runtime System.Type values. The inversion is defined by: • For the runtime type Tuple<ty1,...,tyN> when n <= 7, the corresponding F# tuple type is ty*1*** * ... * ty*N*** • For the runtime type Tuple<ty1,..., Tuple<tyN>> when n = 8, the corresponding F# tuple type is ty*1*** * ... * ty*8*** • For the runtime type Tuple<ty1,..., ty*7,tyBn>* , if ty*Bn*** corresponds to the F# tuple type ty*8*** * ... * ty*N, then the corresponding runtime type is ty1* * ... * ty*N***. Runtime types of other forms do not have a corresponding tuple type. In particular, runtime types that are instantiations of the eight-tuple type Tuple<_,_,_,_,_,_,_,_> must always have Tuple<_> in the final position. Syntactic types that have some other form of type in this position are not permitted, and if such an instantiation occurs in F# code or CLI library metadata that is referenced by F# code, an F# implementation may report an error. ### List Expressions An expression of the form [expr1;...; expr*n***] is a list expression. The initial type of the expression is asserted to be FSharp.Collections.List<ty> for a fresh type ty. If ty is a named type, each expression expr*i*** is checked using a fresh type ty' as its initial type, with the constraint ty' :> ty. Otherwise, each expression expr*i*** is checked using ty as its initial type. List expressions elaborate to uses of FSharp.Collections.List<_> as op_Cons(expr1,(op_Cons(expr2... op_Cons (exprn, op_Nil)...) where op_Cons and op_Nil are the union cases with symbolic names :: and [] respectively. ### Array Expressions An expression of the form [|expr1;...; expr*n*** |] is an array expression. The initial type of the expression is asserted to be ty**[]** for a fresh type ty. If this assertion determines that ty is a named type, each expression expr*i*** is checked using a fresh type ty' as its initial type, with the constraint ty' :> ty. Otherwise, each expression expr*i*** is checked using ty as its initial type. Array expressions are a primitive elaborated form. Note: The F# implementation ensures that large arrays of constants of type bool, char, byte, sbyte, int16, uint16, int32, uint32, int64, and uint64 are compiled to an efficient binary representation based on a call to System.Runtime.CompilerServices.RuntimeHelpers.InitializeArray. ### Record Expressions An expression of the form { field-initializer*1*** ; … ; field-initializer*n*** } is a record construction expression. For example: type Data = { Count : int; Name : string } let data1 = { Count = 3; Name = "Hello"; } let data2 = { Name = "Hello"; Count= 3 } In the following example, data4 uses a long identifier to indicate the relevant field: module M = type Data = { Age : int; Name : string; Height : float } let data3 = { M.Age = 17; M.Name = "John"; M.Height = 186.0 } let data4 = { data3 with M.Name = "Bill"; M.Height = 176.0 } Fields may also be referenced by using the name of the containing type: module M2 = type Data = { Age : int; Name : string; Height : float } let data5 = { M2.Data.Age = 17; M2.Data.Name = "John"; M2.Data.Height = 186.0 } let data6 = { data5 with M2.Data.Name = "Bill"; M2.Data.Height=176.0 } open M2 let data7 = { Data.Age = 17; Data.Name = "John"; Data.Height = 186.0 } let data8 = { data5 with Data.Name = "Bill"; Data.Height=176.0 } Each field-initializer*i*** has the form field-label*i*** = expr*i. Each field-labeli* is a long-ident, which must resolve to a field Fi in a unique record type R as follows: • If field-labeli is a single identifier fld and the initial type is known to be a record type R**<_,...,_>** that has field Fi with name fld, then the field label resolves to Fi. • If field-labeli is not a single identifier or if the initial type is a variable type, then the field label is resolved by performing Field Label Resolution (see §14.1) on field-labeli. This procedure results in a set of fields FSeti. Each element of this set has a corresponding record type, thus resulting in a set of record types RSeti. The intersection of all RSeti must yield a single record type R, and each field then resolves to the corresponding field in R. The set of fields must be complete. That is, each field in record type R must have exactly one field definition. Each referenced field must be accessible (see §10.5), as must the type R. After all field labels are resolved, the overall record expression is asserted to be of type R**<ty1,...,tyN>** for fresh types ty*1,...,tyN. Each expri* is then checked in turn. The initial type is determined as follows: 1. Assume the type of the corresponding field Fi in R**<ty1,...,tyN>** is ftyi 2. If the type of Fi prior to taking into account the instantiation <ty1,...,tyN> is a named type, then the initial type is a fresh type inference variable fty'i with a constraint fty'i :> ftyi. 3. Otherwise the initial type is fty*i***. Primitive record constructions are an elaborated form in which the fields appear in the same order as in the record type definition. Record expressions themselves elaborate to a form that may introduce local value definitions to ensure that expressions are evaluated in the same order that the field definitions appear in the original expression. For example: type R = {b : int; a : int } { a = 1 + 1; b = 2 } The expression on the last line elaborates to let v = 1 + 1 in { b = 2; a = v }. Records expressions are also used for object initializations in additional object constructor definitions (§8.6.3). For example: type C = val x : int val y : int new() = { x = 1; y = 2 } Note: The following record initialization form is deprecated: { new type with Field*1*** = expr*1*** and … and Field*n*** = expr*n*** } The F# implementation allows the use of this form only with uppercase identifiers. F# code should not use this expression form. A future version of the F# language will issue a deprecation warning. ### Copy-and-update Record Expressions A copy-and-update record expression has the following form: { expr with field-initializers } where field-initializers is of the following form: field-label*1*** = expr*1*** ; … ; field-label*n*** = expr*n*** Each field-label*i*** is a long-ident. In the following example, data2 is defined by using such an expression: type Data = { Age : int; Name : string; Height : float } let data1 = { Age = 17; Name = "John"; Height = 186.0 } let data2 = { data1 with Name = "Bill"; Height = 176.0 } The expression expr is first checked with the same initial type as the overall expression. Next, the field definitions are resolved by using the same technique as for record expressions. Each field label must resolve to a field Fi in a single record type R, all of whose fields are accessible. After all field labels are resolved, the overall record expression is asserted to be of type R**<ty1,...,tyN>** for fresh types ty*1***,...,tyN. Each expri is then checked in turn with initial type that results from the following procedure: 1. Assume the type of the corresponding field Fi in R**<ty1,...,tyN>** is ftyi. 2. If the type of Fi before considering the instantiation <ty1,...,tyN> is a named type, then the initial type is a fresh type inference variable fty'i with a constraint fty'i :> ftyi. 3. Otherwise, the initial type is fty*i***. A copy-and-update record expression elaborates as if it were a record expression written as follows: let v = expr in { field-label*1*** = expr*1*** ; … ; field-label*n*** = expr*n; F1** = v.F**1; ... ; FM** = v.F**M*** **} **where F1 ... FM are the fields of R that are not defined in field-initializers and v is a fresh variable. ### Function Expressions An expression of the form fun pat*1*** ... pat*n*** -> expr is a function expression. For example: (fun x -> x + 1) (fun x y -> x + y) (fun [x] -> x) // note, incomplete match (fun (x,y) (z,w) -> x + y + z + w) Function expressions that involve only variable patterns are a primitive elaborated form. Function expressions that involve non-variable patterns elaborate as if they had been written as follows: fun v*1*** ... v*n*** -> let pat*1** = v**1*** ... let pat*n** = v**n*** expr No pattern matching is performed until all arguments have been received. For example, the following does not raise a MatchFailureException exception: let f = fun [x] y -> y let g = f [] // ok However, if a third line is added, a MatchFailureException exception is raised: let z = g 3 // MatchFailureException is raised ### Object Expressions An expression of the following form is an object expression: { new ty*0*** args-expropt object-members interface ty*1*** object-members*1*** interface ty*n*** object-members*n*** } In the case of the interface declarations, the object-members are optional and are considered empty if absent. Each set of object-members has the form: with member-defns endopt Lexical filtering inserts simulated$end tokens when lightweight syntax is used.

Each member of an object expression members can use the keyword member, override, or default. The keyword member can be used even when overriding a member or implementing an interface.

For example:

let obj1 =

{ new System.Collections.Generic.IComparer<int> with

member x.Compare(a,b) = compare (a % 7) (b % 7) }

let obj2 =

{ new System.Object() with
member x.ToString () = "Hello" }

let obj3 =

{ new System.Object() with
member x.ToString () = "Hello, base.ToString() = " + base.ToString() }

let obj4 =

{ new System.Object() with
member x.Finalize() = printfn "Finalize";
interface System.IDisposable with
member x.Dispose() = printfn "Dispose"; }

An object expression can specify additional interfaces beyond those required to fulfill the abstract slots of the type being implemented. For example, obj4 in the preceding examples has static type System.Object but the object additionally implements the interface System.IDisposable. The additional interfaces are not part of the static type of the overall expression, but can be revealed through type tests.

Object expressions are statically checked as follows.

1. First, ty*0*** to ty*n*** are checked to verify that they are named types. The overall type of the expression is ty*0*** and is asserted to be equal to the initial type of the expression. However, if ty*0*** is type equivalent to System.Object and ty*1*** exists, then the overall type is instead ty*1***.

2. The type ty*0*** must be a class or interface type. The base construction argument args-expr must appear if and only if ty*0*** is a class type. The type must have one or more accessible constructors; the call to these constructors is resolved and elaborated using Method Application Resolution (see §14.4). Except for ty*0, each tyi* must be an interface type.

3. The F# compiler attempts to associate each member with a unique dispatch slot by using dispatch slot inference (§14.7). If a unique matching dispatch slot is found, then the argument types and return type of the member are constrained to be precisely those of the dispatch slot.

4. The arguments, patterns, and expressions that constitute the bodies of all implementing members are next checked one by one to verify the following:

• For each member, the “this” value for the member is in scope and has type ty0.

• Each member of an object expression can initially access the protected members of ty0.

• If the variable base-ident appears, it must be named base, and in each member a base variable with this name is in scope. Base variables can be used only in the member implementations of an object expression, and are subject to the same limitations as byref values described in §14.9.

The object must satisfy dispatch slot checking (§14.8) which ensures that a one-to-one mapping exists between dispatch slots and their implementations.

Object expressions elaborate to a primitive form. At execution, each object expression creates an object whose runtime type is compatible with all of the ty*i*** that have a dispatch map that is the result of dispatch slot checking (§14.8).

The following example shows how to both implement an interface and override a method from System.Object. The overall type of the expression is INewIdentity.

type public INewIdentity =

abstract IsAnonymous : bool

let anon =

{ new System.Object() with

member i.ToString() = "anonymous"

interface INewIdentity with

member i.IsAnonymous = true }

### Delayed Expressions

An expression of the form lazy expr is a delayed expression. For example:

lazy (printfn "hello world")

is syntactic sugar for

new System.Lazy (fun () -> expr)

The behavior of the System.Lazy library type ensures that expression expr is evaluated on demand in response to a .Value operation on the lazy value.

### Computation Expressions

The following expression forms are all computation expressions:

expr { for ... }

expr { let ... }

expr { let! ... }

expr { use ... }

expr { while ... }

expr { yield ... }

expr { yield! ... }

expr { try ... }

expr { return ... }

expr { return! ... }

More specifically, computation expressions have the following form:

builder-expr { cexpr }

where cexpr is, syntactically, the grammar of expressions with the additional constructs that are defined in comp-expr. Computation expressions are used for sequences and other non-standard interpretations of the F# expression syntax. For a fresh variable b, the expression

builder-expr { cexpr }

translates to

let b = builder-expr in {| cexpr |}C

The type of b must be a named type after the checking of builder-expr. The subscript indicates that custom operations (C) are acceptable but are not required.

If the inferred type of b has one or more of the Run, Delay, or Quote methods when builder-expr is checked, the translation involves those methods. For example, when all three methods exist, the same expression translates to:

let b = builder-expr in b.Run (<@ b.Delay(fun () -> {| cexpr |}C) >@)

If a Run method does not exist on the inferred type of b, the call to Run is omitted. Likewise, if no Delay method exists on the type of b, that call and the inner lambda are omitted, so the expression translates to the following:

let b = builder-expr in b.Run (<@ {| cexpr |}C >@)

Similarly, if a Quote method exists on the inferred type of b, at-signs <@ @> are placed around {| cexpr |}C or b.Delay(fun () -> {| cexpr |}C) if a Delay method also exists.

The translation {| cexpr |}C , which rewrites computation expressions to core language expressions, is defined recursively according to the following rules:

{| cexpr |}C ≡ T (cexpr, [], fun v -> v, true)

During the translation, we use the helper function {| cexpr |}0 to denote a translation that does not involve custom operations:

{| cexpr |}0 ≡ T (cexpr, [], fun v -> v, false)

T(e, V, C, q) where e : the computation expression being translated

V : a set of scoped variables

C : continuation (or context where “e” occurs,

up to a hole to be filled by the result of translating “e”)

q : Boolean that indicates whether a custom operator is allowed

Then, T is defined for each computation expression e:

T(let p = e in ce, V, C, q) = T(ce, Vvar(p), λv.C(let p = e in v), q)

T(let! p = e in ce, V, C, q) = T(ce, Vvar(p), λv.C(b.Bind(src(e),fun p -> v), q)

T(yield e, V, C, q) = C(b.Yield(e))

T(yield! e, V, C, q) = C(b.YieldFrom(src(e)))

T(return e, V, C, q) = C(b.Return(e))

T(return! e, V, C, q) = C(b.ReturnFrom(src(e)))

T(use p = e in ce, V, C, q) = C(b.Using(e, fun p -> {| ce |}0))

T(use! p = e in ce, V, C, q) = C(b.Bind(src(e), fun p -> b.Using(p, fun p -> {| ce |}0))

T(match e with pi -> cei, V, C, q) = C(match e with pi -> {| cei |}0)

T(while e do ce, V, C, q) = T(ce, V, λv.C(b.While(fun () -> e, b.Delay(fun () -> v))), q)

T(try ce with pi -> cei, V, C, q) =
Assert(not q); C(b.TryWith(b.Delay(fun () -> {| ce |}0), fun pi -> {| cei |}0))

T(try ce finally e, V, C, q) =
Assert(not q); C(b.TryFinally(b.Delay(fun () -> {| ce |}0), fun () -> e))

T(if e then ce, V, C, q) = T(ce, V, λv.C(if e then v else b.Zero()), q)

T(if e then ce1 else ce2, V, C, q) = Assert(not q); C(if e then {| ce1 |}0) else {| ce2 |}0)

T(for x = e1 to e2 do ce, V, C, q) = T(for x in e1 .. e2 do ce, V, C, q)

T(for p1 in e1 do joinOp p2 in e2 onWord (e3 eop e4) ce, V, C, q) =
Assert(q); T(for pat(V) in b.Join(src(e1), src(e2), λp1.e3, λp2.e4,
λp1. λp2.(p1,p2)) do ce, V , C, q)

T(for p1 in e1 do groupJoinOp p2 in e2 onWord (e3 eop e4) into p3 ce, V, C, q) =
Assert(q); T(for pat(V) in b.GroupJoin(src(e1),
src(e2), λp1.e3, λp2.e4, λp1. λp3.(p1,p3)) do ce, V , C, q)

T(for x in e do ce, V, C, q) = T(ce, V ⊕ {x}, λv.C(b.For(src(e), fun x -> v)), q)

T(do e in ce, V, C, q) = T(ce, V, λv.C(e; v), q)

T(do! e in ce, V, C, q) = T(let! () = e in ce, V, C, q)

T(joinOp p2 in e2 on (e3 eop e4) ce, V, C, q) = **
T**(for pat(V) in C({| yield exp(V) |}0) do join p2 in e2 onWord (e3 eop e4) ce, V, λv.v, q)

T(groupJoinOp p2 in e2 onWord (e3 eop e4) into p3 ce, V, C, q) = **
T**(for pat(V) in C({| yield exp(V) |}0) do groupJoin p2 in e2 on (e3 eop e4) into p3 ce,
V, λv.v, q)

T([<CustomOperator("Cop")>]cop arg, V, C, q) = Assert (q); [| cop arg, C(b.Yield exp(V)) |]V

T([<CustomOperator("Cop", MaintainsVarSpaceUsingBind=true)>]cop arg; e, V, C, q) =
Assert (q); CL (cop arg; e, V, C(b.Return exp(V)), false)

T([<CustomOperator("Cop")>]cop arg; e, V, C, q) =
Assert (q); CL (cop arg; e, V, C(b.Yield exp(V)), false)

T(ce1; ce2, V, C, q) = C(b.Combine({| ce1 |}0, b.Delay(fun () -> {| ce2 |}0)))

T(do! e;, V, C, q) = T(let! () = src(e) in b.Return(), V, C, q)

T(e;, V, C, q) = C(e;b.Zero())

The following notes apply to the translations:

• The lambda expression (fun f x -> b) is represented by λx.b.

• The auxiliary function var(p) denotes a set of variables that are introduced by a pattern p. For example:
var(x) = {x}, var((x,y)) = {x,y} or var(S (x,y)) = {x,y}
where S is a type constructor.

• ⊕ is an update operator for a set V to denote extended variable spaces. It updates the existing variables. For example, {x,y} ⊕ var((x,z)) becomes {x,y,z} where the second x replaces the first x.

• The auxiliary function pat(V) denotes a pattern tuple that represents a set of variables in V. For example, pat({x,y}) becomes (x,y), where x and y represent pattern expressions.

• The auxiliary function exp(V) denotes a tuple expression that represents a set of variables in V. For example, exp({x,y}) becomes (x,y), where x and y represent variable expressions.

• The auxiliary function src(e) denotes b.Source(e) if the innermost ForEach is from the user code instead of generated by the translation, and a builder b contains a Source method. Otherwise, src(e) denotes e.

• Assert() checks whether a custom operator is allowed. If not, an error message is reported. Custom operators may not be used within try/with, try/finally, if/then/else, use, match, or sequential execution expressions such as **(**e1;e2). For example, you cannot use if/then/else in any computation expressions for which a builder defines any custom operators, even if the custom operators are not used.

• The operator eop denotes one of =, ?=, =? or ?=?.

• joinOp and onWord represent keywords for join-like operations that are declared in CustomOperationAttribute. For example, [<CustomOperator("join", IsLikeJoin=true, JoinConditionWord="on")>] declares “join” and “on”.

• Similarly, groupJoinOp represents a keyword for groupJoin-like operations, declared in CustomOperationAttribute. For example, [<CustomOperator("groupJoin", IsLikeGroupJoin=true, JoinConditionWord="on")>] declares “groupJoin” and “on”.

• The auxiliary translation CL is defined as follows:

CL (e1, V, e2, bind) where e1: the computation expression being translated

V: a set of scoped variables

e2: the expression that will be translated after e1 is done

bind: indicator if it is for Bind (true) or iterator (false).

The following shows translations for the uses of CL in the preceding computation expressions:

CL (cop arg, V, e’, bind) = [| cop arg, e’ |]V

CL ([<MaintainsVariableSpaceUsingBind=true>]cop arg into p; e, V, e’, bind) =
T(let! p = e’ in e, [], λv.v, true)

CL (cop arg into p; e, V, e’, bind) = T(for p in e’ do e, [], λv.v, true)

CL ([<MaintainsVariableSpace=true>]cop arg; e, V, e’, bind) = **
CL** (e, V, [| cop arg, e’ |]V, true)

CL ([<MaintainsVariableSpaceUsingBind=true>]cop arg; e, V, e’, bind) = **
CL** (e, V, [| cop arg, e’ |]V, true)

CL (cop arg; e, V, e’, bind) = CL (e, [], [| cop arg, e’ |]V, false)

CL (e, V, e’, true) = T(let! pat(V) = e’ in e, V, λv.v, true)

CL (e, V, e’, false) = T(for pat(V) in e’ do e, V, λv.v, true)

• The auxiliary translation [| e1, e2 |]V is defined as follows:

[|[ e1**, e2 |]V** where e1: the custom operator available in a build

e2: the context argument that will be passed to a custom operator

V: a list of bound variables

[|[<CustomOperator(" Cop")>] cop [<ProjectionParameter>] arg, e |]V =

b.Cop (e, fun pat(V) -> arg)

[|[<CustomOperator("Cop")>] cop arg, e |]V = b.Cop (e, arg)

• The final two translation rules (for do! e; and do! e;) apply only for the final expression in the computation expression. The semicolon (;) can be omitted.

The following attributes specify custom operations:

• CustomOperationAttribute indicates that a member of a builder type implements a custom operation in a computation expression. The attribute has one parameter: the name of the custom operation. The operation can have the following properties:

• MaintainsVariableSpace indicates that the custom operation maintains the variable space of a computation expression.

• MaintainsVariableSpaceUsingBind indicates that the custom operation maintains the variable space of a computation expression through the use of a bind operation.

• AllowIntoPattern indicates that the custom operation supports the use of ‘into’ immediately following the operation in a computation expression to consume the result of the operation.

• IsLikeJoin indicates that the custom operation is similar to a join in a sequence computation, which supports two inputs and a correlation constraint.

• IsLikeGroupJoin indicates that the custom operation is similar to a group join in a sequence computation, which support two inputs and a correlation constraint, and generates a group.

• JoinConditionWord indicates the names used for the ‘on’ part of the custom operator for join-like operators.

• ProjectionParameterAttribute indicates that, when a custom operation is used in a computation expression, a parameter is automatically parameterized by the variable space of the computation expression.

The following examples show how the translation works. Assume the following simple sequence builder:

 type SimpleSequenceBuilder() = member __.For (source : seq<'a>, body : 'a -> seq<'b>) = seq { for v in source do yield! body v } member __.Yield (item:'a) : seq<'a> = seq { yield item } let myseq = SimpleSequenceBuilder()

Then, the expression

myseq {

for i in 1 .. 10 do

yield i*i

}

translates to

let b = myseq

b.For([1..10], fun i ->

b.Yield(i*i))

CustomOperationAttribute allows us to define custom operations. For example, the simple sequence builder can have a custom operator, “where”:

 type SimpleSequenceBuilder() = member __.For (source : seq<'a>, body : 'a -> seq<'b>) = seq { for v in source do yield! body v } member __.Yield (item:'a) : seq<'a> = seq { yield item } [] member __.Where (source : seq<'a>, f: 'a -> bool) : seq<'a> = Seq.filter f source let myseq = SimpleSequenceBuilder()

Then, the expression

myseq {

for i in 1 .. 10 do

where (fun x -> x > 5)

}

translates to

let b = myseq

b.Where(

b.For([1..10], fun i ->

b.Yield (i)),

fun x -> x > 5)

ProjectionParameterAttribute automatically adds a parameter from the variable space of the computation expression. For example, ProjectionParameterAttribute can be attached to the second argument of the where operator:

 type SimpleSequenceBuilder() = member __.For (source : seq<'a>, body : 'a -> seq<'b>) = seq { for v in source do yield! body v } member __.Yield (item:'a) : seq<'a> = seq { yield item } [] member __.Where (source: seq<'a>, []f: 'a -> bool) : seq<'a> = Seq.filter f source let myseq = SimpleSequenceBuilder()

Then, the expression

myseq {

for i in 1 .. 10 do

where (i > 5)

}

translates to

let b = myseq

b.Where(

b.For([1..10], fun i ->

b.Yield (i)),

fun i -> i > 5)

ProjectionParameterAttribute is useful when a let binding appears between ForEach and the custom operators. For example, the expression

myseq {

for i in 1 .. 10 do

let j = i * i

where (i > 5 && j < 49)

}

translates to

let b = myseq

b.Where(

b.For([1..10], fun i ->

let j = i * i

b.Yield (i,j)),

fun (i,j) -> i > 5 && j < 49)

Without ProjectionParameterAttribute, a user would be required to write “fun (i,j) ->” explicitly.

Now, assume that we want to write the condition “where (i > 5 && j < 49)” in the following syntax:

where (i > 5)

where (j < 49)

To support this style, the where custom operator should produce a computation that has the same variable space as the input computation. That is, j should be available in the second where. The following example uses the MaintainsVariableSpace property on the custom operator to specify this behavior:

 type SimpleSequenceBuilder() = member __.For (source : seq<'a>, body : 'a -> seq<'b>) = seq { for v in source do yield! body v } member __.Yield (item:'a) : seq<'a> = seq { yield item } [] member __.Where (source: seq<'a>, []f: 'a -> bool) : seq<'a> = Seq.filter f source let myseq = SimpleSequenceBuilder()

Then, the expression

myseq {

for i in 1 .. 10 do

let j = i * i

where (i > 5)

where (j < 49)

}

translates to

let b = myseq

b.Where(

b.Where(

b.For([1..10], fun i ->

let j = i * i

b.Yield (i,j)),

fun (i,j) -> i > 5),

fun (i,j) -> j < 49)

When we may not want to produce the variable space but rather want to explicitly express the chain of the where operator, we can design this simple sequence builder in a slightly different way. For example, we can express the same expression in the following way:

myseq {

for i in 1 .. 10 do

where (i > 5) into j

where (j*j < 49)

}

In this example, instead of having a let-binding (for j in the previous example) and passing variable space (including j) down to the chain, we can introduce a special syntax that captures a value into a pattern variable and passes only this variable down to the chain, which is arguably more readable. For this case, AllowIntoPattern allows the custom operation to have an into syntax:

 type SimpleSequenceBuilder() = member __.For (source : seq<'a>, body : 'a -> seq<'b>) = seq { for v in source do yield! body v } member __.Yield (item:'a) : seq<'a> = seq { yield item } [] member __.Where (source: seq<'a>, []f: 'a -> bool) : seq<'a> = Seq.filter f source let myseq = SimpleSequenceBuilder()

Then, the expression

myseq {

for i in 1 .. 10 do

where (i > 5) into j

where (j*j < 49)

}

translates to

let b = myseq

b.Where(

b.For(

b.Where(

b.For([1..10], fun i -> b.Yield (i))

fun i -> i>5),

fun j -> b.Yield (j)),

fun j -> j*j < 49)

Note that the into keyword is not customizable, unlike join and on.

In addition to MaintainsVariableSpace, MaintainsVariableSpaceUsingBind is provided to pass variable space down to the chain in a different way. For example:

 type SimpleSequenceBuilder() = member __.For (source : seq<'a>, body : 'a -> seq<'b>) = seq { for v in source do yield! body v } member __.Return (item:'a) : seq<'a> = seq { yield item } member __.Bind (value , cont) = cont value [] member __.Where (source: seq<'a>, []f: 'a -> bool) : seq<'a> = Seq.filter f source let myseq = SimpleSequenceBuilder()

The presence of MaintainsVariableSpaceUsingBindAttribute requires Return and Bind methods during the translation.

Then, the expression

myseq {

for i in 1 .. 10 do

where (i > 5 && i*i < 49) into j

return j

}

translates to

let b = myseq

b.Bind(

b.Where(B.For([1..10], fun i -> b.Return (i)),

fun i -> i > 5 && i*i < 49),

fun j -> b.Return (j))

where Bind is called to capture the pattern variable j. Note that For and Yield are called to capture the pattern variable when MaintainsVariableSpace is used.

Certain properties on the CustomOperationAttribute introduce join-like operators. The following example shows how to use the IsLikeJoin property.

 type SimpleSequenceBuilder() = member __.For (source : seq<'a>, body : 'a -> seq<'b>) = seq { for v in source do yield! body v } member __.Yield (item:'a) : seq<'a> = seq { yield item } [] member __.Merge (src1:seq<'a>, src2:seq<'a>, ks1, ks2, ret) = seq { for a in src1 do for b in src2 do if ks1 a = ks2 b then yield((ret a ) b) } let myseq = SimpleSequenceBuilder()

IsLikeJoin indicates that the custom operation is similar to a join in a sequence computation; that is, it supports two inputs and a correlation constraint.

The expression

myseq {

for i in 1 .. 10 do

merge j in [5 .. 15] whenever (i = j)

yield j

}

translates to

let b = myseq

b.For(

b.Merge([1..10], [5..15],

fun i -> i, fun j -> j,

fun i -> fun j -> (i,j)),

fun j -> b.Yield (j))

This translation implicitly places type constraints on the expected form of the builder methods. For example, for the async builder found in the FSharp.Control library, the translation phase corresponds to implementing a builder of a type that has the following member signatures:

type AsyncBuilder with

member For: seq<'T> * ('T -> Async<unit>) -> Async<unit>

member Zero : unit -> Async<unit>

member Combine : Async<unit> * Async<'T> -> Async<'T>

member While : (unit -> bool) * Async<unit> -> Async<unit>

member Return : 'T -> Async<'T>

member Delay : (unit -> Async<'T>) -> Async<'T>

member Using: 'T * ('T -> Async<'U>) -> Async<'U>

when 'U :> System.IDisposable

member Bind: Async<'T> * ('T -> Async<'U>) -> Async<'U>

member TryFinally: Async<'T> * (unit -> unit) -> Async<'T>

member TryWith: Async<'T> * (exn -> Async<'T>) -> Async<'T>

The following example shows a common approach to implementing a new computation expression builder for a monad. The example uses computation expressions to define computations that can be partially run by executing them step-by-step, for example, up to a time limit.

/// Computations that can cooperatively yield by returning a continuation

type Eventually<'T> =

| Done of 'T

| NotYetDone of (unit -> Eventually<'T>)

[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]

module Eventually =

/// The bind for the computations. Stitch 'k' on to the end of the computation.

/// Note combinators like this are usually written in the reverse way,

/// for example,

/// e |> bind k

let rec bind k e =

match e with

| Done x -> NotYetDone (fun () -> k x)

| NotYetDone work -> NotYetDone (fun () -> bind k (work()))

/// The return for the computations.

let result x = Done x

type OkOrException<'T> =

| Ok of 'T

| Exception of System.Exception

/// The catch for the computations. Stitch try/with throughout

/// the computation and return the overall result as an OkOrException.

let rec catch e =

match e with

| Done x -> result (Ok x)

| NotYetDone work ->

NotYetDone (fun () ->

let res = try Ok(work()) with | e -> Exception e

match res with

| Ok cont -> catch cont // note, a tailcall

| Exception e -> result (Exception e))

/// The delay operator.

let delay f = NotYetDone (fun () -> f())

/// The stepping action for the computations.

let step c =

match c with

| Done _ -> c

| NotYetDone f -> f ()

// The rest of the operations are boilerplate.

/// The tryFinally operator.

/// This is boilerplate in terms of "result", "catch" and "bind".

let tryFinally e compensation =

catch (e)

|> bind (fun res -> compensation();

match res with

| Ok v -> result v

| Exception e -> raise e)

/// The tryWith operator.

/// This is boilerplate in terms of "result", "catch" and "bind".

let tryWith e handler =

catch e

|> bind (function Ok v -> result v | Exception e -> handler e)

/// The whileLoop operator.

/// This is boilerplate in terms of "result" and "bind".

let rec whileLoop gd body =

if gd() then body |> bind (fun v -> whileLoop gd body)

else result ()

/// The sequential composition operator

/// This is boilerplate in terms of "result" and "bind".

let combine e1 e2 =

e1 |> bind (fun () -> e2)

/// The using operator.

let using (resource: #System.IDisposable) f =

tryFinally (f resource) (fun () -> resource.Dispose())

/// The forLoop operator.

/// This is boilerplate in terms of "catch", "result" and "bind".

let forLoop (e:seq<_>) f =

let ie = e.GetEnumerator()

tryFinally (whileLoop (fun () -> ie.MoveNext())

(delay (fun () -> let v = ie.Current in f v)))

(fun () -> ie.Dispose())

// Give the mapping for F# computation expressions.

type EventuallyBuilder() =

member x.Bind(e,k) = Eventually.bind k e

member x.Return(v) = Eventually.result v

member x.ReturnFrom(v) = v

member x.Combine(e1,e2) = Eventually.combine e1 e2

member x.Delay(f) = Eventually.delay f

member x.Zero() = Eventually.result ()

member x.TryWith(e,handler) = Eventually.tryWith e handler

member x.TryFinally(e,compensation) = Eventually.tryFinally e compensation

member x.For(e:seq<_>,f) = Eventually.forLoop e f

member x.Using(resource,e) = Eventually.using resource e

let eventually = new EventuallyBuilder()

After the computations are defined, they can be built by using eventually { ... }:

let comp =

eventually { for x in 1 .. 2 do

printfn " x = %d" x

return 3 + 4 }

These computations can now be stepped. For example:

let step x = Eventually.step x

comp |> step

// returns "NotYetDone <closure>"

comp |> step |> step

// prints "x = 1"

// returns "NotYetDone <closure>"

comp |> step |> step |> step |> step |> step |> step

// prints "x = 1"

// prints "x = 2"

// returns “NotYetDone <closure>”

comp |> step |> step |> step |> step |> step |> step |> step |> step

// prints "x = 1"

// prints "x = 2"

// returns "Done 7"

### Sequence Expressions

An expression in one of the following forms is a sequence expression:

seq { comp-expr }

seq { short-comp-expr }

For example:

seq { for x in [ 1; 2; 3 ] do for y in [5; 6] do yield x + y }

seq { for x in [ 1; 2; 3 ] do yield x + x }

seq { for x in [ 1; 2; 3 ] -> x + x }

Logically speaking, sequence expressions can be thought of as computation expressions with a builder of type FSharp.Collections.SeqBuilder. This type can be considered to be defined as follows:

type SeqBuilder() =

member x.Yield (v) = Seq.singleton v

member x.YieldFrom (s:seq<_>) = s

member x.Return (():unit) = Seq.empty

member x.Combine (xs1,xs2) = Seq.append xs1 xs2

member x.For (xs,g) = Seq.collect f xs

member x.While (guard,body) = SequenceExpressionHelpers.EnumerateWhile guard body

member x.TryFinally (xs,compensation) =

SequenceExpressionHelpers.EnumerateThenFinally xs compensation

member x.Using (resource,xs) = SequenceExpressionHelpers.EnumerateUsing resource xs

However, this builder type is not actually defined in the F# library. Instead, sequence expressions are elaborated directly as follows:

{| yield expr |} Seq.singleton expr

{| yield! expr |} expr

{| expr1 ; expr2 |} Seq.append {| expr1 |} {| expr2 |}

{| for pat in expr1 -> expr2 |} Seq.map (fun pat -> {| expr2 |}) expr1

{| for pat in expr1 do expr2 |} Seq.collect (fun pat -> {| expr2 |}) expr1

{| while expr1 do expr2 |} RuntimeHelpers.EnumerateWhile

(fun () -> expr1)

{| expr2 |})

{| try expr1 finally expr2 |} RuntimeHelpers.EnumerateThenFinally

(| expr1 |})

(fun () -> expr2)

{| use v = expr1 in expr2 |} let v = expr1 in

RuntimeHelpers.EnumerateUsing v {| expr2 |}

{| let v = expr1 in expr2 |} let v = expr1 in {| expr2 |}

{| match expr with pat*i*** -> expr*i*** |} .match expr with pat*i*** -> {| cexpr*i*** |}

{| expr1 |} expr1 ; Seq.empty

{| if expr then expr*0*** |}C if expr then {| expr*0*** |}C else Seq.empty

{| if expr then expr*0*** else expr*1 |} if expr then {| expr0* |}C else {| expr*1*** |}C

Here the use of Seq and RuntimeHelpers refers to the corresponding functions in FSharp.Collections.Seq and FSharp.Core.CompilerServices.RuntimeHelpers respectively. This means that a sequence expression generates an object of type System.Collections.Generic.IEnumerable<ty> for some type ty. Such an object has a GetEnumerator method that returns a System.Collections.Generic.IEnumerator<ty> whose MoveNext, Current and Dispose methods implement an on-demand evaluation of the sequence expressions.

### Range Expressions

Expressions of the following forms are range expressions.

{ e1 .. e2 }

{ e1 .. e2 .. e3 }

seq { e1 .. e2 }

seq { e1 .. e2 .. e3 }

Range expressions generate sequences over a specified range. For example:

seq { 1 .. 10 } // 1; 2; 3; 4; 5; 6; 7; 8; 9; 10

seq { 1 .. 2 .. 10 } // 1; 3; 5; 7; 9

Range expressions involving expr*1*** .. expr*2 are translated to uses of the (..) operator, and those involving expr1* .. expr*1*** .. expr*3 ***are translated to uses of the (.. ..) operator:

seq { e1 .. e2 }(..) e1 e2

seq { e1 .. e2 .. e3 }(.. ..) e1 e2 e3

The default definition of these operators is in FSharp.Core.Operators. The (..)** operator generates an IEnumerable<_> for the range of values between the start (expr*1) and finish (expr2) values, using an increment of 1 (as defined by FSharp.Core.LanguagePrimitives.GenericOne). The (.. ..)*** operator generates an IEnumerable<_> for the range of values between the start (expr*1) and finish (expr3) values, using an increment of expr2***.

The seq keyword, which denotes the type of computation expression, can be omitted for simple range expressions, but this is not recommended and might be deprecated in a future release. It is always preferable to explicitly mark the type of a computation expression.

Range expressions also occur as part of the translated form of expressions, including the following:

• **[ **expr1 .. expr2 ]

• [| expr1 .. expr2 |]

• for var in expr1 .. expr2 do expr3

A sequence iteration expression of the form for var in expr1 .. expr2 do expr3 done is sometimes elaborated as a simple for loop-expression (§6.5.7).

### Lists via Sequence Expressions

A list sequence expression is an expression in one of the following forms

[ comp-expr ]

[ short-comp-expr ]

[ range-expr ]

In all cases [ cexpr ] elaborates to FSharp.Collections.Seq.toList(seq { cexpr }).

For example:

let x2 = [ yield 1; yield 2 ]

let x3 = [ yield 1

if System.DateTime.Now.DayOfWeek = System.DayOfWeek.Monday then

yield 2]

### Arrays Sequence Expressions

An expression in one of the following forms is an array sequence expression:

[| comp-expr |]

[| short-comp-expr |]

[| range-expr |]

In all cases [| cexpr |] elaborates to FSharp.Collections.Seq.toArray(seq { cexpr }).

For example:

let x2 = [| yield 1; yield 2 |]

let x3 = [| yield 1

if System.DateTime.Now.DayOfWeek = System.DayOfWeek.Monday then

yield 2 |]

### Null Expressions

An expression in the form null is a null expression. A null expression imposes a nullness constraint (§5.2.2, §5.4.8) on the initial type of the expression. The constraint ensures that the type directly supports the value null.

Null expressions are a primitive elaborated form.

### 'printf' Formats

Format strings are strings with % markers as format placeholders. Format strings are analyzed at compile time and annotated with static and runtime type information as a result of that analysis. They are typically used with one of the functions printf, fprintf, sprintf, or bprintf in the FSharp.Core.Printf module. Format strings receive special treatment in order to type check uses of these functions more precisely.

More concretely, a constant string is interpreted as a printf-style format string if it is expected to have the type FSharp.Core.PrintfFormat<'Printer,'State,'Residue,'Result,'Tuple>. The string is statically analyzed to resolve the generic parameters of the PrintfFormat type, of which 'Printer and 'Tuple are the most interesting:

• 'Printer is the function type that is generated by applying a printf-like function to the format string.

• 'Tuple is the type of the tuple of values that are generated by treating the string as a generator (for example, when the format string is used with a function similar to scanf in other languages).

A format placeholder has the following shape:

%[flags][width][.precision][type]

where:

flags

Are 0, -, +, and the space character. The # flag is invalid and results in a compile-time error.

width

Is an integer that specifies the minimum number of characters in the result.

precision

Is the number of digits to the right of the decimal point for a floating-point type. .

type

Is as shown in the following table.

Placeholder string Type
%b bool
%s string
%c char
%d, %i One of the basic integer types:
byte, sbyte, int16, uint16, int32, uint32, int64, uint64, nativeint, or unativeint
%u Basic integer type formatted as an unsigned integer
%x Basic integer type formatted as an unsigned hexadecimal integer with lowercase letters a through f.
%X Basic integer type formatted as an unsigned hexadecimal integer with uppercase letters A through F.
%o Basic integer type formatted as an unsigned octal integer.
%e, %E, %f, %F, %g, %G float or float32
%M System.Decimal
%O System.Object
%A Fresh variable type 'T
%a Formatter of type 'State -> 'T -> 'Residue for a fresh variable type 'T
%t Formatter of type 'State -> 'Residue

For example, the format string "%s %d %s" is given the type PrintfFormat<(string -> int -> string -> 'd), 'b, 'c, 'd,(string * int * string)> for fresh variable types 'b, 'c, 'd. Applying printf to it yields a function of type string -> int -> string -> unit.

## Application Expressions

### Basic Application Expressions

Application expressions involve variable names, dot-notation lookups, function applications, method applications, type applications, and item lookups, as shown in the following table.

Expression Description
long-ident-or-op Long-ident lookup expression
expr '.' long-ident-or-op Dot lookup expression
expr expr Function or member application expression
expr(expr) High precedence function or member application expression
expr**<types>** Type application expression
expr**<** > Type application expression with an empty type list
type expr Simple object expression

The following are examples of application expressions:

System.Math.PI

System.Math.PI.ToString()

(3 + 4).ToString()

System.Environment.GetEnvironmentVariable("PATH").Length

System.Console.WriteLine("Hello World")

Application expressions may start with object construction expressions that do not include the new keyword:

System.Object()

System.Collections.Generic.List<int>(10)

System.Collections.Generic.KeyValuePair(3,"Three")

System.Object().GetType()

System.Collections.Generic.Dictionary<int,int>(10).[1]

If the long-ident-or-op starts with the special pseudo-identifier keyword global, F# resolves the identifier with respect to the global namespace—that is, ignoring all open directives (see §14.2). For example:

global.System.Math.PI

is resolved to System.Math.PI ignoring all open directives.

The checking of application expressions is described in detail as an algorithm in §14.2. To check an application expression, the expression form is repeatedly decomposed into a lead expression expr and a list of projections projs through the use of Unqualified Lookup (§14.2.1). This in turn uses procedures such as Expression-Qualified Lookup and Method Application Resolution.

As described in §14.2, checking an application expression results in an elaborated expression that contains a series of lookups and method calls. The elaborated expression may include:

• Uses of named values

• Uses of union cases

• Record constructions

• Applications of functions

• Applications of methods (including methods that access properties)

• Applications of object constructors

• Uses of fields, both static and instance

• Uses of active pattern result elements

Additional constructs may be inserted when resolving method calls into simpler primitives:

• The use of a method or value as a first-class function may result in a function expression.

For example, System.Environment.GetEnvironmentVariable elaborates to:
**(fun v -> System.Environment.GetEnvironmentVariable(v))
**for some fresh variable v.

• The use of post-hoc property setters results in the insertion of additional assignment and sequential execution expressions in the elaborated expression.

For example, new System.Windows.Forms.Form(Text="Text") elaborates to
let v = new System.Windows.Forms.Form() in v.set_Text("Text"); v
for some fresh variable v.

• The use of optional arguments results in the insertion of Some(_) and None data constructions in the elaborated expression.

For uses of active pattern results (see §10.2.4), for result i in an active pattern that has N possible results of types types, the elaborated expression form is a union case ChoiceNOfi of type FSharp.Core.Choice<types>.

### Object Construction Expressions

An expression of the following form is an object construction expression:

new ty**(e1** ... e*n***)

An object construction expression constructs a new instance of a type, usually by calling a constructor method on the type. For example:

new System.Object()

new System.Collections.Generic.List<int>()

new System.Windows.Forms.Form (Text="Hello World")

new 'T()

The initial type of the expression is first asserted to be equal to ty. The type ty must not be an array, record, union or tuple type. If ty is a named class or struct type:

• ty must not be abstract.

• If ty is a struct type, n is 0, and ty does not have a constructor method that takes zero arguments, the expression elaborates to the default “zero-bit pattern” value for ty.

• Otherwise, the type must have one or more accessible constructors. The overloading between these potential constructors is resolved and elaborated by using Method Application Resolution (see §14.4).

If ty is a delegate type the expression is a delegate implementation expression.

• If the delegate type has an Invoke method that has the following signature
Invoke(ty1,...,tyn) -> rty*A***,

then the overall expression must be in this form:

new ty**(expr)** where expr has type ty*1*** -> ... -> ty*n*** -> rty*B***

If type rty*A*** is a CLI void type, then rty*B*** is unit, otherwise it is rty*A***.

• If any of the types ty*i*** is a byref-type then an explicit function expression must be specified. That is, the overall expression must be of the form new ty**(fun pat1 ...* pat**n*** -> expr*body***).

If ty is a type variable:

• There must be no arguments (that is, n = 0).

• The type variable is constrained as follows:

ty : (new : unit -> ty**) -- CLI default constructor constraint**

• The expression elaborates to a call to FSharp.Core.LanguagePrimitives.IntrinsicFunctions.CreateInstance<ty>(), which in turn calls System.Activator.CreateInstance<ty>(), which in turn uses CLI reflection to find and call the null object constructor method for type ty. On return from this function, any exceptions are wrapped by using System.TargetInvocationException.

### Operator Expressions

Operator expressions are specified in terms of their shallow syntactic translation to other constructs. The following translations are applied in order:

infix-or-prefix-op e1 → (~infix-or-prefix-op) e1

prefix-op e1 → (prefix-op) e1

e1 infix-op e2 → (infix-op) e1 e2

Note: When an operator that may be used as either an infix or prefix operator is used in prefix position, a tilde character ~ is added to the name of the operator during the translation process.

These rules are applied after applying the rules for dynamic operators (§6.4.4).

The parenthesized operator name is then treated as an identifier and the standard rules for unqualified name resolution (§14.1) in expressions are applied. The expression may resolve to a specific definition of a user-defined or library-defined operator. For example:

let (+++) a b = (a,b)

3 +++ 4

In some cases, the operator name resolves to a standard definition of an operator from the F# library. For example, in the absence of an explicit definition of (+),

3 + 4

resolves to a use of the infix operator FSharp.Core.Operators.(+).

Some operators that are defined in the F# library receive special treatment in this specification. In particular:

• The **&**expr and **&&**expr address-of operators (§6.4.5)

• The expr && expr and expr || expr shortcut control flow operators (§6.5.4)

• The **%**expr and **%%**expr expression splice operators in quotations (§6.8.3)

• The library-defined operators, such as +, -, *, /, %, **, <<<, >>>, &&&, |||, and ^^^ (§18.2).

If the operator does not resolve to a user-defined or library-defined operator, the name resolution rules (§14.1) ensure that the operator resolves to an expression that implicitly uses a static member invocation expression (§0) that involves the types of the operands. This means that the effective behavior of an operator that is not defined in the F# library is to require a static member that has the same name as the operator, on the type of one of the operands of the operator. In the following code, the otherwise undefined operator --> resolves to the static member on the Receiver type, based on a type-directed resolution:

let r = Receiver "no message"

r <-- "Message One"

"Message Two" --> r

### Dynamic Operator Expressions

Expressions of the following forms are dynamic operator expressions:

expr*1*** ? expr*2***

expr*1*** ? expr*2*** <- expr*3***

These expressions are defined by their syntactic translation:

expr ? ident → (?) expr "ident"

expr*1*** ? (expr2) → (?) expr*1** expr**2***

expr*1*** ? ident <- expr*2*** → (?<-) expr*1 "ident" expr2*

expr*1*** ? (expr2) <- expr*3*** → (?<-) expr*1** expr**2** expr**3***

Here "ident" is a string literal that contains the text of ident.

Note: The F# core library FSharp.Core.dll does not define the (?) and (?<‑) operators. However, user code may define these operators. For example, it is common to define the operators to perform a dynamic lookup on the properties of an object by using reflection.

This syntactic translation applies regardless of the definition of the (?) and (?<-) operators. However, it does not apply to uses of the parenthesized operator names, as in the following:

(?) x y

Under default definitions, expressions of the following forms are address-of expressions, called byref-address-of expression and nativeptr-address-of expression, respectively:

**&**expr

**&&**expr

Such expressions take the address of a mutable local variable, byref-valued argument, field, array element, or static mutable global variable.

For **&**expr and **&&**expr , the initial type of the overall expression must be of the form byref<ty> and nativeptr<ty> respectively, and the expression expr is checked with initial type ty.

The overall expression is elaborated recursively by taking the address of the elaborated form of expr, written AddressOf(expr, DefinitelyMutates), defined in §6.9.4.

Use of these operators may result in unverifiable or invalid common intermediate language (CIL) code; when possible, a warning or error is generated. In general, their use is recommended only:

• To pass addresses where byref or nativeptr parameters are expected.

• To pass a byref parameter on to a subsequent function.

• When required to interoperate with native code.

Addresses that are generated by the && operator must not be passed to functions that are in tail call position. The F# compiler does not check for this.

Direct uses of byref types, nativeptr types, or values in the FSharp.NativeInterop module may result in invalid or unverifiable CIL code. In particular, byref and nativeptr types may NOT be used within named types such as tuples or function types.

When calling an existing CLI signature that uses a CLI pointer type ty*, use a value of type nativeptr<ty>.

Note: The rules in this section apply to the following prefix operators, which are defined in the F# core library for use with one argument.

FSharp.Core.LanguagePrimitives.IntrinsicOperators.(~&)

FSharp.Core.LanguagePrimitives.IntrinsicOperators.(~&&)

Other uses of these operators are not permitted.

### Lookup Expressions

Lookup expressions are specified by syntactic translation:

e*1.[eargs] →* e*1.get_Item(eargs)*

e*1.[eargs] <- e*3 e*1.set_Item(eargs,* e*3***)

In addition, for the purposes of resolving expressions of this form, array types of rank 1, 2, 3, and 4 are assumed to support a type extension that defines an Item property that has the following signatures:

type 'T[] with

member arr.Item : int -> 'T

type 'T[,] with

member arr.Item : int * int -> 'T

type 'T[,,] with

member arr.Item : int * int * int -> 'T

type 'T[,,,] with

member arr.Item : int * int * int * int -> 'T

In addition, if type checking determines that the type of e*1 ***is a named type that supports the DefaultMember attribute, then the member name identified by the DefaultMember attribute is used instead of Item.

### Slice Expressions

Slice expressions are defined by syntactic translation:

e1.[sliceArg1, ,,, sliceArgN] → e1.GetSlice( args1,…,argsN)

e1.[sliceArg1, ,,, sliceArgN] <- expr → e1.SetSlice( args1,…,argsN, expr)

where each sliceArgN is one of the following and translated to argsN (giving one or two args) as indicated

* → None, None
e1.. → Some e1, None
..e2 → None, Some e2
e1..e2 → Some e1, Some e2
idx → idx

Because this is a shallow syntactic translation, the GetSlice and SetSlice name may be resolved by any of the relevant Name Resolution (§14.1) techniques, including defining the method as a type extension for an existing type.

For example, if a matrix type has the appropriate overloads of the GetSlice method (see below), it is possible to do the following:

matrix.[1..,*] -- get rows 1.. from a matrix (returning a matrix)

matrix.[1..3,*] -- get rows 1..3 from a matrix (returning a matrix)

matrix.[*,1..3] -- get columns 1..3from a matrix (returning a matrix)

matrix.[1..3,1,.3] -- get a 3x3 sub-matrix (returning a matrix)

matrix.[3,*] -- get row 3 from a matrix as a vector

matrix.[*,3] -- get column 3 from a matrix as a vector

In addition, CIL array types of rank 1 to 4 are assumed to support a type extension that defines a method GetSlice that has the following signature:

type 'T[] with

member arr.GetSlice : ?start1:int * ?end1:int -> 'T[]

type 'T[,] with

member arr.GetSlice : ?start1:int * ?end1:int * ?start2:int * ?end2:int -> 'T[,]

member arr.GetSlice : idx1:int * ?start2:int * ?end2:int -> 'T[]

member arr.GetSlice : ?start1:int * ?end1:int * idx2:int -> 'T[]

type 'T[,,] with

member arr.GetSlice : ?start1:int * ?end1:int * ?start2:int * ?end2:int *

?start3:int * ?end3:int

-> 'T[,,]

type 'T[,,,] with

member arr.GetSlice : ?start1:int * ?end1:int * ?start2:int * ?end2:int *

?start3:int * ?end3:int * ?start4:int * ?end4:int

-> 'T[,,,]

In addition, CIL array types of rank 1 to 4 are assumed to support a type extension that defines a method SetSlice that has the following signature:

type 'T[] with

member arr.SetSlice : ?start1:int * ?end1:int * values:T[] -> unit

type 'T[,] with

member arr.SetSlice : ?start1:int * ?end1:int * ?start2:int * ?end2:int *
values:T[,] -> unit

member arr.SetSlice : idx1:int * ?start2:int * ?end2:int * values:T[] -> unit

member arr.SetSlice : ?start1:int * ?end1:int * idx2:int * values:T[] -> unit

type 'T[,,] with

member arr.SetSlice : ?start1:int * ?end1:int * ?start2:int * ?end2:int *

?start3:int * ?end3:int * values:T[,,] -> unit

type 'T[,,,] with

member arr.SetSlice : ?start1:int * ?end1:int * ?start2:int * ?end2:int *

?start3:int * ?end3:int * ?start4:int * ?end4:int *
values:T[,,,] -> unit

### Member Constraint Invocation Expressions

An expression of the following form is a member constraint invocation expression:

(static-typars : (member-sig) expr)

Type checking proceeds as follows:

1. The expression is checked with initial type ty.

2. A statically resolved member constraint is applied (§5.2.3):
static-typars : (member-sig)

3. ty is asserted to be equal to the return type of the constraint.

4. expr is checked with an initial type that corresponds to the argument types of the constraint.

The elaborated form of the expression is a member invocation. For example:

let inline speak (a: ^a) =

let x = (^a : (member Speak: unit -> string) (a))

printfn "It said: %s" x

let y = (^a : (member MakeNoise: unit -> string) (a))

printfn "Then it went: %s" y

type Duck() =

member x.Speak() = "I'm a duck"

member x.MakeNoise() = "quack"

type Dog() =

member x.Speak() = "I'm a dog"

member x.MakeNoise() = "grrrr"

let x = new Duck()

let y = new Dog()

speak x

speak y

Outputs:

It said: I'm a duck

Then it went: quack

It said: I'm a dog

Then it went: grrrr

### Assignment Expressions

An expression of the following form is an assignment expression:

expr1 <- expr2

A modified version of Unqualified Lookup (§14.2.1) is applied to the expression expr1 using a fresh expected result type ty, thus producing an elaborate expression expr1. The last qualification for expr1 must resolve to one of the following constructs:

• An invocation of a property with a setter method. The property may be an indexer.

Type checking incorporates expr*2*** as the last argument in the method application resolution for the setter method. The overall elaborated expression is a method call to this setter property and includes the last argument.

• A mutable value path of type ty.

Type checking of expr*2*** uses the expected result type ty and generates an elaborated expression expr2. The overall elaborated expression is an assignment to a value reference &path <-stobj expr**2**.

• A reference to a value path of type byref<ty>.

Type checking of expr*2*** uses the expected result type ty and generates an elaborated expression expr2. The overall elaborated expression is an assignment to a value reference path <-stobj expr**2**.

• A reference to a mutable field expr**1a**.field with the actual result type ty.

Type checking of expr*2*** uses the expected result type ty and generatesan elaborated expression expr2. The overall elaborated expression is an assignment to a field (see §6.9.4):

• A array lookup expr**1a.[expr1b]** where expr**1a** has type ty**[]**.

Type checking of expr*2*** uses the expected result type ty and generates thean elaborated expression expr2. The overall elaborated expression is an assignment to a field (see §6.9.4):

Note: Because assignments have the preceding interpretations, local values must be mutable so that primitive field assignments and array lookups can mutate their immediate contents. In this context, “immediate” contents means the contents of a mutable value type. For example, given

**[<Struct>]
type SA =
new(v) = { x = v }
val mutable x : int

[<Struct>]
type SB =
new(v) = { sa = v }
val mutable sa : SA

let s1 = SA(0)
let mutable s2 = SA(0)
let s3 = SB(0)
let mutable s4 = SB(0)**

Then these are not permitted:

s1.x <- 3
s3.sa.x <- 3

and these are:

s2.x <- 3
s4.sa.x <- 3
s4.sa <- SA(2)

## Control Flow Expressions

### Parenthesized and Block Expressions

A parenthesized expression has the following form:

(expr)

A block expression has the following form:

begin expr end

The expression expr is checked with the same initial type as the overall expression.

The elaborated form of the expression is simply the elaborated form of expr.

### Sequential Execution Expressions

A sequential execution expression has the following form:

expr1; expr2

For example:

printfn "Hello"; printfn "World"; 3

The ; token is optional when both of the following are true:

• The expression expr2 occurs on a subsequent line that starts in the same column as expr1.

• The current pre-parse context that results from the syntax analysis of the program text is a SeqBlock (§15).

When the semicolon is optional, parsing inserts a $sep token automatically and applies an additional syntax rule for lightweight syntax (§15.1.1). In practice, this means that code can omit the ; token for sequential execution expressions that implement functions or immediately follow tokens such as begin and (. The expression expr1 is checked with an arbitrary initial type ty. After checking expr1, ty is asserted to be equal to unit. If the assertion fails, a warning rather than an error is reported. The expression expr2 is then checked with the same initial type as the overall expression. Sequential execution expressions are a primitive elaborated form. ### Conditional Expressions A conditional expression has the following form:s if expr1a then expr1b elif expr3a then expr2b elif exprna then exprnb else exprlast The elif and else branches may be omitted. For example: if (1 + 1 = 2) then "ok" else "not ok" if (1 + 1 = 2) then printfn "ok" Conditional expressions are equivalent to pattern matching on Boolean values. For example, the following expression forms are equivalent: if expr1 then expr2 else expr3 match (expr1:bool) with true -> expr2 | false -> expr3 If the else branch is omitted, the expression is a sequential conditional expression and is equivalent to: match (expr1:bool) with true -> expr2 | false -> () with the exception that the initial type of the overall expression is first asserted to be unit. ### Shortcut Operator Expressions Under default definitions, expressions of the following form are respectively an shortcut and expression and a shortcut or expression: expr && expr expr || expr These expressions are defined by their syntactic translation: expr*1*** && expr*2*** → if expr*1*** then expr*2 ***else false expr*1*** || expr*2*** → if expr*1*** then true else expr*2 *** Note: The rules in this section apply when the following operators, as defined in the F# core library, are applied to two arguments. FSharp.Core.LanguagePrimitives.IntrinsicOperators.(&&) FSharp.Core.LanguagePrimitives.IntrinsicOperators.(||) If the operator is not immediately applied to two arguments, it is interpreted as a strict function that evaluates both its arguments before use. ### Pattern-Matching Expressions and Functions A pattern-matching expressionhas the following form: match expr with rules Pattern matching is used to evaluate the given expression and select a rule (§7). For example: match (3, 2) with | 1, j -> printfn "j = %d" j | i, 2 -> printfn "i = %d" i | _ -> printfn "no match" A pattern-matching function is an expression of the following form: function rules A pattern-matching function is syntactic sugar for a single-argument function expression that is followed by immediate matches on the argument. For example: function | 1, j -> printfn "j = %d" j | _ -> printfn "no match" is syntactic sugar for the following, where x is a fresh variable: fun x -> match x with | 1, j -> printfn "j = %d" j | _ -> printfn "no match" ### Sequence Iteration Expressions An expression of the following form is a sequence iteration expression: for pat in expr1 do expr2 done The done token is optional if expr2 appears on a later line and is indented from the column position of the for token. In this case, parsing inserts a$done token automatically and applies an additional syntax rule for lightweight syntax (§15.1.1).

For example:

for x, y in [(1, 2); (3, 4)] do

printfn "x = %d, y = %d" x y

The expression expr1 is checked with a fresh initial type tyexpr, which is then asserted to be a subtype of type IEnumerable<ty>, for a fresh type ty. If the assertion succeeds, the expression elaborates to the following, where v is of type IEnumerator<ty> and pat is a pattern of type ty:

let v = expr1.GetEnumerator()

try

while (v.MoveNext()) do

match v**.Current with**

| pat -> expr2

| _ -> ()

finally

match box(v) with

| :? System.IDisposable as d -> d**.Dispose()**

| _ -> ()

If the assertion fails, the type tyexpr may also be of any static type that satisfies the “collection pattern” of CLI libraries. If so, the enumerable extraction process is used to enumerate the type. In particular, tyexpr may be any type that has an accessible GetEnumerator method that accepts zero arguments and returns a value that has accessible MoveNext and Current properties. The type of pat is the same as the return type of the Current property on the enumerator value. However, if the Current property has return type obj and the collection type ty has an Item property with a more specific (non-object) return type ty*2, type ty2* is used instead, and a dynamic cast is inserted to convert v.Current to ty*2***.

A sequence iteration of the form

for var in expr1 .. expr2 do expr3 done

where the type of expr1 or expr2 is equivalent to int, is elaborated as a simple for-loop expression (§6.5.7)

### Simple for-Loop Expressions

An expression of the following form is a simple for loop expression:

for var = expr1 to expr2 do expr3 done

The done token is optional when e2 appears on a later line and is indented from the column position of the for token. In this case, a $done token is automatically inserted, and an additional syntax rule for lightweight syntax applies (§15.1.1). For example: for x = 1 to 30 do printfn "x = %d, x^2 = %d" x (x*x) The bounds expr1 and expr2 are checked with initial type int. The overall type of the expression is unit. A warning is reported if the body expr3 of the for loop does not have static type unit. The following shows the elaborated form of a simple for-loop expression for fresh variables start and finish: let start = expr1 in let finish = expr2 in for var = start to finish do expr3 done For-loops over ranges that are specified by variables are a primitive elaborated form. When executed, the iterated range includes both the starting and ending values in the range, with an increment of 1. An expression of the form for var in expr1 .. expr2 do expr3 done is always elaborated as a simple for-loop expression whenever the type of expr1 or expr2 is equivalent to int. ### While Expressions A while loop expression has the following form: while expr1 do expr2 done The done token is optional when expr2 appears on a subsequent line and is indented from the column position of the while. In this case, a$done token is automatically inserted, and an additional syntax rule for lightweight syntax applies (§15.1.1).

For example:

while System.DateTime.Today.DayOfWeek = System.DayOfWeek.Monday do

printfn "I don't like Mondays"

The overall type of the expression is unit. The expression expr1 is checked with initial type bool. A warning is reported if the body expr2 of the while loop cannot be asserted to have type unit.

### Try-with Expressions

A try-with expression has the following form:

try expr with rules

For example:

try "1" with _ -> "2"

try

failwith "fail"

with

| Failure msg -> "caught"

| :? System.InvalidOperationException -> "unexpected"

Expression expr is checked with the same initial type as the overall expression. The pattern matching clauses are then checked with the same initial type and with input type System.Exception.

Try-with expressions are a primitive elaborated form.

### Reraise Expressions

A reraise expression is an application of the reraise F# library function. This function must be applied to an argument and can be used only on the immediate right-hand side of rules in a try-with expression.

try

failwith "fail"

with e -> printfn "Failing"; reraise()

Note: The rules in this section apply to any use of the function FSharp.Core.Operators.reraise, which is defined in the F# core library.

When executed, reraise() continues exception processing with the original exception information.

### Try-finally Expressions

A try-finally expression has the following form:

try expr1 finally expr2

For example:

try "1" finally printfn "Finally!"

try

failwith "fail"

finally

printfn "Finally block"

Expression expr1 is checked with the initial type of the overall expression. Expression expr2 is checked with arbitrary initial type, and a warning occurs if this type cannot then be asserted to be equal to unit.

Try-finally expressions are a primitive elaborated form.

### Assertion Expressions

An assertion expression has the following form:

assert expr

The expression assert expr is syntactic sugar for System.Diagnostics.Debug.Assert(expr)

Note: System.Diagnostics.Debug.Assert is a conditional method call. This means that assertions are triggered only if the DEBUG conditional compilation symbol is defined.

## Definition Expressions

A definition expression has one of the following forms:

let function-defn in expr

let value-defn in expr

let rec function-or-value-defns in expr

use ident = expr*1*** in expr

Such an expression establishes a local function or value definition within the lexical scope of expr and has the same overall type as expr.

In each case, the in token is optional if expr appears on a subsequent line and is aligned with the token let. In this case, a in token is automatically inserted, and an additional syntax rule for lightweight syntax applies (§15.1.1) For example: let x = 1 x + x and let x, y = ("One", 1) x.Length + y and let id x = x in (id 3, id "Three") and let swap (x, y) = (y,x) List.map swap [ (1, 2); (3, 4) ] and let K x y = x in List.map (K 3) [ 1; 2; 3; 4 ] Function and value definitions in expressions are similar to function and value definitions in class definitions (§8.6.1.3), modules (§10.2.1), and computation expressions (§6.3.10), with the following exceptions: • Function and value definitions in expressions may not define explicit generic parameters (§5.3). For example, the following expression is rejected: let f<'T> (x:'T) = x in f 3 • Function and value definitions in expressions are not public and are not subject to arity analysis (§14.10). • Any custom attributes that are specified on the declaration, parameters, and/or return arguments are ignored and result in a warning. As a result, function and value definitions in expressions may not have the ThreadStatic or ContextStatic attribute. ### Value Definition Expressions A value definition expression has the following form: let value-defn in expr where value-defn has the form: mutableopt access*opt*** pat typar-defns*opt*** return-type*opt*** = rhs-expr Checking proceeds as follows: 1. Check the value-defn (§14.6), which defines a group of identifiers ident*j*** with inferred types ty*j*** 2. Add the identifiers ident*j*** to the name resolution environment, each with corresponding type ty*j***. 3. Check the body expr against the initial type of the overall expression. In this case, the following rules apply: • If pat is a single value pattern ident, the resulting elaborated form of the entire expression is let ident1 <typars1> = expr1 in body-expr where ident*1, typars1* and expr*1*** are defined in §14.6. • Otherwise, the resulting elaborated form of the entire expression is let tmp <typars1… typarsn> = expr in let ident1 <typars1> = expr1 in let identn <typarsn> = exprn in body-expr where tmp is a fresh identifier and ident*i, typarsi, and expri*** all result from the compilation of the pattern pat (§7) against the input tmp. Value definitions in expressions may be marked as mutable. For example: let mutable v = 0 while v < 10 do v <- v + 1 printfn "v = %d" v Such variables are implicitly dereferenced each time they are used. ### Function Definition Expressions A function definition expression has the form: let function-defn in expr where function-defn has the form: inline*opt* access*opt*** ident-or-op typar-defns*opt*** pat*1*** ... pat*n*** return-type*opt*** = rhs-expr Checking proceeds as follows: 1. Check the function-defn (§14.6), which defines ident*1, ty1, typars1*** and expr*1*** 2. Add the identifier ident*1*** to the name resolution environment, each with corresponding type ty*1***. 3. Check the body expr against the initial type of the overall expression. The resulting elaborated form of the entire expression is let ident1 <typars1> = expr1 in expr where ident*1, typars1* and expr*1*** are as defined in §14.6. ### Recursive Definition Expressions An expression of the following form is a recursive definition expression: let rec function-or-value-defns in expr The defined functions and values are available for use within their own definitions—that is can be used within any of the expressions on the right-hand side of function-or-value-defns. Multiple functions or values may be defined by using let rec … and …. For example: let test() = let rec twoForward count = printfn "at %d, taking two steps forward" count if count = 1000 then "got there!" else oneBack (count + 2) and oneBack count = printfn "at %d, taking one step back " count twoForward (count - 1) twoForward 1 test() In the example, the expression defines a set of recursive functions. If one or more recursive values are defined, the recursive expressions are analyzed for safety (§14.6.6). This may result in warnings (including some reported as compile-time errors) and runtime checks. ### Deterministic Disposal Expressions A deterministic disposal expression has the form: use ident = expr*1*** in expr*2*** For example: use inStream = System.IO.File.OpenText "input.txt" let line1 = inStream.ReadLine() let line2 = inStream.ReadLine() (line1,line2) The expression is first checked as an expression of form let ident = expr*1*** in expr*2*** (§Error! Reference source not found.), which results in an elaborated expression of the following form: let ident1 : ty1 = expr1 in expr2. Only one value may be defined by a deterministic disposal expression, and the definition is not generalized (§14.6.7). The type ty1, is then asserted to be a subtype of System.IDisposable. If the dynamic value of the expression after coercion to type obj is non-null, the Dispose method is called on the value when the value goes out of scope. Thus the overall expression elaborates to this: let ident1 : ty1 = expr1 try expr2 finally (match (ident :> obj) with | null -> () | _ -> (ident :> System.IDisposable).Dispose()) ## Type-Related Expressions ### Type-Annotated Expressions A type-annotated expression has the following form, where ty indicates the static type of expr: expr : ty For example: (1 : int) let f x = (x : string) + x When checked, the initial type of the overall expression is asserted to be equal to ty. Expression expr is then checked with initial type ty. The expression elaborates to the elaborated form of expr. This ensures that information from the annotation is used during the analysis of expr itself. ### Static Coercion Expressions A static coercion expression—also called a flexible type constraint—has the following form: expr :> ty The expression upcast expr is equivalent to expr :> _, so the target type is the same as the initial type of the overall expression. For example: (1 :> obj) ("Hello" :> obj) ([1;2;3] :> seq<int>).GetEnumerator() (upcast 1 : obj) The initial type of the overall expression is ty. Expression expr is checked using a fresh initial type ty*e, with constraint tye* :> ty. Static coercions are a primitive elaborated form. ### Dynamic Type-Test Expressions A dynamic type-test expression has the following form: expr :? ty For example: ((1 :> obj) :? int) ((1 :> obj) :? string) The initial type of the overall expression is bool. Expression expr is checked using a fresh initial type ty*e***. After checking: • The type ty*e*** must not be a variable type. • A warning is given if the type test will always be true and therefore is unnecessary. • The type ty*e*** must not be sealed. • If type ty is sealed, or if ty is a variable type, or if type ty*e*** is not an interface type, then ty :> ty*e*** is asserted. Dynamic type tests are a primitive elaborated form. ### Dynamic Coercion Expressions A dynamic coercion expression has the following form: expr :?> ty The expression downcast e1 is equivalent to expr :?> _, so the target type is the same as the initial type of the overall expression. For example: let obj1 = (1 :> obj) (obj1 :?> int) (obj1 :?> string) (downcast obj1 : int) The initial type of the overall expression is ty. Expression expr is checked using a fresh initial type ty*e***. After these checks: • The type ty*e*** must not be a variable type. • A warning is given if the type test will always be true and therefore is unnecessary. • The type ty*e*** must not be sealed. • If type ty is sealed, or if ty is a variable type, or if type ty*e*** is not an interface type, then ty :> ty*e*** is asserted. Dynamic coercions are a primitive elaborated form. ## Quoted Expressions An expression in one of these forms is a quoted expression: <@ expr @> <@@ expr @@> The former is a strongly typed quoted expression, and the latter is a weakly typed quoted expression. In both cases, the expression forms capture the enclosed expression in the form of a typed abstract syntax tree. The exact nodes that appear in the expression tree are determined by the elaborated form of expr that type checking produces. For details about the nodes that may be encountered, see the documentation for the FSharp.Quotations.Expr type in the F# core library. In particular, quotations may contain: • References to module-bound functions and values, and to type-bound members. For example: let id x = x let f (x : int) = <@ id 1 @> In this case the value appears in the expression tree as a node of kind FSharp.Quotations.Expr.Call. • A type, module, function, value, or member that is annotated with the ReflectedDefinition attribute. If so, the expression tree that forms its definition may be retrieved dynamically using the FSharp.Quotations.Expr.TryGetReflectedDefinition. If the ReflectedDefinition attribute is applied to a type or module, it will be recursively applied to all members, too. • References to defined values, such as the following: let f (x : int) = <@ x + 1 @> Such a value appears in the expression tree as a node of kind FSharp.Quotations.Expr.Value. • References to generic type parameters or uses of constructs whose type involves a generic parameter, such as the following: let f (x:'T) = <@ (x, x) : 'T * 'T @> In this case, the actual value of the type parameter is implicitly substituted throughout the type annotations and types in the generated expression tree. As of F# 3.1, the following limitations apply to quoted expressions: • Quotations may not use object expressions. • Quotations may not define expression-bound functions that are themselves inferred to be generic. Instead, expression-bound functions should either include type annotations to refer to a specific type or should be written by using module-bound functions or class-bound members. ### Strongly Typed Quoted Expressions A strongly typed quoted expression has the following form: <@ expr @> For example: <@ 1 + 1 @> <@ (fun x -> x + 1) @> In the first example, the type of the expression is FSharp.Quotations.Expr<int>. In the second example, the type of the expression is FSharp.Quotations.Expr<int -> int>. When checked, the initial type of a strongly typed quoted expression <@ expr @> is asserted to be of the form FSharp.Quotations.Expr<ty> for a fresh type ty. The expression expr is checked with initial type ty. ### Weakly Typed Quoted Expressions A weakly typed quoted expression has the following form: <@@ expr @@> Weakly typed quoted expressions are similar to strongly quoted expressions but omit any type annotation. For example: <@@ 1 + 1 @@> <@@ (fun x -> x + 1) @@> In both these examples, the type of the expression is FSharp.Quotations.Expr. When checked, the initial type of a weakly typed quoted expression <@@ expr @@> is asserted to be of the form FSharp.Quotations.Expr. The expression expr is checked with fresh initial type ty. ### Expression Splices Both strongly typed and weakly typed quotations may contain expression splices in the following forms: %expr %%expr These are respectively strongly typed and weakly typed splicing operators. #### Strongly Typed Expression Splices An expression of the following form is a strongly typed expression splice: **%**expr For example, given open FSharp.Quotations let f1 (v:Expr<int>) = <@ %v + 1 @> let expr = f1 <@ 3 @> the identifier expr evaluates to the same expression tree as **<@ 3 • 1 @>**. The expression tree for <@ 3 @> replaces the splice in the corresponding expression tree node. A strongly typed expression splice may appear only in a quotation. Assuming that the splice expression **%**expr is checked with initial type ty, the expression expr is checked with initial type FSharp.Quotations.Expr<ty>. Note: The rules in this section apply to any use of the prefix operator FSharp.Core.ExtraTopLevelOperators.(~%). Uses of this operator must be applied to an argument and may only appear in quoted expressions. #### Weakly Typed Expression Splices An expression of the following form is a weakly typed expression splice: **%%**expr For example, given open FSharp.Quotations let f1 (v:Expr) = <@ %%v + 1 @> let tree = f1 <@@ 3 @@> the identifier tree evaluates to the same expression tree as **<@ 3 • 1 @>**. The expression tree replaces the splice in the corresponding expression tree node. A weakly typed expression splice may appear only in a quotation. Assuming that the splice expression **%%**expr is checked with initial type ty, then the expression expr is checked with initial type FSharp.Quotations.Expr. No additional constraint is placed on ty. Additional type annotations are often required for successful use of this operator. Note: The rules in this section apply to any use of the prefix operator FSharp.Core.ExtraTopLevelOperators.(~%%), which is defined in the F# core library. Uses of this operator must be applied to an argument and may only occur in quoted expressions. ## Evaluation of Elaborated Forms At runtime, execution evaluates expressions to values. The evaluation semantics of each expression form are specified in the subsections that follow. ### Values and Execution Context The execution of elaborated F# expressions results in values. Values include: • Primitive constant values • The special value null • References to object values in the global heap of object values • Values for value types, containing a value for each field in the value type • Pointers to mutable locations (including static mutable locations, mutable fields and array elements) Evaluation assumes the following evaluation context: • A global heap of object values. Each object value contains: • A runtime type and dispatch map • A set of fields with associated values • For array objects, an array of values in index order • For function objects, an expression which is the body of the function • An optional union case label, which is an identifier • A closure environment that assigns values to all variables that are referenced in the method bodies that are associated with the object • A global environment that maps runtime-type/name pairs to values.Each name identifies a static field in a type definition or a value in a module. • A local environment mapping names of variables to values. • A local stack of active exception handlers, made up of a stack of try/with and try/finally handlers. Evaluation may also raise an exception. In this case, the stack of active exception handlers is processed until the exception is handled, in which case additional expressions may be executed (for try/finally handlers), or an alternative expression may be evaluated (for try/with handlers), as described below. ### Parallel Execution and Memory Model In a concurrent environment, evaluation may involve both multiple active computations (multiple concurrent and parallel threads of execution) and multiple pending computations (pending callbacks, such as those activated in response to an I/O event). If multiple active computations concurrently access mutable locations in the global environment or heap, the atomicity, read, and write guarantees of the underlying CLI implementation apply. The guarantees are related to the logical sizes and characteristics of values, which in turn depend on their type: • F# reference types are guaranteed to map to CLI reference types. In the CLI memory model, reference types have atomic reads and writes. • F# value types map to a corresponding CLI value type that has corresponding fields. Reads and writes of sizes less than or equal to one machine word are atomic. The VolatileField attribute marks a mutable location as volatile in the compiled form of the code. Ordering of reads and writes from mutable locations may be adjusted according to the limitations specified by the CLI memory model. The following example shows situations in which changes to read and write order can occur, with annotations about the order of reads: type ClassContainingMutableData() = let value = (1, 2) let mutable mutableValue = (1, 2) [<VolatileField>] let mutable volatileMutableValue = (1, 2) member x.ReadValues() = // Two reads on an immutable value let (a1, b1) = value // One read on mutableValue, which may be duplicated according // to ECMA CLI spec. let (a2, b2) = mutableValue // One read on volatileMutableValue, which may not be duplicated. let (a3, b3) = volatileMutableValue a1, b1, a2, b2, a3, b3 member x.WriteValues() = // One read on mutableValue, which may be duplicated according // to ECMA CLI spec. let (a2, b2) = mutableValue // One write on mutableValue. mutableValue <- (a2 + 1, b2 + 1) // One read on volatileMutableValue, which may not be duplicated. let (a3, b3) = volatileMutableValue // One write on volatileMutableValue. volatileMutableValue <- (a3 + 1, b3 + 1) let obj = ClassContainingMutableData() Async.Parallel [ async { return obj.WriteValues() }; async { return obj.WriteValues() }; async { return obj.ReadValues() }; async { return obj.ReadValues() } ] ### Zero Values Some types have a zero value. The zero value is the“default” value for the type in the CLI execution environment. The following types have the following zero values: • For reference types, the null value. • For value types, the value with all fields set to the zero value for the type of the field. The zero value is also computed by the F# library function Unchecked.defaultof<ty>. ### Taking the Address of an Elaborated Expression When the F# compiler determines the elaborated forms of certain expressions, it must compute a “reference” to an elaborated expression expr, written AddressOf(expr, mutation). The AddressOf operation is used internally within this specification to indicate the elaborated forms of address-of expressions, assignment expressions, and method and property calls on objects of variable and value types. The AddressOf operation is computed as follows: • If expr has form path where path is a reference to a value with type byref<ty>, the elaborated form is &path. • If expr has form expra.field where field is a mutable, non-readonly CLI field, the elaborated form is &(AddressOf(expra).field)**. • If expr has form expra.[exprb] where the operation is an array lookup, the elaborated form is &(AddressOf(expra).[exprb])**. • If expr has any other form, the elaborated form is **&**v,where v is a fresh mutable local value that is initialized by adding let v = expr to the overall elaborated form for the entire assignment expression. This initialization is known as a defensive copy of an immutable value. If expr is a struct, expr is copied each time the AddressOf operation is applied, which results in a different address each time. To keep the struct in place, the field that contains it should be marked as mutable. The AddressOf operation is computed with respect to mutation, which indicates whether the relevant elaborated form uses the resulting pointer to change the contents of memory. This assumption changes the errors and warnings reported. • If mutation is DefinitelyMutates, then an error is given if a defensive copy must be created. • If mutation is PossiblyMutates, then a warning is given if a defensive copy arises. An F# compiler can optionally upgrade PossiblyMutates to DefinitelyMutates for calls to property setters and methods named MoveNext and GetNextArg, which are the most common cases of struct-mutators in CLI library design. This is done by the F# compiler. Note:In F#, the warning “copy due to possible mutation of value type” is a level 4 warning and is not reported when using the default settings of the F# compiler. This is because the majority of value types in CLI libraries are immutable. This is warning number 52 in the F# implementation. CLI libraries do not include metadata to indicate whether a particular value type is immutable. Unless a value is held in arrays or locations marked mutable, or a value type is known to be immutable to the F# compiler, F# inserts copies to ensure that inadvertent mutation does not occur. ### Evaluating Value References At runtime, an elaborated value reference v is evaluated by looking up the value of v in the local environment. ### Evaluating Function Applications At runtime, an elaborated application of a function f e1 ... en is evaluated as follows: • The expressions f and e1 ... en, are evaluated. • If f evaluates to a function value with closure environment E, arguments v1 ... vm, and body expr, where m <= n, then E is extended by mapping v1 ... vm to the argument values for e1 ... em. The expression expr is then evaluated in this extended environment and any remaining arguments applied. • If f evaluates to a function value with more than n arguments, then a new function value is returned with an extended closure mapping n additional formal argument names to the argument values for e1 ... em. The result of calling the obj.GetType() method on the resulting object is under-specified (see §6.9.24). ### Evaluating Method Applications At runtime an elaborated application of a method is evaluated as follows: • The elaborated form is e0.M(e1,…,en) for an instance method or M(e1,…,en) for a static method. • The (optional) e0 and e1,…,en are evaluated in order. • If e0 evaluates to null, a NullReferenceException is raised. • If the method is declared abstract—that is, if it is a virtual dispatch slot—then the body of the member is chosen according to the dispatch maps of the value of e0 (§14.8). • The formal parameters of the method are mapped to corresponding argument values. The body of the method member is evaluated in the resulting environment . ### Evaluating Union Cases At runtime, an elaborated use of a union case Case**(e***1,…,en)* for a union type ty is evaluated as follows: • The expressions e1,…,en are evaluated in order. • The result of evaluation is an object value with union case label Case and fields given by the values of e1,…,en. • If the type ty uses null as a representation (§5.4.8) and Case is the single union case without arguments, the generated value is null. • The runtime type of the object is either ty or an internally generated type that is compatible with ty. ### Evaluating Field Lookups At runtime, an elaborated lookup of a CLI or F# fields is evaluated as follows: • The elaborated form is expr**.**F for an instance field or F for a static field. • The(optional) expr is evaluated. • If expr evaluates to null, a NullReferenceException is raised. • The value of the field is read from either the global field table or the local field table associated with the object. ### Evaluating Array Expressions At runtime, an elaborated array expression [| e1; … ; en |]ty is evaluated as follows: • Each expression e1 … en is evaluated in order. • The result of evaluation is a new array of runtime type ty[] that contains the resulting values in order. ### Evaluating Record Expressions At runtime, an elaborated record construction { field1 = e1; … ; fieldn = en }ty is evaluated as follows: • Each expression e1 … en is evaluated in order. • The result of evaluation is an object of type ty with the given field values ### Evaluating Function Expressions At runtime, an elaborated function expression (fun v1 vn -> expr**)** is evaluated as follows: • The expression evaluates to a function object with a closure that assigns values to all variables that are referenced in expr and a function body that is expr. • The values in the closure are the current values of those variables in the execution environment. • The result of calling the obj.GetType() method on the resulting object is under-specified (see §6.9.24). ### Evaluating Object Expressions At runtime, elaborated object expressions { new ty0 args-expropt object-members interface ty1 object-members1 interface tyn object-membersn } is evaluated as follows: • The expression evaluates to an object whose runtime type is compatible with all of the ty*i*** and which has the corresponding dispatch map (§14.8). If present, the base construction expression ty0 (args-expr) is executed as the first step in the construction of the object. • The object is given a closure that assigns values to all variables that are referenced in expr. • The values in the closure are the current values of those variables in the execution environment. The result of calling the obj.GetType() method on the resulting object is under-specified (see §6.9.24). ### Evaluating Definition Expressions At runtime, each elaborated definition pat = expr is evaluated as follows: • The expression expr is evaluated. • The expression is then matched against pat to produce a value for each variable pattern (§7.2) in pat. • These mappings are added to the local environment. ### Evaluating Integer For Loops At runtime, an integer for loop **for var = expr1 to expr2 do expr3 done is evaluated as follows: • Expressions expr1 and expr2 are evaluated once to values v1 and v2. • The expression expr3 is evaluated repeatedly with the variable var assigned successive values in the range of v1 up to v2. • If v1 is greater than v2, then expr3 is never evaluated. ### Evaluating While Loops As runtime, while-loops while expr1 do expr2 done are evaluated as follows: • Expression **expr1 is evaluated to a value v1. • If v*1*** is true, expression expr2 is evaluated, and the expression while expr1 do expr2 done is evaluated again. • If v*1*** is false, the loop terminates and the resulting value is null (the representation of the only value of type unit) ### Evaluating Static Coercion Expressions At runtime, elaborated static coercion expressions of the form expr :> ty are evaluated as follows: • Expression expr is evaluated to a value v. • If the static type of e is a value type, and ty is a reference type, v is boxed; that is, v is converted to an object on the heap with the same field assignments as the original value. The expression evaluates to a reference to this object. • Otherwise, the expression evaluates to v. ### Evaluating Dynamic Type-Test Expressions At runtime, elaborated dynamic type test expressions expr :? ty are evaluated as follows: 1. Expression expr is evaluated to a value v. 2. If v is null, then: • If ty*e ***uses null as a representation (§5.4.8), the result is true. • Otherwise the expression evaluates to false. 3. If v is not null and has runtime type vty which dynamically converts to ty (§5.4.10), the expression evaluates to true. However, if ty is an enumeration type, the expression evaluates to true if and only if ty is precisely vty. ### Evaluating Dynamic Coercion Expressions At runtime, elaborated dynamic coercion expressions expr :?> ty are evaluated as follows: 1. Expression expr is evaluated to a value v. 2. If v is null: • If ty*e ***uses null as a representation (§5.4.8), the result is the null value. • Otherwise a NullReferenceException is raised. 3. If v is not null: • If v has dynamic type vty which dynamically converts to ty (§5.4.10), the expression evaluates to the dynamic conversion of v to ty. • If vty is a reference type and ty is a value type, then v is unboxed; that is, v is converted from an object on the heap to a struct value with the same field assignments as the object. The expression evaluates to this value. • Otherwise, the expression evaluates to v. • Otherwise an InvalidCastException is raised. Expressions of the form expr :?> ty evaluate in the same way as the F# library function unbox<ty>*(expr)*. Note: Some F# types—most notably the option<_> type—use null as a representation for efficiency reasons (§5.4.8),. For these types, boxing and unboxing can lose type distinctions. For example, contrast the following two examples: **> (box([]:string list) :?> int list);; **System.InvalidCastException… **> (box(None:string option) :?> int option);; **val it : int option = None In the first case, the conversion from an empty list of strings to an empty list of integers (after first boxing) fails. In the second case, the conversion from a string option to an integer option (after first boxing) succeeds. ### Evaluating Sequential Execution Expressions At runtime, elaborated sequential expressions expr1; expr2 are evaluated as follows: • The expression expr1 is evaluated for its side effects and the result is discarded. • The expression expr2 is evaluated to a value v2 and the result of the overall expression is v2. ### Evaluating Try-with Expressions At runtime, elaborated try-with expressions try expr*1* with rules are evaluated as follows: • The expression expr1 is evaluated to a value v1. • If no exception occurs, the result is the value v1. • If an exception occurs, the pattern rules are executed against the resulting exception value. • If no rule matches, the exception is reraised. • If a rule pat -> expr2 matches, the mapping pat = v1 is added to the local environment, and expr2 is evaluated. ### Evaluating Try-finally Expressions At runtime, elaborated try-finally expressions try expr1 finally expr2 are evaluated as follows: • The expression expr1 is evaluated. • If the result of this evaluation is a value v , then expr2 is evaluated. 1. If this evaluation results in an exception, then the overall result is that exception. 2. If this evaluation does not result in an exception, then the overall result is v. • If the result of this evaluation is an exception, then expr2 is evaluated. 1. If this evaluation results in an exception, then the overall result is that exception. 2. If this evaluation does not result in an exception, then the original exception is re-raised. ### Evaluating AddressOf Expressions At runtime, an elaborated address-of expression is evaluated as follows. First, the expression has one of the following forms: • &path where path is a static field. • &(expr.field) • &(expra.[exprb]) • **&**v where v is a local mutable value. The expression evaluates to the address of the referenced local mutable value, mutable field, or mutable static field. Note: The underlying CIL execution machinery that F# uses supports covariant arrays, as evidenced by the fact that the type string[] dynamically converts to obj[] (§5.4.10). Although this feature is rarely used in F#, its existence means that array assignments and taking the address of array elements may fail at runtime with a System.ArrayTypeMismatchException if the runtime type of the target array does not match the runtime type of the element being assigned. For example, the following code fails at runtime: let f (x: byref<obj>) = () let a = Array.zeroCreate<obj> 10 let b = Array.zeroCreate<string> 10 f (&a.[0]) let bb = ((b :> obj) :?> obj[]) // The next line raises a System.ArrayTypeMismatchException exception. F (&bb.[1]) ### Values with Underspecified Object Identity and Type Identity The CLI and F# support operations that detect object identity—that is, whether two object references refer to the same “physical” object. For example, System.Object.ReferenceEquals(obj1, obj2) returns true if the two object references refer to the same object. Similarly, System.Runtime.CompilerServices.RuntimeHelpers.GetHashCode() returns a hash code that is partly based on physical object identity, and the AddHandler and RemoveHandler operations (which register and unregister event handlers) are based on the object identity of delegate values. The results of these operations are underspecified when used with values of the following F# types: • Function types • Tuple types • Immutable record types • Union types • Boxed immutable value types For two values of such types, the results of System.Object.ReferenceEquals and System.Runtime.CompilerServices.RuntimeHelpers.GetHashCode are underspecified; however, the operations terminate and do not raise exceptions. An implementation of F# is not required to define the results of these operations for values of these types. For function values and objects that are returned by object expressions, the results of the following operations are underspecified in the same way: • Object.GetHashCode() • Object.GetType() For union types the results of the following operations are underspecified in the same way: • Object.GetType() # Patterns Patterns are used to perform simultaneous case analysis and decomposition on values together with the match, try...with, function, fun, and let expression and declaration constructs. Rules are attempted in order from top to bottom and left to right. The syntactic forms of patterns are shown in the subsequent table. rule := pat pattern-guard*opt*** -> expr -- pattern, optional guard and action pattern-guard := when expr pat := const -- constant pattern long-ident pat-param*opt*** pat*opt*** -- named pattern _ -- wildcard pattern pat as ident -- "as" pattern pat '|' pat -- disjunctive pattern pat '&' pat -- conjunctive pattern pat :: pat -- "cons" pattern pat : type -- pattern with type constraint pat**,...,**pat -- tuple pattern (pat) -- parenthesized pattern list-pat -- list pattern array-pat -- array pattern record-pat -- record pattern :? atomic-type -- dynamic type test pattern :? atomic-type as ident -- dynamic type test pattern null -- null-test pattern attributes pat -- pattern with attributes list-pat := [ ] [ pat ; ... ; pat ] array-pat := [| |] [| pat ; ... ; pat |] record-pat := { field-pat ; ... ; field-pat } atomic-pat := pat : one of const long-ident list-pat record-pat array-pat (pat) :? atomic-type null _ field-pat := long-ident = pat pat-param := | const | long-ident | [ pat-param ; ... ; pat-param ] | ( pat-param**, ...,** pat-param ) | long-ident pat-param | pat-param : type | <@ expr @> | <@@ expr @@> | null pats := pat , ... , pat field-pats := field-pat ; ... ; field-pat rules := '|'opt rule '|' ... '|' rule Patterns are elaborated to expressions through a process called pattern match compilation. This reduces pattern matching to decision trees which operate on an input value, called the pattern input. The decision tree is composed of the following constructs: • Conditionals on integers and other constants • Switches on union cases • Conditionals on runtime types • Null tests • Value definitions • An array of pattern-match targets referred to by index ## Simple Constant Patterns The pattern const is a constant pattern which matches values equal to the given constant. For example: let rotate3 x = match x with | 0 -> "two" | 1 -> "zero" | 2 -> "one" | _ -> failwith "rotate3" In this example, the constant patterns are 0, 1, and 2. Any constant listed in §6.3.1 may be used as a constant pattern except for integer literals that have the suffixes Q, R, Z, I, N, G. Simple constant patterns have the corresponding simple type. Such patterns elaborate to a call to the F# structural equality function FSharp.Core.Operators.(=) with the pattern input and the constant as arguments. The match succeeds if this call returns true; otherwise, the match fails. Note: The use of FSharp.Core.Operators.(=) means that CLI floating-point equality is used to match floating-point values, and CLI ordinal string equality is used to match strings. ## Named Patterns Patterns in the following forms are named patterns: Long-ident Long-ident pat Long-ident pat-params pat If long-ident is a single identifier that does not begin with an uppercase character, it is interpreted as a variable pattern. During checking, the variable is assigned the same value and type as the pattern input. If long-ident is more than one-character long or begins with an uppercase character (that is, if System.Char.IsUpperInvariant is true and System.Char.IsLowerInvariant is false on the first character), it is resolved by using Name Resolution in Patterns (§14.1.6). This algorithm produces one of the following: • A union case • An exception label • An active pattern case name • A literal value Otherwise, long-ident must be a single uppercase identifier ident. In this case, pat is a variable pattern. An F# implementation may optionally generate a warning if the identifier is uppercase. Such a warning is recommended if the length of the identifier is greater than two. After name resolution, the subsequent treatment of the named pattern is described in the following sections. ### Union Case Patterns If long-ident from §7.2 resolves to a union case, the pattern is a union case pattern. If long-ident resolves to a union case Case, then long-ident and long-ident pat are patterns that match pattern inputs that have union case label Case. The long-ident form is used if the corresponding case takes no arguments, and the long-ident pat form is used if it takes arguments. At runtime, if the pattern input is an object that has the corresponding union case label, the data values carried by the union are matched against the given argument patterns. For example: type Data = | Kind1 of int * int | Kind2 of string * string let data = Kind1(3, 2) let result = match data with | Kind1 (a, b) -> a + b | Kind2 (s1, s2) -> s1.Length + s2.Length In this case, result is given the value 5. When a union case has named fields, these names may be referenced in a union case pattem. When using pattern matching with multiple fields, semicolons are used to delimit the named fields. For example type Shape = | Rectangle of width: float * height: float | Square of width: float let getArea (s: Shape) = match s with | Rectangle (width = w; height = h) -> w*h | Square (width = w) -> w*w ### Literal Patterns If long-ident from §7.2 resolves to a literal value, the pattern is a literal pattern. The pattern is equivalent to the corresponding constant pattern. In the following example, the Literal attribute (§10.2.2) is first used to define two literals, and these literals are used as identifiers in the match expression: [<Literal>] let Case1 = 1 [<Literal>] let Case2 = 100 let result = match 100 with | Case1 -> "Case1" | Case2 -> "Case2" | _ -> "Some other case" In this case, result is given the value "Case2”. ### Active Patterns If long-ident from §7.2 resolves to an active pattern case name CaseName*i*** then the pattern is an active pattern. The rules for name resolution in patterns (§14.1.6) ensure that CaseName*i*** is associated with an active pattern function f in one of the following forms: • (|CaseName|) inp Single case. The function accepts one argument (the value being matched) and can return any type. • (|CaseName|_|) inp Partial. The function accepts one argument (the value being matched) and must return a value of type FSharp.Core.option<_> • (|CaseName1| ...|CaseNamen|) inp Multi-case. The function accepts one argument (the value being matched), and must return a value of type FSharp.Core.Choice<_,...,_> based on the number of case names. In F#, the limitation n ≤ 7 applies. • (|CaseName|) arg*1*** ... arg*n*** inp Single case with parameters. The function accepts n**+1** arguments, where the last argument (inp) is the value to match, and can return any type. • (|CaseName|_|) arg*1*** ... arg*n*** inp Partial with parameters. The function accepts n**+1** arguments, where the last argument (inp) is the value to match, and must return a value of type FSharp.Core.option<_>. Other active pattern functions are not permitted. In particular, multi-case, partial functions such as the following are not permitted: (|CaseName1| ... |CaseNamen|_|) When an active pattern function takes arguments, the pat-params are interpreted as expressions that are passed as arguments to the active pattern function. The pat-params are converted to the syntactically identical corresponding expression forms and are passed as arguments to the active pattern function f. At runtime, the function f is applied to the pattern input, along with any parameters. The pattern matches if the active pattern function returns v, ChoicekOfN v, or Some v, respectively, when applied to the pattern input. If the pattern argument pat is present, it is then matched against v. The following example shows how to define and use a partial active pattern function: let (|Positive|_|) inp = if inp > 0 then Some(inp) else None let (|Negative|_|) inp = if inp < 0 then Some(-inp) else None match 3 with | Positive n -> printfn "positive, n = %d" n | Negative n -> printfn "negative, n = %d" n | _ -> printfn "zero" The following example shows how to define and use a multi-case active pattern function: let (|A|B|C|) inp = if inp < 0 then A elif inp = 0 then B else C match 3 with | A -> "negative" | B -> "zero" | C -> "positive" The following example shows how to define and use a parameterized active pattern function: let (|MultipleOf|_|) n inp = if inp%n = 0 then Some (inp / n) else None match 16 with | MultipleOf 4 n -> printfn "x = 4*%d" n | _ -> printfn "not a multiple of 4" An active pattern function is executed only if a left-to-right, top-to-bottom reading of the entire pattern indicates that execution is required. For example, consider the following active patterns: let (|A|_|) x = if x = 2 then failwith "x is two" elif x = 1 then Some() else None let (|B|_|) x = if x=3 then failwith "x is three" else None let (|C|) x = failwith "got to C" let f x = match x with | 0 -> 0 | A -> 1 | B -> 2 | C -> 3 | _ -> 4 These patterns evaluate as follows: f 0 // 0 f 1 // 1 f 2 // failwith "x is two" f 3 // failwith "x is three" f 4 // failwith "got to C" An active pattern function may be executed multiple times against the same pattern input during resolution of a single overall pattern match. The precise number of times that the active pattern function is executed against a particular pattern input is implementation-dependent. ## “As” Patterns An “as” pattern is of the following form: pat as ident The “as” pattern defines ident to be equal to the pattern input and matches the pattern input against pat. For example: let t1 = (1, 2) let (x, y) as t2 = t1 printfn "%d-%d-%A" x y t2 // 1-2-(1, 2) This example binds the identifiers x, y, and t1 to the values 1, 2, and (1,2), respectively. ## Wildcard Patterns The pattern _ is a wildcard pattern and matches any input. For example: let categorize x = match x with | 1 -> 0 | 0 -> 1 | _ -> 0 In the example, if x is 0, the match returns 1. If x has any other value, the match returns 0. ## Disjunctive Patterns A disjunctive pattern matches an input value against one or the other of two patterns: pat | pat At runtime, the patterm input is matched against the first pattern. If that fails, the pattern input is matched against the second pattern. Both patterns must bind the same set of variables with the same types. For example: type Date = Date of int * int * int let isYearLimit date = match date with | (Date (year, 1, 1) | Date (year, 12, 31)) -> Some year | _ -> None let result = isYearLimit (Date (2010,12,31)) In this example, result is given the value true, because the pattern input matches the second pattern. ## Conjunctive Patterns A conjunctive pattern matches the pattern input against two patterns. pat1 & pat2 For example: let (|MultipleOf|_|) n inp = if inp%n = 0 then Some (inp / n) else None let result = match 56 with | MultipleOf 4 m & MultipleOf 7 n -> m + n | _ -> false In this example, result is given the value 22 (= 16 + 8), because the pattern input match matches both patterns. ## List Patterns The pattern pat :: pat is a union case pattern that matches the “cons” union case of F# list values. The pattern [] is a union case pattern that matches the “nil” union case of F# list values. The pattern [pat1 ; ... ; patn] is shorthand for a series of :: and empty list patterns pat1 :: … :: patn :: []. For example: let rec count x = match x with | [] -> 0 | h :: t -> h + count t let result1 = count [1;2;3] let result2 = match [1;2;3] with | [a;b;c] -> a + b + c | _ -> 0 In this example, both result1 and result2 are given the value 6. ## Type-Annotated Patterns A type-annotated pattern specifies the type of the value to match to a pattern. pat : type For example: let rec sum xs = match xs with | [] -> 0 | (h : int) :: t -> h + sum t In this example, the initial type of h is asserted to be equal to int before the pattern h is checked. Through type inference, this in turn implies that xs and t have static type int list, and sum has static type int list -> int. ## Dynamic Type-Test Patterns Dynamic type-test patterns have the following two forms: :? type :? type as ident A dynamic type-test pattern matches any value whose runtime type is type or a subtype of type. For example: let message (x : System.Exception) = match x with | :? System.OperationCanceledException -> "cancelled" | :? System.ArgumentException -> "invalid argument" | _ -> "unknown error" If the type-test pattern is of the form :? type as ident, then the value is coerced to the given type and ident is bound to the result. For example: let findLength (x : obj) = match x with | :? string as s -> s.Length | _ -> 0 In the example, the identifier s is bound to the value x with type string. If the pattern input has type ty*in, pattern checking uses the same conditions as both a dynamic type-test expression e :? type and a dynamic coercion expression e :?> type where e has type tyin. An error occurs if type cannot be statically determined to be a subtype of the type of the pattern input.* A warning occurs if the type test will always succeed based on type and the static type of the pattern input. A warning is issued if an expression contains a redundant dynamic type-test pattern, after any coercion is applied. For example: match box "3" with | :? string -> 1 | :? string -> 1 // a warning is reported that this rule is "never matched" | _ -> 2 match box "3" with | :? System.IComparable -> 1 | :? string -> 1 // a warning is reported that this rule is "never matched" | _ -> 2 At runtime, a dynamic type-test pattern succeeds if and only if the corresponding dynamic type-test expression e** :? **ty would return true where e is the pattern input. The value of the pattern is bound to the results of a dynamic coercion expression e :?> ty. ## Record Patterns The following is a record pattern: { long-ident*1*** = pat*1; ... ; long-identn* = pat*n***} For example: type Data = { Header:string; Size: int; Names: string list } let totalSize data = match data with | { Header = "TCP"; Size = size; Names = names } -> size + names.Length * 12 | { Header = "UDP"; Size = size } -> size | _ -> failwith "unknown header" The long-ident*i*** are resolved in the same way as field labels for record expressions and must together identify a single, unique F# record type. Not all record fields for the type need to be specified in the pattern. ## Array Patterns An array pattern matches an array of a partciular length: [|pat ; ... ; pat|] For example: let checkPackets data = match data with | [| "HeaderA"; data1; data2 |] -> (data1, data2) | [| "HeaderB"; data2; data1 |] -> (data1, data2) | _ -> failwith "unknown packet" ## Null Patterns The null pattern null matches values that are represented by the CLI value null. For example: let path = match System.Environment.GetEnvironmentVariable("PATH") with | null -> failwith "no path set!" | res -> res Most F# types do not use null as a representation; consequently, the null pattern is generally used to check values passed in by CLI method calls and properties. For a list of F# types that use null as a representation, see §5.4.8. ## Guarded Pattern Rules Guarded pattern rules have the following form: pat when expr For example: let categorize x = match x with | _ when x < 0 -> -1 | _ when x < 0 -> 1 | _ -> 0 The guards on a rule are executed only after the match value matches the corresponding pattern. For example, the following evaluates to 2 with no output. match (1, 2) with | (3, x) when (printfn "not printed"; true) -> 0 | (_, y) -> y # Type Definitions Type definitions define new named types. The grammar of type definitions is shown below. type-defn := abbrev-type-defn record-type-defn union-type-defn anon-type-defn class-type-defn struct-type-defn interface-type-defn enum-type-defn delegate-type-defn type-extension type-name := attributes*opt** access**opt** ident* typar-defnsopt abbrev-type-defn := type-name = type union-type-defn := type-name '=' union-type-cases type-extension-elements*opt*** union-type-cases := '|'opt union-type-case '|' ... '|' union-type-case union-type-case := attributes*opt** union-type-case-data* union-type-case-data := ident -- null union case ident of union-type-field * ... * union-type-field -- n-ary union case ident : uncurried-sig -- n-ary union case union-type-field := type -- unnamed union fiels ident **: type -- named union field ** record-type-defn := type-name = '{' record-fields '}' type-extension-elements*opt*** record-fields := record-field ; ... ; record-field ;opt record-field := attributes*opt*** mutableopt** access*opt*** ident : type anon-type-defn := type-name primary-constr-args*opt*** object-val*opt*** '=' begin class-type-body end class-type-defn := type-name primary-constr-args*opt*** object-val*opt*** '=' class class-type-body end as-defn := as ident class-type-body := class-inherits-decl*opt** class-function-or-value-defns**opt** type-defn-elements**opt*** class-inherits-decl := inherit type expr*opt*** class-function-or-value-defn := attributes*opt*** staticopt let rec*opt*** function-or-value-defns attributes*opt*** staticopt do** expr struct-type-defn := type-name primary-constr-args*opt*** as-defn*opt*** '=' struct struct-type-body end struct-type-body := type-defn-elements interface-type-defn := type-name '=' interface interface-type-body end interface-type-body := type-defn-elements exception-defn := attributes*opt*** exception union-type-case-data -- exception definition attributes*opt*** exception ident = long-ident -- exception abbreviation enum-type-defn := type-name '=' enum-type-cases enum-type-cases = '|'opt enum-type-case '|' ... '|' enum-type-case enum-type-case := ident '=' const -- enum constant definition delegate-type-defn := type-name '=' delegate-sig delegate-sig := delegate of uncurried-sig -- CLI delegate definition type-extension := type-name type-extension-elements type-extension-elements := with type-defn-elements end type-defn-element := member-defn interface-impl interface-spec type-defn-elements := type-defn-element ... type-defn-element primary-constr-args := attributes*opt*** access*opt*** **(simple-pat, ... , simple-pat) simple-pat := | ident | simple-pat : type additional-constr-defn := attributes*opt*** access*opt*** new pat as-defn = additional-constr-expr additional-constr-expr := stmt ';' additional-constr-expr -- sequence construction (after) additional-constr-expr then expr -- sequence construction (before) if expr then additional-constr-expr else additional-constr-expr let function-or-value-defn in additional-constr-expr additional-constr-init-expr additional-constr-init-expr := '{' class-inherits-decl field-initializers '}' -- explicit construction new type expr -- delegated construction member-defn := attributes*opt*** staticopt member** access*opt*** method-or-prop-defn -- concrete member attributes*opt*** abstract memberopt** access*opt*** member-sig -- abstract member attributes*opt*** override access*opt*** method-or-prop-defn -- override member attributes*opt*** default access*opt*** method-or-prop-defn -- override member attributes*opt*** staticopt val mutable*opt*** access*opt*** ident : type -- value member additional-constr-defn -- additional constructor method-or-prop-defn := ident.opt function-defn -- method definition ident.opt value-defn -- property definition ident.opt ident with function-or-value-defns -- property definition via get/set methods member ident = exp –- auto-implemented property definition member ident = exp with get –- auto-implemented property definition member ident = exp with set –- auto-implemented property definition member ident = exp with get,set –- auto-implemented property definition member ident = exp with set,get –- auto-implemented property definition member-sig := ident typar-defns*opt*** : curried-sig -- method or property signature ident typar-defns*opt*** : curried-sig with get -- property signature ident typar-defns*opt*** : curried-sig with set -- property signature ident typar-defns*opt*** : curried-sig with get,set -- property signature ident typar-defns*opt*** : curried-sig with set,get -- property signature curried-sig := args-spec -> ... -> args-spec -> type uncurried-sig := args-spec -> type args-spec := arg-spec * ... * arg-spec arg-spec := attributes*opt*** arg-name-spec*opt** type* arg-name-spec := ?opt ident : interface-spec := interface type For example: type int = System.Int32 type Color = Red | Green | Blue type Map<'T> = { entries: 'T[] } Type definitions can be declared in: • Module definitions • Namespace declaration groups F# supports the following kinds of type definitions: • Type abbreviations (§8.3) • Record type definitions (§8.4) • Union type definitions (§8.5) • Class type definitions (§8.6) • Interface type definitions (§8.7) • Struct type definitions (§8.8) • Enum type definitions (§8.9) • Delegate type definitions (§8.10) • Exception type definitions (§8.11) • Type extension definitions (§8.12) • Measure type definitions (§9.4) With the exception of type abbreviations and type extension definitions, type definitions define fresh, named types that are distinct from other types. A type definition group defines several type definitions or extensions simultaneously: type ... and ... For example: type RowVector(entries: seq<int>) = let entries = Seq.toArray entries member x.Length = entries.Length member x.Permute = ColumnVector(entries) and ColumnVector(entries: seq<int>) = let entries = Seq.toArray entries member x.Length = entries.Length member x.Permute = RowVector(entries) A type definition group can include any type definitions except for exception type definitions and module definitions. Most forms of type definitions may contain both static elements and instance elements. Static elements are accessed by using the type definition. Within a static definition, only the static elements are in scope. Most forms of type definitions may contain members (§8.13). Custom attributes may be placed immediately before a type definition group, in which case they apply to the first type definition, or immediately before the name of the type definition: [<Obsolete>] type X1() = class end type [<Obsolete>] X2() = class end and [<Obsolete>] Y2() = class end ## Type Definition Group Checking and Elaboration F# checks type definition groups by determining the basic shape of the definitions and then filling in the details. In overview, a type definition group is checked as follows: 1. For each type definition: • Determine the generic arguments, accessibility and kind of the type definition • Determine whether the type definition supports equality and/or comparison • Elaborate the explicit constraints for the generic parameters. 2. For each type definition: • Establish type abbreviations • Determine the base types and implemented interfaces of each new type definition • Detect any cyclic abbreviations • Verify the consistency of types in fields, union cases, and base types. 3. For each type definition: • Determine the union cases, fields, and abstract members (§8.14) of each new type definition. • Check the union cases, fields, and abstract members themselves, as described in the corresponding sections of this chapter. 4. For each member, add items that represent the members to the environment as a recursive group. 5. Check the members, function, and value definitions in order and apply incremental generalization. In the context in which type definitions are checked, the type definition itself is in scope, as are all members and other accessible functionality of the type. This context enables recursive references to the accessible static content of a type. It also enables recursive references to the accessible properties of any object that has the same type as the type definition or a related type. In more detail, given an initial environment env, a type definition group is checked as described in the following paragraphs. First, check the individual type definitions. For each type definition: 1. Determine the number, names, and sorts of generic arguments of the type definition. • For each generic argument, if a Measure attribute is present, mark the generic argument as a measure parameter. The generic arguments are initially inference parameters, and additional constraints may be inferred for these parameters. • For each type definition T, the subsequent steps use an environment env*T*** that is produced by adding the type definitions themselves and the generic arguments for T to env. 2. Determine the accessibility of the type definition. 3. Determine and check the basic kind of the type definition, using Type Kind Inference if necessary (§8.2). 4. Mark the type definition as a measure type definition if a Measure attribute is present. 5. If the type definition is generic, infer whether the type definition supports equality and/or comparison. 6. Elaborate and add the explicit constraints for the generic parameters of the type definition, and then generalize the generic parameters. Inference of additional constraints is not permitted. 7. If the type definition is a type abbreviation, elaborate and establish the type being abbreviated. 8. Check and elaborate any base types and implemented interfaces. 9. If the type definition is a type abbreviation, check that the type abbreviation is not cyclic. 10. Check whether the type definition has a single, zero-argument constructor, and hence forms a type that satisfies the default constructor constraint. 11. Recheck the following to ensure that constraints are consist: • The type being abbreviated, if any. • The explicit constraints for any generic parameters, if any. • The types and constraints occurring in the base types and implemented interfaces, if any. 12. Determine the union cases, fields, and abstract members, if any, of the type definition. Check and elaborate the types that the union cases, fields, and abstract members include. 13. Make additional checks as defined elsewhere in this chapter. For example, check that the AbstractClass attribute does not appear on a union type. 14. For each type definition that is a struct, class, or interface, check that the inheritance graph and the struct-inclusion graph are not cyclic. This check ensures that a struct does not contain itself and that a class or interface does not inherit from itself. This check includes the following steps: 1. Create a graph with one node for each type definition. 2. Close the graph under edges. • (T, base-type-definition) • (T, interface-type-definition) • (T1, T2) where T1 is a struct and T2 is a type that would store a value of type T1 <…> for some instantiation. Here “X storing Y” means that X is Y or is a struct type with an instance field that stores Y. 1. Check for cycles. The special case of a struct S<typars> storing a static field of type S<typars> is allowed. 15. Collectively add the elaborated member items that represent the members for all new type definitions to the environment as a recursive group (§8.13), excluding interface implementation members. 16. If the type definition has a primary constructor, create a member item to represent the primary constructor. After these steps are complete for each type definition, check the members. For each member: 1. If the member is in a generic type, create a copy of the type parameters for the generic type and add the copy to the environment for that member. 2. If the member has explicit type parameters, elaborate these type parameters and any explicit constraints. 3. If the member is an override, default, or interface implementation member, apply dispatch-slot inference. 4. If the member has syntactic parameters, assign an initial type to the elaborated member item based on the patterns that specify arguments for the members. 5. If the member is an instance member, assign a type to the instance variable. Finally, check the function, value, and member definitions of each new type definition in order as a recursive group. ## Type Kind Inference A type that is specified in one of the following ways has an anonymous type kind: • By using begin and end on the right-hand side of the = token. • In lightweight syntax, with an implicit begin/end. F# infers the kind of an anonymous type by applying the following rules, in order: 1. If the type has a Class attribute, Interface attribute, or Struct attribute, this attribute identifies the kind of the type. 2. If the type has any concrete elements, the type is a class. Concrete elements are primary constructors, additional object constructors, function definitions, value definitions, non-abstract members, and any inherit declarations that have arguments. 3. Otherwise, the type is an interface type. For example: // This is implicitly an interface type IName = abstract Name : string // This is implicitly a class, because it has a constructor type ConstantName(n:string) = member x.Name = n // This is implicitly a class, because it has a constructor type AbstractName(n:string) = abstract Name : string default x.Name = "<no-name>" If a type is not an anonymous type, any use of the Class attribute, Interface attribute, or Struct attribute must match the class/end, interface/end, and struct/end tokens, if such tokens are present. These attributes cannot be used with other kinds of type definitions such as type abbreviations, record, union, or enum types. ## Type Abbreviations Type abbreviations define new names for other types. For example: type PairOfInt = int * int Type abbreviations are expanded and erased during compilation and do not appear in the elaborated form of F# declarations, nor can they be referred to or accessed at runtime. The process of repeatedly eliminating type abbreviations in favor of their equivalent types must not result in an infinite type derivation. For example, the following are not valid type definitions: **type X = option<X> type Identity<'T> = 'T and Y = Identity<Y>** The constraints on a type abbreviation must satisfy any constraints that the abbreviated type requires. For example, assuming the following declarations: **type IA = abstract AbstractMember : int -> int type IB = abstract AbstractMember : int -> int type C<'T when 'T :> IB>() = static member StaticMember(x : 'a) = x.AbstractMember(1)** the following is permitted: type D<'T when 'T :> IB> = C<'T> whereas the following is not permitted: type E<'T> = C<'T> // invalid: missing constraint Type abbreviations can define additional constraints, so the following is permitted: type F<'T when 'T :> IA and 'T :> IB> = C<'T> The right side of a type abbreviation must use all the declared type variables that appear on the left side. For this purpose, the order of type variables that are used on the right-hand side of a type definition is determined by their left-to-right occurrence in the type. For example, the following is not a valid type abbreviation. type Drop<'T,'U> = 'T * 'T // invalid: dropped type variable Note: This restriction simplifies the process of guaranteeing a stable and consistent compilation to generic CLI code. Flexible type constraints #type may not be used on the right side of a type abbreviation, because they expand to a type variable that has not been named in the type arguments of the type abbreviation. For example, the following type is disallowed: type BadType = #Exception -> int // disallowed Type abbreviations may be declared internal or private. Note: Private type abbreviations are still, for all purposes, considered equivalent to the abbreviated types. ## Record Type Definitions A record type definition introduces a type in which all the inputs that are used to construct a value are accessible as properties on values of the type. For example: type R1 = { x : int; y : int } member this.Sum = this.x + this.y In this example, the integers x and y can be accessed as properties on values of type R1. Record fields may be marked mutable. For example: type R2 = { mutable x : int; mutable y : int } member this.Move(dx,dy) = this.x <- this.x + dx this.y <- this.y + dy The mutable attribute on x and y makes the assignments valid. Record types are implicitly sealed and may not be given the Sealed attribute. Record types may not be given the AbstractClass attribute. Record types are implicitly marked serializable unless the AutoSerializable(false) attribute is used. ### Members in Record Types Record types may declare members (§8.13), overrides, and interface implementations. Like all types with overrides and interface implementations, they are subject to Dispatch Slot Checking (§14.8). ### Name Resolution and Record Field Labels For a record type, the record field labels field1** ... fieldN** are added to the FieldLabels table of the current name resolution environmentunless the record type has the RequireQualifiedAccess attribute. Record field labels in the FieldLabels table play a special role in Name Resolution for Members (§14.1): an expression’s type may be inferred from a record label. For example: type R = { dx : int; dy: int } let f x = x.dx // x is inferred to have type R In this example, the lookup .dx is resolved to be a field lookup. ### Structural Hashing, Equality, and Comparison for Record Types Record types implicitly implement the following interfaces and dispatch slots unless they are explicitly implemented as part of the definition of the record type: interface System.Collections.IStructuralEquatable interface System.Collections.IStructuralComparable interface System.IComparable override GetHashCode : unit -> int override Equals : obj -> bool The implicit implementations of these interfaces and overrides are described in §8.15. ### With/End in Record Type Definitions Record type definitions can include with/end tokens, as the following shows: type R1 = { x : int; y : int } with member this.Sum = this.x + this.y end The with/end tokens can be omitted if the type-defn-elements vertically align with the { in the record-fields. The semicolon (;) tokens can be omitted if the next record-field vertically aligns with the previous record-field. ### CLIMutable Attributes Adding the CLIMutable attribute to a record type causes it to be compiled to a CLI representation as a plain-old CLR object (POCO) with a default constructor along with property getters and setters. Adding the default constructor and mutable properties makes objects of the record type usable with .NET tools and frameworks such as database queries, serialization frameworks, and data models in XAML programming. For example, an F# immutable record cannot be serialized because it does not have a constructor. However, if you attach the CLIMutable attribute as in the following example, the XmlSerializer is enable to serialize or deserialize this record type: [<CLIMutable>] type R1 = { x : string; y : int } ## Union Type Definitions A union type definition is a type definition that includes one or more union cases. For example: type Message = | Result of string | Request of int * string member x.Name = match x with Result(nm) -> nm | Request(_,nm) -> nm Union case names must begin with an uppercase letter, which is defined to mean any character for which the CLI library function System.Char.IsUpper returns true and System.Char.IsLower returns false. The union cases Case1 ... CaseN have module scope and are added to the ExprItems and PatItems tables in the name resolution environment. This means that their unqualified names can be used to form both expressions and patterns, unless the record type has the RequireQualifiedAccess attribute. Parentheses are significant in union definitions. Thus, the following two definitions differ: type CType = C of int * int type CType = C of (int * int) The lack of parentheses in the first example indicates that the union case takes two arguments. The parentheses in the second example indicate that the union case takes one argument that is a first-class tuple value. Union fields may optionally be named within each case of a union type. For example: type Shape = | Rectangle of width: float * length: float | Circle of radius: float | Prism of width: float * float * height: float The names are referenced when pattern matching on union values of this type. When using pattern matching with multiple fields, semicolons are used to delimit the named fields, e.g. Prism(width=w; height=h). The following declaration defines a type abbreviation if the named type A exists in the name resolution environment. Otherwise it defines a union type. type OneChoice = A To disambiguate this case and declare an explicit union type, use the following: type OneChoice = | A Union types are implicitly marked serializable unless the AutoSerializable(false) attribute is used. ### Members in Union Types Union types may declare members (§8.13), overrides, and interface implementations. As with all types that declare overrides and interface implementations, they are subject to Dispatch Slot Checking (§14.8). ### Structural Hashing, Equality, and Comparison for Union Types Union types implicitly implement the following interfaces and dispatch slots unless they are explicitly implemented as part of the definition of the union type: interface System.Collections.IStructuralEquatable interface System.Collections.IStructuralComparable interface System.IComparable override GetHashCode : unit -> int override Equals : obj -> bool The implicit implementations of these interfaces and overrides are described in §8.15. ### With/End in Union Type Definitions Union type definitions can include with/end tokens, as the following shows: type R1 = { x : int; y : int } with member this.Sum = this.x + this.y end The with/end tokens can be omitted if the type-defn-elements vertically align with the { in the record-fields. The semicolon (;) tokens can be omitted if the next record-field vertically aligns with the previous record-field. For union types, the with/end tokens can be omitted if the type-defn-elements vertically alignwith the first | in the union-type-cases. However, with/end must be present if the | tokens align with the type token. For example: **/// Note: this layout is permitted type Message = | Result of string | Request of int * string member x.Name = match x with Result(nm) -> nm | Request(_,nm) -> nm /// Note: this layout is not permitted type Message = | Result of string | Request of int * string member x.Name = match x with Result(nm) -> nm | Request(_,nm) -> nm** ### Compiled Form of Union Types for Use from Other CLI Languages A compiled union type U has: • One CLI static getter property U.C for each null union case C. This property gets a singleton object that represents each such case. • One CLI nested type U.C for each non-null union case C. This type has instance properties Item1, Item2.... for each field of the union case, or a single instance property Item if there is only one field. However, a compiled union type that has only one case does not have a nested type. Instead, the union type itself plays the role of the case type. • One CLI static method U.NewC for each non-null union case C. This method constructs an object for that case. • One CLI instance property U.IsC for each case C. This property returns true or false for the case. • One CLI instance property U.Tag for each case C. This property fetches or computes an integer tag corresponding to the case. • If U has more than one case, it has one CLI nested type U.Tags. The U.Tags typecontains one integer literal for each case, in increasing order starting from zero. • A compiled union type has the methods that are required to implement its auto-generated interfaces, in addition to any user-defined properties or methods. These methods and properties may not be used directly from F#. However, these types have user-facing List.Empty, List.Cons, Option.None, and Option.Some properties and/or methods. A compiled union type may not be used as a base type in another CLI language, because it has at least one assembly-private constructor and no public constructors. ## Class Type Definitions A class type definition encapsulates values that are constructed by using one or more object constructors. Class types have the form: type type-name pat*opt*** as-defn*opt*** = class class-inherits-decl*opt*** class-function-or-value-defns*opt*** type-defn-elements end The class/end tokens can be omitted, in which case Type Kind Inference (§8.2) is used to determine the kind of the type. In F#, class types are implicitly marked serializable unless the AutoSerializable(false) attribute is present. ### Primary Constructors in Classes An object constructor represents a way of initializing an object. Object constructors can create values of the type and can partially initialize an object from a subclass. A class can have an optional primary constructor and zero or more additional object constructors. If a type definition has a pattern immediately after the type-name and any accessibility annotation, then it has a primary constructor. For example, the following type has a primary constructor: type Vector2D(dx : float, dy : float) = let length = sqrt(dx*x + dy*dy) member v.Length = length member v.DX = dx member v.DY = dy Class definitions that have a primary constructor may contain function and value definitions, including those that use let rec. The pattern for a primary constructor must have zero or more patterns of the following form: (simple-pat, ..., simple-pat) Each simple-pat has this form: simple-pat := | ident | simple-pat : type Specifically, nested patterns may not be used in the primary constructor arguments. For example, the following is not permitted because the primary constructor arguments contain a nested tuple pattern: type TwoVectors((px, py), (qx, qy)) = member v.Length = sqrt((qx-px)*(qx-px) + (qy-py)*(qy-py)) Instead, one or more value definitions should be used to accomplish the same effect: type TwoVectors(pv, qv) = let (px, py) = pv let (qx, qy) = qv member v.Length = sqrt((qx-px)*(qx-px) + (qy-py)*(qy-py)) When a primary constructor is evaluated, the inheritance and function and value definitions are evaluated in order. #### Object References in Primary Constructors For types that have a primary constructor, the name of the object parameter can be bound and used in the non‑static function, value, and member definitions of the type definition as follows: type X(a:int) as x = let mutable currentA = a let mutable currentB = 0 do x.B <- x.A + 3 member self.GetResult()= currentA + currentB member self.A with get() = currentA and set v = currentA <- v member self.B with get() = currentB and set v = currentB <- v During construction, no member on the type may be called before the last value or function definition in the type has completed; such a call results in an InvalidOperationException. For example, the following code raises this exception: type C() as self = let f = (fun (x:C) -> x.F()) let y = f self do printfn "construct" member this.F() = printfn "hi, y = %A" y let r = new C() // raises InvalidOperationException The exception is raised because an attempt may be made to access the value of the field y before initialization is complete. #### Inheritance Declarations in Primary Constructors An inherit declaration specifies that the type being defined is an extension of an existing type. Such declarations have the following form: class-inherits-decl := inherit type expr*opt*** For example: type MyDerived(...) = inherit MyBase(...) If a class definition does not contain an inherit declaration, the class inherits fromSystem.Object by default. The inherit declaration for a type must have arguments if and only if the type has a primary constructor. Unlike §8.6.1.2, members of a base type can be accessed during construction of the derived class. For example, the following code does not raise an exception: type B() = member this.G() = printfn "hello " type C() as self = inherit B() let f = (fun (x:C) -> x.G()) let y = f self do printfn "construct" member this.F() = printfn "hi, y = %A" y let r = new C() // does not raise InvalidOperationException #### Instance Function and Value Definitions in Primary Constructors Classes that have primary constructors may include function definitions, value definitions, and “do” statements. The following rules apply to these definitions: • Each definition may be marked static (see §8.6.2.1). If the definition is not marked static, it is called an instance definition. • The functions and values defined by instance definitions are lexically scoped (and thus implicitly private) to the object being defined. • Each value definition may optionally be marked mutable. • A group of function and value definitions may optionally be marked rec. • Function and value definitions are generalized. • Value definitions that declared in classes are represented in compiled code as follows: • If a value definition is not mutable, and is not used in any function or member, then the value is represented as a local value in the object constructor. • If a value definition is mutable, or used in any function or member, then the value is represented as an instance field in the corresponding CLI type. • Function definitions are represented in compiled code as private members of the corresponding CLI type. For example, consider this type: type C(x:int,y:int) = let z = x + y let f w = x + w member this.Z = z member this.Add(w) = f w The input y is used only during construction, and no field is stored for it. Likewise the function f is represented as a member rather than a field that is a function value. A value definition is considered a function definition if its immediate right-hand-side is an anonymous function, as in this example: let f = (fun w -> x + w) Function and value definitions may have attributes as follows: • Value definitions represented as fields may have attributes that target fields. • Value definitions represented as locals may have attributes that target fields, but these attributes will not be attached to any construct in the resulting CLI assembly. • Function definitions represented as methods may have attributes that target methods. For example: type C(x:int) = [<System.Obsolete>] let unused = x member __.P = 1 In this example, no field is generated for unused, and no corresponding compiled CLI attribute is generated. #### Static Function and Value Definitions in Primary Constructors Classes that have primary constructors may have function definitions, value definitions, and “do” statements that are marked as static: • The values that are defined by static function and value definitions are lexically scoped (and thus implicitly private) to the type being defined. • Each value definition may optionally be marked mutable. • A group of function and value definitions may optionally be marked rec. • Static function and value definitions are generalized. • Static function and value definitions are computed once per generic instantiation. • Static function and value definitions are elaborated to a static initializer associated with each generic instantiation of the generated class. Static initializers are executed on demand in the same way as static initializers for implementation files §12.5. • The compiled representation for static value definitions is as follows: • If the value is not used in any function or member then the value is represented as a local value in the CLI class initializer of the type. • If the value is used in any function or member, then the value is represented as a static field of the CLI class for the type. • The compiled representation for a static function definition is a private static member of the corresponding CLI type. Static function and value definitions may have attributes as follows: • Static function and value definitions represented as fields may have attributes that target fields. • Static function and value definitions represented as methods may have attributes that target methods. For example: type C<'T>() = static let mutable v = 2 + 2 static do v <- 3 member x.P = v static member P2 = v+v printfn "check: %d = 3" (new C<int>()).P printfn "check: %d = 3" (new C<int>()).P printfn "check: %d = 3" (new C<string>()).P printfn "check: %d = 6" (C<int>.P2) printfn "check: %d = 6" (C<string>.P2) In this example, the value v is represented as a static field in the CLI type for C. One instance of this field exists for each generic instantiation of C. The output of the program is check: 3 = 3 check: 3 = 3 check: 3 = 3 check: 6 = 6 check: 6 = 6 ### Members in Classes Class types may declare members (§8.13), overrides, and interface implementations. As with all types that have overrides and interface implementations, such class types are subject to Dispatch Slot Checking (§14.8). ### Additional Object Constructors in Classes Although the use of primary object constructors is generally preferable, additional object constructors may also be specified. Additional object constructors are required in two situations: • To define classes that have more than one constructor. • To specify explicit val fields without the DefaultValue attribute. For example, the following statement adds a second constructor to a class that has a primary constructor: type PairOfIntegers(x:int,y:int) = new (x) = PairOfIntegers(x,x) The next example declares a class without a primary constructor: type PairOfStrings = val s1 : string val s2 : string new (s) = { s1 = s; s2 = s } new (s1,s2) = { s1 = s1; s2 = s2 } If a primary constructor is present, additional object constructors must call another object constructor in the same type, which may be another additional constructor or the primary constructor. If no primary constructor is present, additional constructors must initialize any val fields of the object that do not have the DefaultValue attribute. They must also specify a call to a base class constructor for any inherited class type. A call to a base class constructor is not required if the base class is System.Object. The use of additional object constructors and val fields is required if a class has multiple object constructors that must each call different base class constructors. For example: type BaseClass = val s1 : string new (s) = { s1 = s } new () = { s1 = "default" } type SubClass = inherit BaseClass val s2 : string new (s1,s2) = { inherit BaseClass(s1); s2 = s2 } new (s2) = { inherit BaseClass(); s2 = s2 } To implement additional object constructors, F# uses a restricted subset of expressions that ensure that the code generated for the constructor is valid according to the rules of object construction for CLI objects. Note that precisely one additional-constr-init-expr occurs for each branch of a construction expression. For classes without a primary constructor, side effects can be performed after the initialization of the fields of the object by using the additional-constr-expr then stmt form. For example: type PairOfIntegers(x:int,y:int) = // This additional constructor has a side effect after initialization. new(x) = PairOfIntegers(x, x) then printfn "Initialized with only one integer" The name of the object parameter can be bound within additional constructors. For example: type X = val a : (unit -> string) val mutable b : string new() as x = { a = (fun () -> x.b); b = "b" } A warning is given if x occurs syntactically in or before the additional-constr-init-expr of the construction expression. If any member is called before the completion of execution of the additional-constr-init-expr within the additional-constr-expr then an InvalidOperationException is thrown. ### Additional Fields in Classes Additional field declarations indicate that a value is stored in an object. They are generally used only for classes without a primary constructor, or for mutable fields that use default initialization, and typically occur only in generated code. For example: type PairOfIntegers = val x : int val y : int new(x, y) = {x = x; y = y} The following shows an additional field declaration as a static field in an explicit class type: type TypeWithADefaultMutableBooleanField = [<DefaultValue>] static val mutable ready : bool At runtime, such a field is initially assigned the zero value for its type (§6.9.3). For example: type MyClass(name:string) = // Keep a global count. It is initially zero. [<DefaultValue>] static val mutable count : int // Increment the count each time an object is created do MyClass.count <- MyClass.count + 1 static member NumCreatedObjects = MyClass.count member x.Name = name A val specification in a type that has a primary constructor must be marked mutable and must have the DefaultValue attribute. For example: type X() = [<DefaultValue>] val mutable x : int The DefaultValue attribute takes a check parameter, which indicates whether to ensure that the val specification does not create unexpected null values. The default value for check is true. If this parameter is true, the type of the field must permit default initialization (§5.4.8). For example, the following type is rejected: type MyClass<'T>() = [<DefaultValue>] static val mutable uninitialized : 'T The reason is that the type 'T does not admit default initialization. However, in compiler-generated and hand-optimized code it is sometimes essential to be able to emit fields that are completely uninitialized. In this case, DefaultValue(false) can be used. For example: **type MyNullable<'T>() = [<DefaultValue>] static val mutable ready : bool [<DefaultValue(false)>] static val mutable uninitialized : 'T** ## Interface Type Definitions An interface type definition represents a contract that an object may implement. Such a type definition containsonly abstract members. For example: type IPair<'T,'U> = interface abstract First: 'T abstract Second: 'U end type IThinker<'Thought> = abstract Think: ('Thought -> unit) -> unit abstract StopThinking: (unit -> unit) Note: The interface/end tokens can be omitted when lightweight syntax is used, in which case Type Kind Inference (§8.2) is used to determine the kind of the type. The presence of any non-abstract members or constructors means a type is not an interface type. By convention, interface type names start with I, as in IEvent. However, this convention is not followed as strictly in F# as in other CLI languages. Interface types may be arranged hierarchically by specifying inherit declarations. For example: type IA = abstract One: int -> int type IB = abstract Two: int -> int type IC = inherit IA inherit IB abstract Three: int -> int Each inherit declaration must itself be an interface type. Circular references are not allowed among inherit declarations. F# uses the named types of the inherited interface types to determine whether references are circular. ## Struct Type Definitions A struct type definition is a type definition whose instances are stored inline inside the stack frame or object of which they are a part. The type is represented as a CLI struct type, also called a value type. For example: type Complex = struct val real: float; val imaginary: float member x.R = x.real member x.I = x.imaginary end Note: The struct/end tokens can be omitted when lightweight syntax is used, in which case Type Kind Inference (§8.2) is used to determine the kind of the type. Becaues structs undergo type kind inference (§8.2), the following is valid: [<Struct>] type Complex(r:float, i:float) = member x.R = r member x.I = i Structs may have primary constructors: [<Struct>] type Complex(r : float, I : float) = member x.R = r member x.I = i Structs that have primary constructors must accept at least one argument. Structs may have additional constructors. For example: [<Struct>] type Complex(r : float, I : float) = member x.R = r member x.I = i new(r : float) = new Complex(r, 0.0) The fields in a struct may be mutable only if the struct does not have a primary constructor. For example: [<Struct>] type MutableComplex = val mutable real : float; val mutable imaginary : float member x.R = x.real member x.I = x.imaginary member x.Change(r, i) = x.real <- r; x.imaginary <- i new (r, i) = { real = r; imaginary = i } Struct types may declare members, overrides, and interface implementations. As for all types that declare overrides and interface implementations, struct types are subject to Dispatch Slot Checking (§14.8). Structs may not have inherit declarations. Structs may not have “let” or “do” statements unless they are static. For example, the following is not valid: [<Struct>] type BadStruct1 (def : int) = do System.Console.WriteLine("Structs cannot use 'do'!") Structs may have static “let” or “do” statements. For example, the following is valid: [<Struct>] type GoodStruct1 (def : int) = static do System.Console.WriteLine("Structs can use 'static do'") A struct type must be valid according to the CLI rules for structs; in particular, recursively constructed structs are not permitted. For example, the following type definition is not permitted, because the size of BadStruct2 would be infinite: [<Struct>] type BadStruct2 = val data : float; val rest : BadStruct2 new (data, rest) = { data = data; rest = rest } Likewise, the implied size of the following struct would be infinite: [<Struct>] type BadStruct3 (data : float, rest : BadStruct3) = member s.Data = data member s.Rest = rest If the types of all the fields in a struct type permit default initialization, the struct type has an implicit default constructor,which initializes all the fields to the default value. For example, the Complex type defined earlier in this section permits default initialization. [<Struct>] type Complex(r : float, I : float) = member x.R = r member x.I = i new(r : float) = new Complex(r, 0.0) let zero = Complex() Note: The existence of the implicit default constructor for structs is not recorded in CLI metadata and is an artifact of the CLI specification and implementation itself. A CLI implementation permits default constructors for all struct types, although F# does not permit their direct use for F# struct types unless all field types admit default initialization. This is similar to the way that F# considers some types to have null as an abnormal value. Public struct types for use from other CLI languages should be designed with the existence of the default zero-initializing constructor in mind. ## Enum Type Definitions Occasionally the need arises to represent a type that compiles as a CLI enumeration type. An enum type definition has values that are represented by integer constants and has a CLI enumeration as its compiled form. Enum type definitions are declared by specifying integer constants in a format that is syntactically similar to a union type definition. For example: type Color = | Red = 0 | Green = 1 | Blue = 2 let rgb = (Color.Red, Color.Green, Color.Blue) let show(colorScheme) = match colorScheme with | (Color.Red, Color.Green, Color.Blue) -> printfn "RGB in use" | _ -> printfn "Unknown color scheme in use" The example defines the enum type Color, which has the values Red, Green, and Blue, mapped to the constants 0, 1, and 2 respectively. The values are accessed by their qualified names: Color.Red, Color.Green, and Color.Blue. Each case must be given a constant value of the same type. The constant values dictate the underlying type of the enum, and must be one of the following types: • sbyte, int16, int32, int64, byte, uint16, uint32, uint64, char The declaration of an enumeration type in an implementation file has the following effects on the typing environment: • Brings a named type into scope. • Adds the named type to the inferred signature of the containing namespace or module. Enum types coerce to System.Enum and satisfy the enum<underlying-type> constraint for their underlying type. Each enum type declaration is implicitly annotated with the RequiresQualifiedAccess attribute and does not add the tags of the enumeration to the name environment. type Color = | Red = 0 | Green = 1 | Blue = 2 let red = Red // not accepted, must use Color.Red Unlike unions, enumeration types are fundamentally “incomplete,” because CLI enumerations can be converted to and from their underlying primitive type representation. For example, a Color value that is not in the above enumeration can be generated by using the enum function from the F# library: let unknownColor : Color = enum<Color>(7) This statement adds the value named unknownColor, equal to the constant 7, to the Color enumeration. ## Delegate Type Definitions Occasionally the need arises to represent a type that compiles as a CLI delegate type. A delegate type definition has as its values functions that are represented as CLI delegate values. A delegate type definition is declared by using the delegate keyword with a member signature. For example: type Handler<'T> = delegate of obj * 'T -> unit Delegates are often used when using Platform Invoke (P/Invoke) to interface with CLI libraries, as in the following example: type ControlEventHandler = delegate of int -> bool [<DllImport("kernel32.dll")>] extern void SetConsoleCtrlHandler(ControlEventHandler callback, bool add) ## Exception Definitions An exception definition defines a new way of constructing values of type exn (a type abbreviation for System.Exception). Exception definitions have the form: exception ident of type1 * … * typen An exception definition has the following effect: • The identifier ident can be used to generate values of type exn. • The identifier ident can be used to pattern match on values of type exn. • The definition generates a type with name ident that derives from exn. For example: exception Error of int * string raise (Error (3, "well that didn't work did it")) try raise (Error (3, "well that didn't work did it")) with | Error(sev, msg) -> printfn "severity = %d, message = %s" sev msg The type that corresponds to the exception definition can be used as a type in F# code. For example: let exn = Error (3, "well that didn't work did it") let checkException() = if (exn :? Error) then printfn "It is of type Error" if (exn.GetType() = typeof<Error>) then printfn "Yes, it really is of type Error" Exception abbreviations may abbreviate existing exception constructors. For example: exception ThatWentBadlyWrong of string * int exception ThatWentWrongBadly = ThatWentBadlyWrong let checkForBadDay() = if System.DateTime.Today.DayOfWeek = System.DayOfWeek.Monday then raise (ThatWentWrongBadly("yes indeed",123)) Exception values may also be generated by defining and using classes that extend System.Exception. ## Type Extensions A type extension associates additional members with an existing type. For example, the following associates the additional member IsLong with the existing type System.String: type System.String with member x.IsLong = (x.Length > 1000) Type extensions may be applied to any accessible type definition except those defined by type abbreviations. For example, to add an extension method to a list type, use 'a List because 'a list is a type abbreviation of 'a List. For example: type 'a List with member x.GetOrDefault(n) = if x.Length > n then x.[n] else Unchecked.defaultof<'a> let intlst = [1; 2; 3] intlst.GetOrDefault(1) //2 intlst.GetOrDefault(4) //0 For an array type, backtick marks can be used to define an extension method to the array type: type 'a [] with member x.GetOrDefault(n) = if x.Length > n then x.[n] else Unchecked.defaultof<'a> let arrlist = [| 1; 2; 3 |] arrlist.GetOrDefault(1) //2 arrlist.GetOrDefault(4) //0 A type can have any number of extensions. If the type extension is in the same module or namespace declaration group as the original type definition, it is called an intrinsic extension. Members that are defined in intrinsic extensions follow the same name resolution and other language rules as members that are defined as part of the original type definition. If the type extension is not intrinsic, it must be in a module, and it is called an extension member. Opening a module that contains an extension member extends the name resolution of the dot syntax for the extended type. That is, extension members are accessible only if the module that contains the extension is open. Name resolution for members that are defined in type extensions behaves as follows: • In method application resolution (see §14.4), regular members (that is, members that are part of the original definition of a type, plus intrinsic extensions) are preferred to extension members. • Extension members that are in scope and have the correct name are included in the group of members considered for method application resolution (see §14.4). • An intrinsic member is always preferred to an extension member. If an extension member has the same name and type signature as a member in the original type definition or an inherited member, then it will be inaccessible. The following illustrates the definition of one intrinsic and one extension member for the same type: namespace Numbers type Complex(r : float, i : float) = member x.R = r member x.I = i // intrinsic extension type Complex with static member Create(a, b) = new Complex (a, b) member x.RealPart = x.R member x.ImaginaryPart = x.I namespace Numbers module ComplexExtensions = // extension member type Numbers.Complex with member x.Magnitude = ... member x.Phase = ... Extensions may define both instance members and static members. Extensions are checked as follows: • Checking applies to the member definitions in an extension together with the members and other definitions in the group of type definitions of which the extension is a part. • Two intrinsic extensions may not contain conflicting members because intrinsic extensions are considered part of the definition of the type. • Extensions may not define fields, interfaces, abstract slots, inherit declarations, or dispatch slot (interface and override) implementations. • Extension members must be in modules. • Extension members are compiled as CLI static members with encoded names. • The elaborated form of an application of a static extension member C.M(arg1,…,argn) is a call to this static member with arguments arg1,…,argn.. • The elaborated form of an application of an instance extension member obj.M(arg1,…,argn) is an invocation of the static instance member where the object parameter is supplied as the first argument to the extension member followed by arguments arg1argn. ### Imported CLI C# Extensions Members The CLI C# language defines an “extension member,” which commonly occurs in CLI libraries, along with some other CLI languages. C# limits extension members to instance methods. C#-defined extension members are made available to F# code in environments where the C#-authored assembly is referenced and an open declaration of the corresponding namespace is in effect. The encoding of compiled names for F# extension members is not compatible with C# encodings of C# extension members. However, for instance extension methods, the naming can be made compatible. For example: open System.Runtime.CompilerServices [<Extension>] module EnumerableExtensions = [<CompiledName("OutputAll"); Extension>] type System.Collections.Generic.IEnumerable<'T> with member x.OutputAll (this:seq<'T>) = for x in this do System.Console.WriteLine (box x) C#-style extension members may also be declared directly in F#. When combined with the “inline” feature of F#, this allows the definition of generic, constrained extension members that are not otherwise definable in C# or F#. [<Extension>] type ExtraCSharpStyleExtensionMethodsInFSharp () = [<Extension>] static member inline Sum(xs: seq<'T>) = Seq.sum xs Such an extension member can be used as follows: let listOfIntegers = [ 1 .. 100 ] let listOfBigIntegers = [ 1I .. 100I ] listOfIntegers.Sum() listOfBigIntegers.Sum() ## Members Member definitions describe functions that are associated with type definitions and/or values of particular types. Member definitions can be used in type definitions. Members can be classified as follows: • Property members • Method members A static member is prefixed by static and is associated with the type, rather than with any particular object. Here are some examples of static members: type MyClass() = static let mutable adjustableStaticValue = "3" static let staticArray = [| "A"; "B" |] static let staticArray2 = [|[| "A"; "B" |]; [| "A"; "B" |] |] static member StaticMethod(y:int) = 3 + 4 + y static member StaticProperty = 3 + staticArray.Length static member StaticProperty2 with get() = 3 + staticArray.Length static member MutableStaticProperty with get() = adjustableStaticValue and set(v:string) = adjustableStaticValue <- v static member StaticIndexer with get(idx) = staticArray.[idx] static member StaticIndexer2 with get(idx1,idx2) = staticArray2.[idx1].[idx2] static member MutableStaticIndexer with get (idx1) = staticArray.[idx1] and set (idx1) (v:string) = staticArray.[idx1] <- v An instance member is a member without static. Here are some examples of instance members: type MyClass() = let mutable adjustableInstanceValue = "3" let instanceArray = [| "A"; "B" |] let instanceArray2 = [| [| "A"; "B" |]; [| "A"; "B" |] |] member x.InstanceMethod(y:int) = 3 + y + instanceArray.Length member x.InstanceProperty = 3 + instanceArray.Length member x.InstanceProperty2 with get () = 3 + instanceArray.Length member x.InstanceIndexer with get (idx) = instanceArray.[idx] member x.InstanceIndexer2 with get (idx1,idx2) = instanceArray2.[idx1].[idx2] member x.MutableInstanceProperty with get () = adjustableInstanceValue and set (v:string) = adjustableInstanceValue <- v member x.MutableInstanceIndexer with get (idx1) = instanceArray.[idx1] and set (idx1) (v:string) = instanceArray.[idx1] <- v Members from a set of mutually recursive type definitions are checked as a single mutually recursive group. As with collections of recursive functions, recursive calls to potentially-generic methods may result in inconsistent type constraints: type Test() = static member Id x = x member t.M1 (x: int) = Test.Id(x) member t.M2 (x: string) = Test.Id(x) // error, x has type 'string' not 'int' A target method that has a full type annotation is eligible for early generalization (§14.6.7). type Test() = static member Id<'T> (x:'T) : 'T = x member t.M1 (x: int) = Test.Id(x) member t.M2 (x: string) = Test.Id(x) ### Property Members A property member is a method-or-prop-defn in one of the following forms: staticopt member** ident**.opt** ident = expr staticopt member** ident**.opt** ident with get pat = expr staticopt member** ident**.opt** ident with set pat*opt** pat***=** expr staticopt member** ident**.opt** ident with get pat = expr and set pat*opt** pat* = expr staticopt member** ident**.opt** ident with set pat*opt** pat* = expr and get pat = expr A property member in the form staticopt member** ident**.opt** ident with get pat*1*** = expr*1*** and set pat*2a** pat**2b opt = expr2* is equivalent to two property members of the form: staticopt member** ident**.opt** ident with get pat*1*** = expr*1*** staticopt member** ident**.opt** ident with set pat*2a** pat**2b*** opt = expr*2*** Furthermore, the following two members are equivalent: staticopt member** ident**.opt** ident = expr staticopt member** ident**.opt** ident with get () = expr These two are also equivalent: staticopt member** ident**.opt** ident with set pat = expr*2*** staticopt member** ident**.opt** ident with set () pat = expr Thus, property members may be reduced to the following two forms: staticopt member** ident**.opt** ident with get pat*idx*** = expr staticopt member** ident**.opt** ident with set pat*idx** pat* = expr The ident**.opt** must be present if and only if the property member is an instance member. When evaluated, the identifier ident is bound to the “this” or “self” object parameter that is associated with the object within the expression expr. A property member is an indexer property if pat*idx*** is not the unit pattern (). Indexer properties called Item are special in the sense that they are accessible via the .[] notation. An Item property that takes one argument is accessed by using x.[i]; with two arguments by x.[i,j], and so on. Setter properties must return type unit. Note: As of F# 3.1, the special .[] notation for Item properties is available only for instance members. A static indexer property cannot be accessible by using the .[] notation. Property members may be declared abstract. If a property has both a getter and a setter, then both must be abstract or neither must be abstract. Each property member has an implied property type. The property type is the type of the value that the getter property returns or the setter property accepts. If a property member has both a getter and a setter, and neither is an indexer property, the signatures of both the getter and the setter must imply the same property type. Static and instance property members are evaluated every time the member is invoked. For example, in the following, the body of the member is evaluated each time C.Time is evaluated: type C () = static member Time = System.DateTime.Now Note that a static property member may also be written with an explicit get method: static member ComputerName with get() = System.Environment.GetEnvironmentVariable("COMPUTERNAME") Property members that have the same name may not appear in the same type definition even if their signatures are different. For example: type C () = static member P = false // error: Duplicate property. member this.P = true However, methods that have the same name can be overloaded when their signatures are different. ### Auto-implemented Properties Properties can be declared in two ways: either explicitly specified with the underlying value or automatically generated by the compiler. The compiler creates a backing field automatically if all of the following are true for the declaration: • The declaration uses the member val keywords. • The declaration omits the self-identifier. • The declaration includes an expression to initialize the property. To create a mutable property, include with get, with set,or both: staticopt member val** access*opt*** ident : ty*opt*** = expr staticopt member val** access*opt*** ident : ty*opt*** = expr with get staticopt member val** access*opt*** ident : ty*opt*** = expr with set staticopt member val** access*opt*** ident : ty*opt*** = expr with get, set Automatically implemented properties are part of the initialization of a type, so they must be included before any other member definitions, in the same way as let bindings and do bindings in a type definition. The expression that initializes an automatically implemented property is evaluated only at initialization, and not every time the property is accessed. This behavior is different from the behavior of an explicitly implemented property. For example, the following class type includes two automatically implemented properties. Property1 is read-only and is initialized to the argument provided to the primary constructor and Property2 is a settable property that is initialized to an empty string: type D (x:int) = member val Property1 = x member val Property2 = "" with get, set Auto-implemented properties can also be used to implement default or override properties: type MyBase () = abstract Property : string with get, set default val Property = “default” with get, set type MyDerived() = inherit MyBase() override val Property = "derived" with get, set The following example shows how to use an auto-implemented property to implement an interface: type MyInterface () = abstract Property : string with get, set type MyImplementation () = interface MyInterface with member val Property = "implemented" with get, set ### Method Members A method member is of the form: staticopt member** ident**.opt** ident pat*1*** ... pat*n*** = expr The ident**.opt** can be present if and only if the property member is an instance member. In this case, the identifier ident corresponds to the “this” (or “self”) variable associated with the object on which the member is being invoked. Arity analysis (§14.10) applies to method members. This is because F# members must compile to CLI methods, which accept only a single fixed collection of arguments. ### Curried Method Members Methods that take multiple arguments may be written in iterated (“curried”) form. For example: static member StaticMethod2 s1 s2 = sprintf "In StaticMethod(%s,%s)" s1 s2 The rules of arity analysis (§14.10) determine the compiled form of these members. The following limitations apply to curried method members: • Additional argument groups may not include optional or byref parameters. • When the member is called, additional argument groups may not use named arguments(§8.13.5). • Curried members may not be overloaded. The compiled representation of a curried method member is a .NET method in which the arguments are concatenated into a single argument group. Note: It is recommended that curried argument members do not appear in the public API of an F# assembly that is designed for use from other .NET languages. Information about the currying order is not visible to these languages. ### Named Arguments to Method Members Calls to methods—but not to let-bound functions or function values—may use named arguments. For example: System.Console.WriteLine(format = "Hello {0}", arg0 = "World") System.Console.WriteLine("Hello {0}", arg0 = "World") System.Console.WriteLine(arg0 = "World", format = "Hello {0}") The argument names that are associated with a method declaration are derived from the names that appear in the first pattern of a member definition, or from the names used in the signature for a method member. For example: type C() = member x.Swap(first, second) = (second, first) let c = C() c.Swap(first = 1,second = 2) // result is '(2,1)' c.Swap(second = 1,first = 2) // result is '(1,2)' Named arguments may be used only with the arguments that correspond to the arity of the member. That is, because members have an arity only up to the first set of tupled arguments, named arguments may not be used with subsequent curried arguments of the member. The resolution of calls that use named arguments is specified in Method Application Resolution (see §14.4). The rules in that section describe how resolution matches a named argument with either a formal parameter of the same name or a “settable” return property of the same name. For example, the following code resolves the named argument to a settable property: System.Windows.Forms.Form(Text = "Hello World") If an ambiguity exists, assigning the named argument is assigned to a formal parameter rather than to a settable return property. The Method Application Resolution (§14.4) rules ensure that: • Named arguments must appear after all other arguments, including optional arguments that are matched by position. After named arguments have been assigned, the remaining required arguments are called the required unnamed arguments. The required unnamed arguments must precede the named arguments in the argument list. The n unnamed arguments are matched to the first n formal parameters; the subsequent named arguments must include only the remaining formal parameters. In addition, the arguments must appear in the correct sequence. For example, the following code is invalid: // error: unnamed args after named System.Console.WriteLine(arg0 = "World", "Hello {0}") Similarly, the following code is invalid: type Foo() = static member M (arg1, arg2, arg3) = 1 // error: arg1, arg3 not a prefix of the argument list Foo.M(1, 2, arg2 = 3) The following code is valid: type Foo() = static member M (arg1, arg2, arg3) = 1 Foo.M (1, 2, arg3 = 3) The names of arguments to members may be listed in member signatures. For example, in a signature file: type C = static member ThreeArgs : arg1:int * arg2:int * arg3:int -> int abstract TwoArgs : arg1:int * arg2:int -> int ### Optional Arguments to Method Members Method members—but not functions definitions—may have optional arguments. Optional arguments must appear at the end of the argument list. An optional argument is marked with a ? before its name in the method declaration. Inside the member, the argument has type option<argType>. The following example declares a method member that has two optional arguments: let defaultArg x y = match x with None -> y | Some v -> v type T() = static member OneNormalTwoOptional (arg1, ?arg2, ?arg3) = let arg2 = defaultArg arg2 3 let arg3 = defaultArg arg3 10 arg1 + arg2 + arg3 Optional arguments may be used in interface and abstract members. In a signature, optional arguments appear as follows: static member OneNormalTwoOptional : arg1:int * ?arg2:int * ?arg3:int -> int Callers may specify values for optional arguments in the following ways: • By name, such as arg2 = 1. • By propagating an existing optional value by name, such as ?arg2=None or ?arg2=Some(3) or ?arg2=arg2. This can be useful when building a method that passes optional arguments on to another method. • By using normal, unnamed arguments that are matched by position. For example: T.OneNormalTwoOptional(3) T.OneNormalTwoOptional(3, 2) T.OneNormalTwoOptional(arg1 = 3) T.OneNormalTwoOptional(arg1 = 3, arg2 = 1) T.OneNormalTwoOptional(arg2 = 3, arg1 = 0) T.OneNormalTwoOptional(arg2 = 3, arg1 = 0, arg3 = 11) T.OneNormalTwoOptional(0, 3, 11) T.OneNormalTwoOptional(0, 3, arg3 = 11) T.OneNormalTwoOptional(arg1 = 3, ?arg2 = Some 1) T.OneNormalTwoOptional(arg2 = 3, arg1 = 0, arg3 = 11) T.OneNormalTwoOptional(?arg2 = Some 3, arg1 = 0, arg3 = 11) T.OneNormalTwoOptional(0, 3, ?arg3 = Some 11) The resolution of calls that use optional arguments is specified in Method Application Resolution (see §14.4). Optional arguments may not be used in member constraints. Note: Imported CLI metadata may specify arguments as optional and may additionally specify a default value for the argument. These are treated as F# optional arguments. CLI optional arguments can propagate an existing optional value by name; for example, ?ValueTitle = Some (…). For example, here is a fragment of a call to a Microsoft Excel COM automation API that uses named and optional arguments. chartobject.Chart.ChartWizard(Source = range5, Gallery = XlChartType.xl3DColumn, PlotBy = XlRowCol.xlRows, HasLegend = true, Title = "Sample Chart", CategoryTitle = "Sample Category Type", ValueTitle = "Sample Value Type") CLI optional arguments are not passed as values of type Option<_>. If the optional argument is present, its value is passed. If the optional argument is omitted, the default value from the CLI metadata is supplied instead. The value System.Reflection.Missing.Value is supplied for any CLI optional arguments of type System.Object that do not have a corresponding CLI default value, and the default (zero-bit pattern) value is supplied for other CLI optional arguments of other types that have no default value. The compiled representation of members varies as additional optional arguments are added. The addition of optional arguments to a member signature results in a compiled form that is not binary-compatible with the previous compiled form. Marking an argument as optional is equivalent to adding the FSharp.Core.OptionalArgument attribute (§17.1) to a required argument. This attribute is added implicitly for optional arguments. Adding the [<OptionalArgument>] attribute to a parameter of type 'a option in a virtual method signature is equivalent to using the (?x:'a) syntax in a method definition. If the attribute is applied to an argument of a method, it should also be applied to all subsequent arguments of the method. Otherwise, it has no effect and callers must provide all of the arguments. ### Type-directed Conversions at Member Invocations As described in Method Application Resolution (see §14.4), three type-directed conversions are applied at method invocations. #### Conversion to Delegates The first type-directed conversion converts anonymous function expressions and other function-valued arguments to delegate types. Given: • A formal parameter of delegate type D • An actual argument farg of known type ty*1*** -> ... -> ty*n*** -> rty • Precisely n arguments to the Invoke method of delegate type D Then: • The parameter is interpreted as if it were written: new D**(fun** arg*1*** ... arg*n*** -> farg arg*1*** ... arg*n***) If the type of the formal parameter is a variable type, then F# uses the known inferred type of the argument including instantiations to determine whether a formal parameter has delegate type. For example, if an explicit type instantiation is given that instantiates a generic type parameter to a delegate type, the following conversion can apply: type GenericClass<'T>() = static member M(arg: 'T) = () GenericClass<System.Action>.M(fun () -> ()) // allowed #### Conversion to Reference Cells The second type-directed conversion enables an F# reference cell to be passed where a byref<ty> is expected. Given: • A formal out parameter of type **byref<**ty> • An actual argument that is not a byref type Then: • The actual parameter is interpreted as if it had type ref<ty>. For example: type C() = static member M1(arg: System.Action) = () static member M2(arg: byref<int>) = () C.M1(fun () -> ()) // allowed let f = (fun () -> ()) in C.M1(f) // not allowed let result = ref 0 C.M2(result) // allowed Note: These type-directed conversions are primarily for interoperability with existing member-based .NET libraries and do not apply at invocations of functions defined in modules or bound locally in expressions. A value of type ref<ty> may be passed to a function that accepts a byref parameter. The interior address of the heap-allocated cell that is associated with such a parameter is passed as the pointer argument. For example, consider the following C# code: public class C { static public void IntegerOutParam(out int x) { x = 3; } } public class D { virtual public void IntegerOutParam(out int x) { x = 3; } } This C# code can be called by the following F# code: let res1 = ref 0 C.IntegerOutParam(res1) // res1.contents now equals 3 Likewise, the abstract signature can be implemented as follows: let x = {new D() with IntegerOutParam(res : byref<int>) = res <- 4} let res2 = ref 0 x.IntegerOutParam(res2); // res2.contents now equals 4 #### Conversion to Quotation Values The third type-directed conversion enables an F# expression to be implicitly quoted at a member call. Conversion to a quotation value is driven by the ReflectedDefinition attribute to a method argument of type FSharp.Quotations.Expr<_>: static member Plot([<ReflectedDefinition>] values:Expr<int>) = (...) The intention is that this gives an implicit quotation from X --> <@ X @> at the callsite. So for Chart.Plot(f x + f y) the caller becomes: Chart.Plot(<@ f x + f y @>) Additionally, the method can declare that it wants both the quotation and the evaluation of the expression, by giving "true" as the "includeValue" argument of the ReflectedDefinitionAttribute. static member Plot([<ReflectedDefinition(true)>] values:Expr<X>) = (...) So for Chart.Plot(f x + f y) the caller becomes: Chart.Plot(Expr.WithValue(f x + f y, <@ f x + f y @>)) and the quotation value Q received by Chart.Plot matches: match Q with | Expr.WithValue(v, ty) --> // v = f x + f y | … Methods with ReflectedDefinition arguments may be used as first class values (including pipelined uses), but it will not normally be useful to use them in this way. This is because, in the above example, a first-class use of the method Chart.Plot is considered shorthand for (fun x -> C.Plot(x)) for some compiler-generated local name “x”, which will become (fun x -> C.Plot( <@ x @> )), so the implicit quotation will just be a local value substitution. This means a pipelines use expr |> C.Plot will not capture a full quotation for expr, but rather just its value. The same applies to auto conversions for LINQ expressions: if you pipeline a method accepting Expression arguments. This is an intrinsic cost of having an auto-quotation meta-programming facility. All uses of auto-quotation need careful use API designers. Auto-quotation of arguments only applies at method calls, and not function calls. The conversion only applies if the called-argument-type is type Expr for some type T, and if the caller-argument type is not of the form Expr for any U. The caller-argument-type is determined as normal, with the addition that a caller argument of the form <@ … @> is always considered to have a type of the form Expr<>, in the same way that caller arguments of the form (fun x -> …) are always assumed to have type of the form  -> _ (i.e. a function type) #### Conversion to LINQ Expressions The third type-directed conversion enables an F# expression to be implicitly converted to a LINQ expression at a method call. Conversion is driven by an argument of type System.Linq.Expressions.Expression. static member Plot(values:Expression<Func<int,int>>) = (...) This attribute results in an implicit quotation from X --> <@ X @> at the callsite and a call for a helper function. So for Chart.Plot(f x + f y) the caller becomes: Chart.Plot(FSharp.Linq.RuntimeHelpers.LeafExpressionConverter. QuotationToLambdaExpression <@ f x + f y @>) ### Overloading of Methods Multiple methods that have the same name may appear in the same type definition or extension. For example: type MyForm() = inherit System.Windows.Forms.Form() member x.ChangeText(text: string) = x.Text <- text member x.ChangeText(text: string, reason: string) = x.Text <- text System.Windows.Forms.MessageBox.Show ("changing text due to " + reason) Methods must be distinct based on their name and fully inferred types, after erasure of type abbreviations and unit-of-measure annotations. Methods that take curried arguments may not be overloaded. ### Naming Restrictions for Members A member in a record type may not have the same name as a record field in that type. A member may not have the same name and signature as another method in the type. This check ignores return types except for members that are named op_Implicit or op_Explicit. ### Members Represented as Events Events are the CLI notion of a “listening point”—that is, a configurable object that holds a set of callbacks, which can be triggered, often by some external action such as a mouse click or timer tick. In F#, events are first-class values; that is, they are objects that mediate the addition and removal of listeners from a backing list of listeners. The F# library supports the type FSharp.Control.IEvent<_,_> and the module FSharp.Control.Event, which contains operations to map, fold, create, and compose events. The type is defined as follows: type IDelegateEvent<'del when 'del :> System.Delegate > = abstract AddHandler : 'del -> unit abstract RemoveHandler : 'del -> unit type IEvent<'Del,'T when 'Del : delegate<'T,unit> and 'del :> System.Delegate > = abstract Add : event : ('T -> unit) -> unit inherit IDelegateEvent<'del> type Handler<'T> = delegate of sender : obj * 'T -> unit type IEvent<'T> = IEvent<Handler<'T>, 'T> The following shows a sample use of events: open System.Windows.Forms type MyCanvas() = inherit Form() let event = new Event<PaintEventArgs>() member x.Redraw = event.Publish override x.OnPaint(args) = event.Trigger(args) let form = new MyCanvas() form.Redraw.Add(fun args -> printfn "OnRedraw") form.Activate() Application.Run(form) Events from CLI languages are revealed as object properties of type FSharp.Control.IEvent<tydelegate, tyargs>. The F# compiler determines the type arguments, which are derived from the CLI delegate type that is associated with the event. Event declarations are not built into the F# language, and event is not a keyword. However, property members that are marked with the CLIEvent attribute and whose type coerces to FSharp.Control.IDelegateEvent<tydelegate> are compiled to include extra CLI metadata and methods that mark the property name as a CLI event. For example, in the following code, the ChannelChanged property is currently compiled as a CLI event: type ChannelChangedHandler = delegate of obj * int -> unit type C() = let channelChanged = new Event<ChannelChangedHandler,_>() [<CLIEvent>] member self.ChannelChanged = channelChanged.Publish Similarly, the following shows the definition and implementation of an abstract event: type I = [<CLIEvent>] abstract ChannelChanged : IEvent<ChannelChanged,int> type ImplI() = let channelChanged = new Event<ChannelChanged,_>() interface I with [<CLIEvent>] member self.ChannelChanged = channelChanged.Publish ### Members Represented as Static Members Most members are represented as their corresponding CLI method or property. However, in certain situations an instance member may be compiled as a static method. This happens when either of the following is true: • The type definition uses null as a representation by placing the CompilationRepresentation(CompilationRepresentationFlags.UseNullAsTrueValue) attribute on the type that declares the member. • The member is an extension member. Compilation of an instance member as a static method can affect the view of the type when seen from other languages or from System.Reflection. A member that might otherwise have a static representation can be reverted to an instance member representation by placing the attribute CompilationRepresentation(CompilationRepresentationFlags.Instance) on the member. For example, consider the following type: **[<CompilationRepresentation(CompilationRepresentationFlags.UseNullAsTrueValue)>] type option<'T> = | None | Some of 'T member x.IsNone = match x with None -> true | _ -> false member x.IsSome = match x with Some _ -> true | _ -> false [<CompilationRepresentation(CompilationRepresentationFlags.Instance)>] member x.Item = match x with | Some x -> x | None -> failwith "Option.Item"** The IsNone and IsSome properties are represented as CLI static methods. The Item property is represented as an instance property. ## Abstract Members and Interface Implementations Abstract member definitions and interface declarations in a type definition represent promises that an object will provide an implementation for a corresponding contract. ### Abstract Members An abstract member definition in a type definition represents a promise that an object will provide an implementation for a dispatch slot. For example: type IX = abstract M : int -> int The abstract member M indicates that an object of type IX will implement a displatch slot for a member that returns an int. A class definition may contain abstract member definitions, but the definition must be labeled with the AbstractClass attribute: [<AbstractClass>] type X() = abstract M : int -> int An abstract member definition has the form abstract access*opt*** member-sig where a member signature has one of the following forms ident typar-defns*opt** : curried-sig* ident typar-defns*opt** : curried-sig* with get ident typar-defns*opt** : curried-sig* with set ident typar-defns*opt** : curried-sig* with get, set ident typar-defns*opt** : curried-sig* with set, get and the curried signature has the form args-spec*1*** -> ... -> args-spec*n** -> type* If n ≥ 2, then args-spec*2*** … args-spec*n*** must all be patterns without attribute or optional argument specifications. If get or set is specified, the abstract member is a property member. If both get and set are specified, the abstract member is equivalent to two abstract members, one with get and one with set. ### Members that Implement Abstract Members An implementation member has the form: override ident**.ident pat1** ... pat*n*** = expr default ident**.ident pat1** ... pat*n*** = expr Implementation members implement dispatch slots. For example: [<AbstractClass>] type BaseClass() = abstract AbstractMethod : int -> int type SubClass(x: int) = inherit BaseClass() override obj.AbstractMethod n = n + x let v1 = BaseClass() // not allowed – BaseClass is abstract let v2 = (SubClass(7) :> BaseClass) v2.AbstractMethod 6 // evaluates to 13 In this example, BaseClass() declares the abstract slot AbstractMethod and the SubClass type supplies an implementation member obj.AbstractMethod, which takes an argument n and returns the sum of n and the argument that was passed in the instantiation of SubClass. The v2 object instantiates SubClass with the value 7, so v2.AbstractMethod 6 evaluates to 13. The combination of an abstract slot declaration and a default implementation of that slot create the F# equivalent of a “virtual” method in some other languages—that is, an abstract member that is guaranteed to have an implementation. For example: type BaseClass() = abstract AbstractMethodWithDefaultImplementation : int -> int default obj.AbstractMethodWithDefaultImplementation n = n type SubClass1(x: int) = inherit BaseClass() override obj.AbstractMethodWithDefaultImplementation n = n + x type SubClass2() = inherit BaseClass() let v1 = BaseClass() // allowed -- BaseClass contains a default implementation let v2 = (SubClass1(7) :> BaseClass) let v3 = (SubClass2() :> BaseClass) v1.AbstractMethodWithDefaultImplementation 6 // evaluates to 6 v2.AbstractMethodWithDefaultImplementation 6 // evaluates to 13 v3.AbstractMethodWithDefaultImplementation 6 // evaluates to 6 Here, the BaseClass type contains a default implementation, so F# allows the instantiation of v1. The instantiation of v2 is the same as in the previous example. The instantiation of v3 is similar to that of v1, because SubClass2 inherits directly from BaseClass and does not override the default method. Note: The keywords override and default are synonyms. However, it is recommended that default be used only when the implementation is in the same class as the corresponding abstract definition; override should be used in other cases. This records the intended role of the member implementation. Implementations may override methods from System.Object: type BaseClass() = override obj.ToString() = "I'm an instance of BaseClass" type SubClass(x: int) = inherit BaseClass() override obj.ToString() = "I'm an instance of SubClass" In this example, BaseClass inherits from System.Object and overrides the ToString method from that class. The SubClass, in turn, inherits from BaseClass and overrides its version of the ToString method. Implementations may include abstract property members: [<AbstractClass>] type BaseClass() = let mutable data1 = 0 let mutable data2 = 0 abstract AbstractProperty : int abstract AbstractSettableProperty : int with get, set abstract AbstractPropertyWithDefaultImplementation : int default obj.AbstractPropertyWithDefaultImplementation = 3 abstract AbstractSettablePropertyWithDefaultImplementation : int with get, set default obj.AbstractSettablePropertyWithDefaultImplementation with get() = data2 and set v = data2 <- v type SubClass(x: int) = inherit BaseClass() let mutable data1b = 0 let mutable data2b = 0 override obj.AbstractProperty = 3 + x override obj.AbstractSettableProperty with get() = data1b + x and set v = data1b <- v - x override obj.AbstractPropertyWithDefaultImplementation = 6 + x override obj.AbstractSettablePropertyWithDefaultImplementation with get() = data2b + x and set v = data2b <- v - x The same rules apply to both property members and method members. In the preceding example, BaseClass includes abstract properties named AbstractProperty, AbstractSettableProperty, AbstractPropertyWithDefaultImplementation, and AbstractSettablePropertyWithDefaultImplementation and provides default implementations for the latter two. SubClass provides implementations for AbstractProperty and AbstractSettableProperty, and overrides the default implementations for AbstractPropertyWithDefaultImplementation and AbstractSettablePropertyWithDefaultImplementation. Implementation members may also implement CLI events (§8.13.10). In this case, the member should be marked with the CLIEvent attribute. For example: type ChannelChangedHandler = delegate of obj * int -> unit [<AbstractClass>] type BaseClass() = [<CLIEvent>] abstract ChannelChanged : IEvent<ChannelChangedHandler, int> type SubClass() = inherit BaseClass() let mutable channel = 7 let channelChanged = new Event<ChannelChangedHandler, int>() [<CLIEvent>] override self.ChannelChanged = channelChanged.Publish member self.Channel with get () = channel and set v = channel <- v; channelChanged.Trigger(self, channel) BaseClass implements the CLI event IEvent, so the abstract member ChannelChanged is marked with [<CLIEvent>] as described earlier in §8.13.10. SubClass provides an implementation of the abstract member, so the [<CLIEvent>] attribute must also precede the override declaration in SubClass. ### Interface Implementations An interface implementation specifies how objects of a given type support a particular interface. An interface in a type definition indicates that objects of the defined type support the interface. For example: type IIncrement = abstract M : int -> int type IDecrement = abstract M : int -> int type C() = interface IIncrement with member x.M(n) = n + 1 interface IDecrement with member x.M(n) = n - 1 The first two definitions in the example are implementations of the interfaces IIncrement and IDecrement. In the last definition,the type C supports these two interfaces. No type may implement multiple different instantiations of a generic interface, either directly or through inheritance. For example, the following is not permitted: // This type definition is not permitted because it implements two instantiations // of the same generic interface type ClassThatTriesToImplemenTwoInstantiations() = interface System.IComparable<int> with member x.CompareTo(n : int) = 0 interface System.IComparable<string> with member x.CompareTo(n : string) = 1 Each member of an interface implementation is checked as follows: • The member must be an instance member definition. • Dispatch Slot Inference (§14.7) is applied. • The member is checked under the assumption that the “this” variable has the enclosing type. In the following example, the value x has type C. type C() = interface IIncrement with member x.M(n) = n + 1 interface IDecrement with member x.M(n) = n - 1 All interface implementations are made explicit. In its first implementation, every interface must be completely implemented, even in an abstract class. However, interface implementations may be inherited from a base class. In particular, if a class C implements interface I, and a base class of C implements interface I, then C is not required to implement all the methods of I;it can implement all, some, or none of the methods instead. For example: type I1 = abstract V1 : string abstract V2 : string type I2 = inherit I1 abstract V3 : string type C1() = interface I1 with member this.V1 = "C1" member this.V2 = "C2" // This is OK type C2() = inherit C1() // This is also OK; C3 implements I2 but not I1. type C3() = inherit C1() interface I2 with member this.V3 = "C3" // This is also OK; C4 implements one method in I1. type C4() = inherit C1() interface I1 with member this.V2 = "C2b" ## Equality, Hashing, and Comparison Functional programming in F# frequently involves the use of structural equality, structural hashing, and structural comparison. For example, the following expression evaluates to true, because tuple types support structural equality: (1, 1 + 1) = (1, 2) Likewise, these two function calls return identical values: hash (1, 1 +1 ) hash (1,2) Similarly, an ordering on constituent parts of a tuple induces an ordering on tuples themselves, so all the following evaluate to true: (1, 2) < (1, 3) (1, 2) < (2, 3) (1, 2) < (2, 1) (1, 2) > (1, 0) The same applies to lists, options, arrays, and user-defined record, union, and struct types whose constituent field types permit structural equality, hashing, and comparison. For example, given: type R = R of int * int then all of the following also evaluate to true: R (1, 1 + 1) = R (1, 2) R (1, 3) <> R (1, 2) hash (R (1, 1 + 1)) = hash (R (1, 2)) R (1, 2) < R (1, 3) R (1, 2) < R (2, 3) R (1, 2) < R (2, 1) R (1, 2) > R (1, 0) To facilitate this, by default, record, union, and struct type definitions—called structural types—implicitly include compiler-generated declarations for structural equality, hashing, and comparison. These implicit declarations consist of the following for structural equality and hashing: override x.GetHashCode() = ... override x.Equals(y:obj) = ... interface System.Collections.IStructuralEquatable with member x.Equals(yobj: obj, comparer: System.Collections.IEqualityComparer) = ... member x.GetHashCode(comparer: System.IEqualityComparer) = ... The following declarations enable structural comparison: interface System.IComparable with member x.CompareTo(y:obj) = ... interface System.Collections.IStructuralComparable with member x.CompareTo(yobj: obj, comparer: System.Collections.IComparer) = ... For exception types, implicit declarations for structural equality and hashings are generated, but declarations for structural comparison are not generated. Implicit declarations are never generated for interface, delegate, class, or enum types. Enum types implicitly derive support for equality, hashing, and comparison through their underlying representation as integers. ### Equality Attributes Several attributes affect the equality behavior of types: FSharp.Core.NoEquality FSharp.Core.ReferenceEquality FSharp.Core.StructuralEquality FSharp.Core.CustomEquality The following table lists the effects of each attribute on a type: Attrribute Effect NoEquality • No equality or hashing is generated for the type. • The type does not satisfy the ty : equality constraint. ReferenceEquality • No equality or hashing is generated for the type. • The defaults for System.Object will implicitly be used. StructuralEquality • The type must be a structural type. • All structural field types ty must satisfy ty : equality. CustomEquality • The type must have an explicit implementation of override Equals(obj: obj) None • For a non-structural type, the default is ReferenceEquality. • For a structural type: The default is NoEquality if any structural field type F fails F : equality. The default is StructuralEquality if all structural field types F satisfy F : equality. Equality inference also determines the constraint dependencies of a generic structural type. That is: • If a structural type has a generic parameter 'T and T : equality is necessary to make the type default to StructuralEquality, then the EqualityConditionalOn constraint dependency is inferred for 'T. ### Comparison Attributes The comparison behavior of types can be affected by the following attributes: FSharp.Core.NoComparison FSharp.Core.StructuralComparison FSharp.Core.CustomComparison The following table lists the effects of each attribute on a type. Attribute Effect NoComparison • No comparisons are generated for the type. • The type does not satisfy the ty : comparison constraint. StructuralComparison • The type must be a structural type other than an exception type. • All structural field types must ty satisfy ty : comparison. • An exception type may not have the StructuralComparison attribute. CustomComparison • The type must have an explicit implementation of one or both of the following: interface System.IComparable interface System.Collections.IStructuralComparable • A structural type that has an explicit implementation of one or both of these contracts must specify the CustomComparison attribute. None • For a non-structural or exception type, the default is NoComparison. • For any other structural type: The default is NoComparison if any structural field type F fails F : comparison. The default is StructuralComparison if all structural field types F satisfy F : comparison. This check also determines the constraint dependencies of a generic structural type. That is: • If a structural type has a generic parameter 'T and T : comparison is necessary to make the type default to StructuralComparison, then the ComparisonConditionalOn constraint dependency is inferred for 'T. For example: [<StructuralEquality; StructuralComparison>] type X = X of (int -> int) results in the following message: The struct, record or union type 'X' has the 'StructuralEquality' attribute but the component type '(int -> int)' does not satisfy the 'equality' constraint For example, given **type R1 = { myData : int } static member Create() = { myData = 0 } [<ReferenceEquality>] type R2 = { mutable myState : int } static member Fresh() = { myState = 0 } [<StructuralEquality; NoComparison >] type R3 = { someType : System.Type } static member Make() = { someType = typeof<int> }** then the following expressions all evaluate to true: R1.Create() = R1.Create() not (R2.Fresh() = R2.Fresh()) R3.Make() = R3.Make() Combinations of equality and comparion attributes are restricted. If any of the following attributes are present, they may be used only in the following combinations: • No attributes • [<NoComparison>] on any type • [<NoEquality; NoComparison>] on any type • [<CustomEquality; NoComparison>] on a structural type • [<ReferenceEquality>] on a non-struct structural type • [<ReferenceEquality; NoComparison>] on a non-struct structural type • [<StructuralEquality; NoComparison>] on a structural type • [<CustomEquality; CustomComparison>] on a structural type • [<StructuralEquality; CustomComparison>] on a structural type • [<StructuralEquality; StructuralComparison>] on a structural type ### Behavior of the Generated Object.Equals Implementation For a type definition T, the behavior of the generated override x.Equals(y:obj) = ... implementation is as follows. 1. If the interface System.IComparable has an explicit implementation, then just call System.IComparable.CompareTo: override x.Equals(y : obj) = ((x :> System.IComparable).CompareTo(y) = 0) 2. Otherwise: • Convert the y argument to type T. If the conversion fails, return false. • Return false if T is a reference type and y is null. • If T is a struct or record type, invoke FSharp.Core.Operators.(=) on each corresponding pair of fields of x and y in declaration order. This method stops at the first false result and returns false. • If T is a union type, invoke FSharp.Core.Operators.(=) first on the index of the union cases for the two values, then on each corresponding field pair of x and y for the data carried by the union case. This method stops at the first false result and returns false. • If T is an exception type, invoke FSharp.Core.Operators.(=) on the index of the tags for the two values, then on each corresponding field pair for the data carried by the exception. This method stops at the first false result and returns false. ### Behavior of the Generated CompareTo Implementations For a type T, the behavior of the generated System.IComparable.CompareTo implementation is as follows: • Convert the y argument to type T . If the conversion fails, raise the InvalidCastException. • If T is a reference type and y is null, return 1. • If T is a struct or record type, invoke FSharp.Core.Operators.compare on each corresponding pair of fields of x and y in declaration order, and return the first non-zero result. • If T is a union type, invoke FSharp.Core.Operators.compare first on the index of the union cases for the two values, and then on each corresponding field pair of x and y for the data carried by the union case. Return the first non-zero result. The first few lines of this code can be written: interface System.IComparable with member x.CompareTo(y:obj) = let y = (obj :?> T) in match obj with | null -> 1 | _ -> ... ### Behavior of the Generated GetHashCode Implementations For a type T, the generated System.Object.GetHashCode() override implements a combination hash of the structural elements of a structural type. ### Behavior of Hash, =, and Compare The generated equality, hashing, and comparison declarations that are described in sections 8.15.3, 8.15.4, and 8.15.5 use the hash, = and compare functions from the F# library. The behavior of these library functions is defined by the pseudocode later in this section. This code ensures: • Ordinal comparison for strings • Structural comparison for arrays • Natural ordering for native integers (which do not support System.IComparable) #### Pseudocode for FSharp.Core.Operators.compare Note: In practice, fast (but semantically equivalent) code is emitted for direct calls to (=), compare, and hash for all base types, and faster paths are used for comparing most arrays. open System /// Pseudo code for code implementation of generic comparison. let rec compare x y = let xobj = box x let yobj = box y match xobj, yobj with | null, null -> 0 | null, _ -> -1 | _, null -> 1 // Use Ordinal comparison for strings | (:? string as x),(:? string as y) -> String.CompareOrdinal(x, y) // Special types not supporting IComparable | (:? Array as arr1), (:? Array as arr2) -> ... compare the arrays by rank, lengths and elements ... | (:? nativeint as x),(:? nativeint as y) -> ... compare the native integers x and y.... | (:? unativeint as x),(:? unativeint as y) -> ... compare the unsigned integers x and y.... // Check for IComparable | (:? IComparable as x),_ -> x.CompareTo(yobj) | _,(:? IComparable as yc) -> -(sign(yc.CompareTo(xobj))) // Otherwise raise a runtime error | _ -> raise (new ArgumentException(...)) #### Pseudo code for FSharp.Core.Operators.(=) Note: In practice, fast (but semantically equivalent) code is emitted for direct calls to (=), compare, and hash for all base types, and faster paths are used for comparing most arrays open System /// Pseudo code for core implementation of generic equality. let rec (=) x y = let xobj = box x let yobj = box y match xobj,yobj with | null,null -> true | null,_ -> false | _,null -> false // Special types not supporting IComparable | (:? Array as arr1), (:? Array as arr2) -> ... compare the arrays by rank, lengths and elements ... // Ensure NaN semantics on recursive calls | (:? float as f1), (:? float as f2) -> ... IEEE equality on f1 and f2... | (:? float32 as f1), (:? float32 as f2) -> ... IEEE equality on f1 and f2... // Otherwise use Object.Equals. This is reference equality // for reference types unless an override is provided (implicitly // or explicitly). | _ -> xobj.Equals(yobj) # Units Of Measure F# supports static checking of units of measure. Units of measure, or measures for short, are like types in that they can appear as parameters to other types and values (as in float<kg>, vector<m/s>, add<m>), can contain variables (as in float<'U>), and are checked for consistency by the type-checker. However, measures differ from types in several important ways: • Measures play no role at runtime; in fact, they are erased. • Measures obey special rules of equivalence, so that N m can be interchanged with m N. • Measures are supported by special syntax. The syntax of constants (§4.3) is extended to support numeric constants with units of measure. The syntax of types is extended with measure type annotations. measure-literal-atom := long-ident -- named measure e.g. kg ( measure-literal-simp ) -- parenthesized measure, such as (N m) measure-literal-power := *measure-literal-atom • measure-literal-atom ^ int32 -- power of measure, such as m^3 measure-literal-seq := measure-literal-power measure-literal-power measure-literal-seq measure-literal-simp := measure-literal-seq -- implicit product, such as m s^-2 measure-literal-simp * measure-literal-simp -- product, such as m * s^3 measure-literal-simp / measure-literal-simp -- quotient, such as m/s^2 / measure-literal-simp -- reciprocal, such as /s 1 -- dimensionless measure-literal := _ -- anonymous measure measure-literal-simp -- simple measure, such as N m const := ... sbyte < measure-literal > -- 8-bit integer constant int16 < measure-literal > -- 16-bit integer constant int32 < measure-literal > -- 32-bit integer constant int64 < measure-literal > -- 64-bit integer constant ieee32 < measure-literal > -- single-precision float32 constant ieee64 < measure-literal > -- double-precision float constant decimal < measure-literal > -- decimal constant measure-atom := typar -- variable measure, such as 'U long-ident -- named measure, such as kg ( measure-simp **) -- parenthesized measure, such as (N m) ** measure-power := measure-atom measure-atom ^ int32 -- power of measure, such as m^3 measure-seq := measure-power measure-power measure-seq measure-simp := measure-seq -- implicit product, such as 'U 'V^3 measure-simp * measure-simp -- product, such as 'U * 'V measure-simp / measure-simp -- quotient, such as 'U / 'V / measure-simp -- reciprocal, such as /'U 1 -- dimensionless measure (no units) measure := _ -- anonymous measure measure-simp -- simple measure, such as 'U 'V Measure definitions use the special Measure attribute on type definitions. Measure parameters use the syntax of generic parameters with the same special Measure attribute to parameterize types and members by units of measure. The primitive types sbyte, int16, int32, int64, float, float32, and decimal have non-parameterized (dimensionless) and parameterized versions. Here is a simple example: [<Measure>] type m // base measure: meters [<Measure>] type s // base measure: seconds [<Measure>] type sqm = m^2 // derived measure: square meters let areaOfTriangle (baseLength:float<m>, height:float<m>) : float<sqm> = baseLength*height/2.0 let distanceTravelled (speed:float<m/s>, time:float<s>) : float<m> = speed*time As with ordinary types, F# can infer that functions are generic in their units. For example, consider the following function definitions: let sqr (x:float<_>) = x*x let sumOfSquares x y = sqr x + sqr y The inferred types are: val sqr : float<'u> -> float<'u ^ 2> val sumOfSquares : float<'u> -> float<'u> -> float<'u ^ 2> Measures are type-like annotations such as kg or m/s or m^2. Their special syntax includes the use of * and / for product and quotient of measures, juxtaposition as shorthand for product, and ^ for integer powers. ## Measures Measures are built from: • Atomic measures from long identifiers such as SI.kg or MyUnits.feet. • Product measures, which are written measure measure (juxtaposition ) or measure * measure. • Quotient measures, which are written measure / measure. • Integer powers of measures, which are written measure ^ int. • Dimensionless measures, which are written 1. • Variable measures, which are written 'u or 'U. Variable measures can include anonymous measures _, which indicates that the compiler can infer the measure from the context. Dimensionless measures indicate “without units,” but are rarely needed, because non-parameterized types such as float are aliases for the parameterized type with 1 as parameter, that is, float = float<1>. The precedence of operations involving measure is similar to that for floating-point expressions: • Products and quotients (* and /) have the same precedence, and associate to the left, but juxtaposition has higher syntactic precedence than both * and /. • Integer powers (^) have higher precedence than juxtaposition. • The / symbol can also be used as a unary reciprocal operator. ## Constants Annotated by Measures A floating-point constant can be annotated with its measure by specifying a literal measure in angle brackets following the constant. Measure annotations on constants may not include measure variables. Here are some examples of annotated constants: let earthGravity = 9.81f<m/s^2> let atmosphere = 101325.0<N m^-2> let zero = 0.0f<_> Constants that are annotated with units of measure are assigned a corresponding numeric type with the measure parameter that is specified in the annotation. In the example above, earthGravity is assigned the type float32<m/s^2>, atmosphere is assigned the type float<N/m^2> and zero is assigned the type float<'U>. ## Relations on Measures After measers are parsed and checked, they are maintained in the following normalized form: measure-int := 1 | long-ident | measure-par | measure-int measure-int | / measure-int Powers of measures are expanded. For example, kg^3 is equivalent to kg kg kg. Two measures are indistinguishable if they can be made equivalent by repeated application of the following rules: • Commutativity. measure-int*1** measure-int**2*** is equivalent to measure-int*2** measure-int**1***. • Associativity. It does not matter what grouping is used for juxtaposition (product) of measures, so parentheses are not required. For example, kg m s can be split as the product of kg m and s, or as the product of kg and m s. • Identity. 1 measure-int is equivalent to measure-int. • Inverses. measure-int / measure-int is equivalent to 1. • Abbreviation. long-ident is equivalent to measure if a measure abbreviation of the form [<Measure>] type long-ident = measure is currently in scope. Note that these are the laws of Abelian groups together with expansion of abbreviations. For example, kg m / s^2 is the same as m kg / s^2. For presentation purposes (for example, in error messages), measures are presented in the normalized form that appears at the beginning of this section, but with the following restrictions: • Powers are positive and greater than 1. This splits the measure into positive powers and negative powers, separated by /. • Atomic measures are ordered as follows: measure parameters first, ordered alphabetically, followed by measure identifiers, ordered alphabetically. For example, the measure expression m^1 kg s^-1 would be normalized to kg m / s. This normalized form provides a convenient way to check the equality of measures: given two measure expressions measure-int*1*** and measure-int*2***, reduce each to normalized form by using the rules of commutativity, associativity, identity, inverses and abbreviation, and then compare the syntax. To check the equality of two measures, abbreviations are expanded to compare their normalized forms. However, abbreviations are not expanded for presentation. For example, consider the following definitions: [<Measure>] type a [<Measure>] type b = a * a let x = 1<b> / 1<a> The inferred type is presented as int<b/a>, not int<a>. If a measure is equivalent to 1, however, abbreviations are expanded to cancel each other and are presented without units: let y = 1<b> / 1<a a> // val y : int = 1 ### Constraint Solving The mechanism described in §14.5 is extended to support equational constraints between measure expressions. Such expressions arise from equations between parameterized types—that is, when type**<tyarg11,..., tyarg1n> = type<tyarg21,..., tyarg2n> is reduced to a series of constraints tyarg1i** = tyarg*2i***. For the arguments that are measures, rather than types, the rules listed in §9.3 are applied to obtain primitive equations of the form 'U = measure-int where 'U is a measure variable and measure-int is a measure expression in internal form. The variable 'U is then replaced by measure-int wherever else it occurs. For example, the equation float<m^2/s^2> = float<'U^2> would be reduced to the constraint m^2/s^2 = 'U^2, which would be further reduced to the primitive equation 'U = m/s. If constraints cannot be solved, a type error occurs. For example, the following expression fun (x : float<m^2>, y : float<s>) -> x + y would eventually)result in the constraint m^2 = s, which cannot be solved, indicating a type error. ### Generalization of Measure Variables Analogous to the process of generalization of type variables described in §14.6.7, a generalization procedure produces measure variables over which a value, function, or member can be generalized. ## Measure Definitions Measure definitions define new named units of measure by using the same syntax as for type definitions, with the addition of the Measure attribute. For example: [<Measure>] type kg [<Measure>] type m [<Measure>] type s [<Measure>] type N = kg / m s^2 A primitive measure abbreviation defines a fresh, named measure that is distinct from other measures. Measure abbreviations, like type abbreviations, define new names for existing measures. Also like type abbreviations, repeatedly eliminating measure abbreviations in favor of their equivalent measures must not result in infinite measure expressions. For example, the following is not a valid measure definition because it results in the infinite squaring of X: [<Measure>] type X = X^2 Measure definitions and abbreviations may not have type or measure parameters. ## Measure Parameter Definitions Measure parameter definitions can appear wherever ordinary type parameter definitions can (see §5.2.9). If an explicit parameter definition is used, the parameter name is prefixed by the special Measure attribute. For example: val sqr<[<Measure>] 'U> : float<'U> -> float<'U^2> type Vector<[<Measure>] 'U> = { X: float<'U>; Y: float<'U>; Z: float<'U>} type Sphere<[<Measure>] 'U> = { Center:Vector<'U>; Radius:float<'U> } type Disc<[<Measure>] 'U> = { Center:Vector<'U>; Radius:float<'U>; Norm:Vector<1> } type SceneObject<[<Measure>] 'U> = | Sphere of Sphere<'U> | Disc of Disc<'U> Internally, the type checker distinguishes between type parameters and measure parameters by assigning one of two sorts (Type or Measure) to each parameter. This technique is used to check the actual arguments to types and other parameterized definitions. The type checker rejects ill-formed types such as float<int> and IEnumerable<m/s>. ## Measure Parameter Erasure In contrast to type parameters on generic types, measure parameters are not exposed in the metadata that the runtime interprets; instead, measures are erased. Erasure has several consequences: • Casting is with respect to erased types. • Method application resolution (see §14.4) is with respect to erased types. • Reflection is with respect to erased types. ## Type Definitions with Measures in the F# Core Library The F# core library defines the following types: type float<[<Measure>] 'U> type float32<[<Measure>] 'U> type decimal<[<Measure>] 'U> type int<[<Measure>] 'U> type sbyte<[<Measure>] 'U> type int16<[<Measure>] 'U> type int64<[<Measure>] 'U> Note: These definitions are called measure-annotated base types and are marked with the MeasureAnnotatedAbbreviation attribute in the implementation of the library. The MeasureAnnotatedAbbreviation attribute is not for use in user code and in future revisions of the language may result in a warning or error. These type definitions have the following special properties: • They extend System.ValueType. • They explicitly implement System.IFormattable, System.IComparable, System.IConvertible, and corresponding generic interfaces, instantiated at the given type—for example, System.IComparable<float<'u>> and System.IEquatable<float<'u>> (so that you can invoke, for example, CompareTo after an explicit upcast). • As a result of erasure, their compiled form is the corresponding primitive type. • For the purposes of constraint solving and other logical operations on types, a type equivalence holds between the unparameterized primitive type and the corresponding measured type definition that is instantiated at <1>: sbyte = sbyte<1> int16 = int16<1> int32 = int32<1> int64 = int64<1> float = float<1> float32 = float32<1> decimal = decimal<1> • The measured type definitions sbyte, int16, int32, int64, float32, float, and decimal are assumed to have additional static members that have the measure types that are listed in the table. Note that N is any of these types, and F is either float32 or float. Member Measure Type Sqrt F<'U^2> -> F<'U> Atan2 F<'U> -> F<'U> -> F<1> op_Addition op_Subtraction op_Modulus N<'U> -> N<'U> -> N<'U> op_Multiply N<'U> -> N<'V> -> N<'U 'V> op_Division N<'U> -> N<'V> -> N<'U/'V> Abs op_UnaryNegation op_UnaryPlus N<'U> -> N<'U> Sign N<'U> -> int This mechanism is used to support units of measure in the following math functions of the F# library: (+),(-), (*), (/),(%),(~+),(~-),abs, sign, atan2 and sqrt. ## Restrictions Measures can be used in range expressions but a properly measured step is required. For example, these are not allowed: [<Measure>] type s [1<s> .. 5<s>] // error: The type 'int<s>' does not match the type 'int' [1<s> .. 1 .. 5<s>] // error: The type 'int<s>' does not match the type 'int' However, the following range expression is valid: [1<s> .. 1<s> .. 5<s>] // int<s> list = [1; 2; 3; 4; 5] # Namespaces and Modules F# is primarily an expression-based language. However, F# source code units are made up of declarations, some of which can contain further declarations. Declarations are grouped using namespace declaration groups, type definitions, and module definitions. These also have corresponding forms in signatures. For example, a file may contain multiple namespace declaration groups, each of which defines types and modules, and the types and modules may contain member, function, and value definitions, which contain expressions. Declaration elements are processed in the context of an environment. The definition of the elements of an environment is found in §14.1. namespace-decl-group := namespace long-ident module-elems -- elements within a namespace namespace global module-elems -- elements within no namespace module-defn := attributes*opt*** module access*opt*** ident = module-defn-body module-defn-body := begin module-elems*opt*** end module-elem := module-function-or-value-defn -- function or value definitions type-defns -- type definitions exception-defn -- exception definitions module-defn -- module definitions module-abbrev -- module abbreviations import-decl -- import declarations compiler-directive-decl -- compiler directives module-function-or-value-defn := attributes*opt*** let function-defn attributes*opt*** let value-defn attributes*opt*** let recopt** function-or-value-defns attributes*opt*** do expr import-decl := open long-ident module-abbrev := module ident = long-ident compiler-directive-decl := # ident string ... string module-elems := module-elem ... module-elem access := private internal public ## Namespace Declaration Groups Modules and types in an F# program are organized into namespaces, which encompass the identifiers that are defined in the modules and types*.* New components may contribute entities to existing namespaces. Each such contribution to a namespace is called a namespace declaration group. In the following example, the MyCompany.MyLibrary namespace contains Values and x: namespace MyCompany.MyLibrary module Values1 = let x = 1 A namespace declaration group is the basic declaration unit within an F# implementation file and is of the form namespace long-ident module-elems The long-ident must be fully qualified. Each such group contains a series of module and type definitions that contribute to the indicated namespace. An implementation file may contain multiple namespace declaration groups, as in this example: namespace MyCompany.MyOtherLibrary type MyType() = let x = 1 member v.P = x + 2 module MyInnerModule = let myValue = 1 namespace MyCompany.MyOtherLibrary.Collections type MyCollection(x : int) = member v.P = x Namespace declaration groups may not be nested. A namespace declaration group can contain type and module definitions, but not function or value definitions. For example: namespace MyCompany.MyLibrary // A type definition in a namespace type MyType() = let x = 1 member v.P = x+2 // A module definition in a namespace module MyInnerModule = let myValue = 1 // The following is not allowed: value definitions are not allowed in namespaces let addOne x = x + 1 When a namespace declaration group N is checked in an environment env, the individual declarations are checked in order and an overall namespace declaration group signature N*sig*** is inferred for the module. An entry for N is then added to the ModulesAndNamespaces table in the environment env (see §14.1.3). Like module declarations, namespace declaration groups are processed sequentially rather than simultaneously, so that later namespace declaration groups are not in scope when earlier ones are processed. This prevents invalid recursive definitions. In the following example, the declaration of x in Module1 generates an error because the Utilities.Part2 namespace is not in scope: namespace Utilities.Part1 module Module1 = let x = Utilities.Part2.Module2.x + 1 // error (Part2 not yet declared) namespace Utilities.Part2 module Module2 = let x = Utilities.Part1.Module1.x + 2 Within a namespace declaration group, the namespace itself is implicitly opened if any preceding namespace declaration groups or referenced assemblies contribute to it. For example: namespace MyCompany.MyLibrary module Values1 = let x = 1 namespace MyCompany.MyLibrary // Here, the implicit open of MyCompany.MyLibrary brings Values1 into scope module Values2 = let x = Values1.x ## Module Definitions A module definition is a named collection of declarations such as values, types, and function values. Grouping code in modules helps keep related code together and helps avoid name conflicts in your program. For example: module MyModule = let x = 1 type Foo = A | B module MyNestedModule = let f y = y + 1 type Bar = C | D When a module definition M is checked in an environment env*0, the individual declarations are checked in order and an overall module signature Msig* is inferred for the module. An entry for M is then added to the ModulesAndNamespaces table to environment env*0*** to form the new environment used for checking subsequent modules. Like namespace declaration groups, module definitions are processed sequentially rather than simultaneously, so that later modules are not in scope when earlier ones are processed. module Part1 = let x = Part2.StorageCache() // error (Part2 not yet declared) module Part2 = type StorageCache() = member cache.Clear() = () No two types or modules may have identical names in the same namespace. The [<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>] attribute adds the suffix Module to the name of a module to distinguish the module name from a type of a similar name. For example, this is frequently used when defining a type and a set of functions and values to manipulate values of this type. type Cat(kind: string) = member x.Meow() = printfn "meow" member x.Purr() = printfn "purr" member x.Kind = kind [<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>] module Cat = let tabby = Cat "Tabby" let purr (c:Cat) = c.Purr() let purrTwice (c:Cat) = purr(); purr() Cat.tabby |> Cat.purr |> Cat.purrTwice ### Function and Value Definitions in Modules Function and value definitionsin modules introduce named values and functions. let rec*opt* function-or-value-defn*1*** and ... and function-or-value-defn*n*** The following example defines value x and functions id and fib: module M = let x = 1 let id x = x let rec fib x = if x <= 2 then 1 else fib (n - 1) + fib (n - 2) Function and value definitions in modules may declare explicit type variables and type constraints: let pair<'T>(x : 'T) = (x, x) let dispose<'T when 'T :> System.IDisposable>(x : 'T) = x.Dispose() let convert<'T, 'U>(x) = unbox<'U>(box<'T>(x)) A value definition that has explicit type variables is called a type function (§10.2.3). Function and value definitions may specify attributes: // A value definition with the System.Obsolete attribute [<System.Obsolete("Don't use this")>] let oneTwoPair = (1, 2) // A function definition with an attribute [<System.Obsolete("Don't use this either")>] let pear v = (v, v) By the use of pattern matching, a value definition can define more than one value . In such cases, the attributes apply to each value. // A value definition that defines two values, each with an attribute [<System.Obsolete("Don't use this")>] let (a, b) = (1, 2) Values may be declared mutable: // A value definition that defines a mutable value let mutable count = 1 let freshName() = (count <- count + 1; count) Function and value definitions in modules are processed in the same way as function and value definitions in expressions (§14.6), with the following adjustments: • Each defined value may have an accessibility annotation (§10.5). By default, the accessibility annotation of a function or value definition in a module is public. • Each defined value is externally accessible if its accessibility annotation is public and it is not hidden by an explicit signature. Externally accessible values are guaranteed to have compiled CLI representations in compiled CLI binaries. • Each defined value can be used to satisfy the requirements of any signature for the module (§11.2). • Each defined value is subject to arity analysis (§14.10). • Values may have attributes, including the ThreadStatic or ContextStatic attribute. ### Literal Definitions in Modules Value definitions in modules may have the Literal attribute. This attribute causes the value to be compiled as a constant. For example: [<Literal>] let PI = 3.141592654 Literal values may be used in custom attributes and pattern matching. For example: [<Literal>] let StartOfWeek = System.DayOfWeek.Monday [<MyAttribute(StartOfWeek)>] let feeling(day) = match day with | StartOfWeek -> "rough" | _ -> "great" A value that has the Literal attribute is subject to the following restrictions: • It may not be marked mutable or inline. • It may not also have the ThreadStatic or ContextStatic attributes. • The right-hand side expression must be a literal constant expression that is both a valid expression after checking, and is made up of either: • A simple constant expression, with the exception of (), native integer literals, unsigned native integer literals, byte array literals, BigInteger literals, and user-defined numeric literals. —OR— • A reference to another literal —OR— • A bitwise combination of literal constant expressions —OR— • A “+” concatenation of two literal constant expressions which are strings —OR— • “enum x” or “LanguagePrimitives.EnumOfValue x” where “x” is a literal constant expression. ### Type Function Definitions in Modules Value definitions within modules may have explicit generic parameters. For example, ‘T is a generic parameter to the value empty: let empty<'T> : (list<'T> * Set<'T>) = ([], Set.empty) A value that has explicit generic parameters but has arity [] (that is, no explicit function parameters) is called a type function. The following are some example type functions from the F# library: val typeof<'T> : System.Type val sizeof<'T> : int module Set = val empty<'T> : Set<'T> module Map = val empty<'Key,'Value> : Map<'Key,'Value> Type functions are rarely used in F# programming, although they are convenient in certain situations. Type functions are typically used for: • Pure functions that compute type-specific information based on the supplied type arguments. • Pure functions whose result is independent of inferred type arguments, such as empty sets and maps. Type functions receive special treatment during generalization (§14.6.7) and signature conformance (§11.2). They typically have either the RequiresExplicitTypeArguments attribute or the GeneralizableValue attribute. Type functions may not be defined inside types, expressions, or computation expressions. In general, type functions should be used only for computations that do not have observable side effects. However, type functions may still perform computations. In this example, r is a type function that calculates the number of times it has been called let mutable count = 1 let r<'T> = (count <- count + 1); ref ([] : 'T list);; // count = 1 let x1 = r<int> // count = 2 let x2 = r<int> // count = 3 let z0 = x1 // count = 3 The elaborated form of a type function is that of a function definition that takes one argument of type unit. That is, the elaborated form of let ident typar-defns = expr is the same as the compiled form for the following declaration: let ident typar-defns () = expr References to type functions are elaborated to invocations of such a function. ### Active Pattern Definitions in Modules A value definition within a module that has an active-pattern-op-name introduces pattern-matching tags into the environment when the module is accessed or opened. For example, let (|A|B|C|) x = if x < 0 then A elif x = 0 then B else C introduces pattern tags A, B, and C into the PatItems table in the name resolution environment. ### “do” statements in Modules A “do” statement within a module has the following form: do expr The expression expr is checked with an arbitrary initial type ty. After checking expr, ty is asserted to be equal to unit. If the assertion fails, a warning rather than an error is reported. This warning is suppressed for plain expressions without do in script files (that is, .fsx and .fsscript files). A “do” statement may have attributes. In this example, the STAThread attribute specifies that main uses the single-threaded apartment (STA) threading model of COM: let main() = let form = new System.Windows.Forms.Form() System.Windows.Forms.Application.Run(form) [<STAThread>] do main() ## Import Declarations Namespace declaration groups and module definitions can include import declarations in the following form: open long-ident Import declarations make elements of other namespace declaration groups and modules accessible by the use of unqualified names. For example: open FSharp.Collections open System Import declarations can be used in: • Module definitions and their signatures. • Namespace declaration groups and their signatures. An import declaration is processed by first resolving the long-ident to one or more namespace declaration groups and/or modules [F*1, ..., Fn] by Name Resolution in Module and Namespace Paths (§14.1.2). For example, System.Collections.Generic may resolve to one or more namespace declaration groups—one for each assembly that contributes a namespace declaration group in the current environment. Next, each Fi*** is added to the environment successively by using the technique specified in §14.1.3. An error occurs if any F*i*** is a module that has the RequireQualifiedAccess attribute. ## Module Abbreviations A module abbreviation defines a local name for a module long identifier, as follows: module ident = long-ident For example: module Ops = FSharp.Core.Operators Module abbreviations can be used in: • Module definitions and their signatures. • Namespace declaration groups and their signatures. Module abbreviations are implicitly private to the module or namespace declaration group in which they appear. A module abbreviation is processed by first resolving the long-ident to a list of modules by Name Resolution in Module and Namespace Paths (see §14.1). The list is then appended to the set of names that are associated with ident in the ModulesAndNamespaces table. Module abbreviations may not be used to abbreviate namespaces. ## Accessibility Annotations Accessibilities may be specified on declaration elements in namespace declaration groups and modules, and on members in types. The table lists the accessibilities that can appear in user code: Accessibility Description public No restrictions on access. private Access is permitted only from the enclosing type, module, or namespace declaration group. internal Access is permitted only from within the enclosing assembly, or from assemblies whose name is listed using the InternalsVisibleTo attribute in the current assembly. The default accessibilities are public. Specifically: • Function definitions, value definitions, type definitions, and exception definitions in modules are public. • Modules, type definitions, and exception definitions in namespaces are public. • Members in type definitions are public. Some function and value definitions may not be given an accessibility and, by their nature, have restricted lexical scope. In particular: • Function and value definitions in classes are lexically available only within the class being defined, and only from the point of their definition onward. • Module type abbreviations are lexically available only within the module or namespace declaration group being defined, and only from their point of their definition onward. Note that: • private on a member means “private to the enclosing type or module.” • private on a function or value definition in a module means “private to the module or namespace declaration group.” • private on a type, module, or type representation in a module means “private to the module.” The CLI compiled form of all non-public entities is internal. Note: The family and protected specifications are not supported in this version of the F# language. Accessibility modifiers can appear only in the locations summarized in the following table. Component Location Example Function or value definition in module Precedes identifier let private x = 1 let inline private f x = 1 let mutable private x = 1 Module definition Precedes identifier module private M = let x = 1 Type definition Precedes identifier type private C = A | B type private C<'T> = A | B val definition in a class Precedes identifier val private x : int Explicit constructor Precedes identifier private new () = { inherit Base } Implicit constructor Precedes identifier type C private() = ... Member definition Precedes identifier, but cannot appear on: • inherit definitions • interface definitions • abstract definitions • Individual union cases Accessibility for inherit, interface, and abstract definitions is always the same as that of the enclosing class. member private x.X = 1 Explicit property get or set in a class Precedes identifier member __.Item with private get i = 1 and private set i v = () Type representation Precedes identifier type Cases = private | A | B # Namespace and Module Signatures A signature file contains one or more namespace or module signatures, and specifies the functionality that is implemented by its corresponding implementation file. It also can hide functionality that the corresponding implementation file contains. namespace-decl-group-signature := namespace long-ident module-signature-elements module-signature = module ident = module-signature-body module-signature-element := val mutableopt** curried-sig -- value signature val value-defn -- literal value signature type type-signatures -- type(s) signature exception exception-signature -- exception signature module-signature -- submodule signature module-abbrev -- local alias for a module import-decl -- locally import contents of a module module-signature-elements := module-signature-element ... module-signature-element module-signature-body = begin module-signature-elements end type-signature := abbrev-type-signature record-type-signature union-type-signature anon-type-signature class-type-signature struct-type-signature interface-type-signature enum-type-signature delegate-type-signature type-extension-signature type-signatures := type-signature ... and ... type-signature type-signature-element := attributes*opt*** accessopt new :** uncurried-sig -- constructor signature attributes*opt*** member accessopt** member-sig -- member signature attributes*opt*** abstract accessopt** member-sig -- member signature attributes*opt*** override member-sig -- member signature attributes*opt*** default member-sig -- member signature attributes*opt*** static member accessopt** member-sig -- static member signature interface type -- interface signature abbrev-type-signature := type-name '=' type union-type-signature := type-name '=' union-type-cases type-extension-elements-signature*opt*** record-type-signature := type-name '=' '{' record-fields '}' type-extension-elements-signature*opt*** anon-type-signature := type-name '=' begin type-elements-signature end class-type-signature := type-name '=' class type-elements-signature end struct-type-signature := type-name '=' struct type-elements-signature end interface-type-signature := type-name '=' interface type-elements-signature end enum-type-signature := type-name '=' enum-type-cases delegate-type-signature := type-name '=' delegate-sig type-extension-signature := type-name type-extension-elements-signature type-extension-elements-signature := with type-elements-signature end The begin and end tokens are optional when lightweight syntax is used. Like module declarations, signature declarations are processed sequentially rather than simultaneously, so that later signature declarations are not in scope when earlier ones are processed. namespace Utilities.Part1 module Module1 = val x : Utilities.Part2.StorageCache // error (Part2 not yet declared) namespace Utilities.Part2 type StorageCache = new : unit -> unit ## Signature Elements A namespace or module signature declares one or more value signatures and one or more type definition signatures. A type definition signature may include one or more member signatures, in addition to other elements of type definitions that are specified in the signature grammar at the start of this chapter. ### Value Signatures A value signature indicates that a value exists in the implementation. For example, in the signature of a module, the following declares two value signatures: module MyMap = val mapForward : index1: int * index2: int -> string val mapBackward : name: string -> (int * int) The corresponding implementation file might contain the following implementation: module MyMap = let mapForward (index1:int, index2:int) = string index1 + "," + string index2 let mapBackward (name:string) = (0, 0) ### Type Definition and Member Signatures A type definition signature indicates that a corresponding type definition appears in the implementation. For example, in an interface type, the following declares a type definition signature for Forward and Backward: type IMap = interface abstract Forward : index1: int * index2: int -> string abstract Backward : name: string -> (int * int) end A member signature indicates that a corresponding member appears on the corresponding type definition in the implementation. Member specifications must specify argument and return types, and can optionally specify names and attributes for parameters. For example, the following declares a type definition signature for a type with one constructor member, one property member Kind and one method member Purr: type Cat = new : kind:string -> Cat member Kind : string member Purr : unit -> Cat The corresponding implementation file might contain the following implementation: type Cat(kind: string) = member x.Meow() = printfn "meow" member x.Purr() = printfn "purr" member x.Kind = kind ## Signature Conformance Values, types, and members that are present in implementations can be omitted in signatures, with the following exceptions: • Type abbreviations may not be hidden by signatures. That is, a type abbreviation type T = ty in an implementation does not match type T (without an abbreviation) in a signature. • Any type that is represented as a record or union must reveal either all or none of its fields or cases, in the same order as that specified in the implementation. Types that are represented as classes may reveal some, all, or none of their fields in a signature. • Any type that is revealed to be an interface, or a type that is a class or struct with one or more constructors may not hide its inherit declaration, abstract dispatch slot declarations, or abstract interface declarations. Note: This section does not yet document all checks made by the F# 3.1 language implementation. ### Signature Conformance for Functions and Values If both a signature and an implementation contain a function or value definition with a given name, the signature and implementation must conform as follows: • The declared accessibilities, inline, and mutable modifiers must be identical in both the signature and the implementation. • If either the signature or the implementation has the [<Literal>] attribute, both must have this attribute. Furthermore, the declared literal values must be identical. • The number of generic parameters—both inferred and explicit—must be identical. • The types and type constraints must be identical up to renaming of inferred and/or explicit generic parameters. For example, assume a signature is written “val head : seq<'T> -> 'T” and the compiler could infer the type “val head : seq<'a> -> 'a” from the implementation. These are considered identical up to renaming the generic parameters. • The arities must match, as described in the next section. #### Arity Conformance for Functions and Values Arities of functions and values must conform between implementation and signature. Arities of values are implicit in module signatures. A signature that contains the following results in the arity [A1...An] for F: val F : ty1,1 * ... * ty1,A1 -> ... -> tyn,1 * ... * tyn,An -> rty Arities in a signature must be equal to or shorter than the corresponding arities in an implementation, and the prefix must match. This means that F# makes a deliberate distinction between the following two signatures: val F: int -> int and val F: (int -> int) The parentheses indicate a top-level function, which might be a first-class computed expression that computes to a function value, rather than a compile-time function value. The first signature can be satisfied only by a true function; that is, the implementation must be a lambda value as in the following: let F x = x + 1 Note: Because arity inference also permits right-hand-side function expressions, the implementation may currently also be: let F = fun x -> x + 1 The second signature val F: (int -> int) can be satisfied by any value of the appropriate type. For example: let f = let myTable = new System.Collections.Generic.Dictionary<int,int>(4) fun x -> if myTable.ContainsKey x then myTable.[x] else let res = x * x myTable.[x] <- res res —or— let f = fun x -> x + 1 —or— // throw an exception as soon as the module initialization is triggered let f : int -> int = failwith "failure" For both the first and second signatures, you can still use the functions as first-class function values from client code—the parentheses simply act as a constraint on the implementation of the value. The reason for this interpretation of types in value and member signatures is that CLI interoperability requires that F# functions compile to methods, rather than to fields that are function values. Thus, signatures must contain enough information to reveal the desired arity of a method as it is revealed to other CLI programming languages. #### Signature Conformance for Type Functions If a value is a type function, then its corresponding value signature must have explicit type arguments. For example, the implementation let empty<'T> : list<'T> = printfn "hello"; [] conforms to this signature: val empty<'T> : list<'T> but not to this signature: val empty : list<'T> The reason for this rule is that the second signature indicates that the value is, by default, generalizable (§14.6.7). ### Signature Conformance for Members If both a signature and an implementation contain a member with a given name, the signature and implementation must conform as follows: • If one is an extension member, both must be extension members. • If one is a constructor, then both must be constructors. • If one is a property, then both must be properties. • The types must be identical up to renaming of inferred or explicit type parameters (as for functions and values). • The static, abstract, and override qualifiers must match precisely. • Abstract members must be present in the signature if a representation is given for a type. Note: This section does not yet document all checks made by the F# 3.1 language implementation. # Program Structure and Execution F# programs are made up of a collection of assemblies. F# assemblies are made up of static references to existing assemblies, called the referenced assemblies, and an interspersed sequence of signature (.fsi) files, implementation (.fs) files, script (.fsx or .fsscript) files, and interactively executed code fragments. implementation-file := namespace-decl-group ... namespace-decl-group named-module anonynmous-module script-file := implementation-file -- script file, additional directives allowed signature-file**:=** namespace-decl-group-signature ... namespace-decl-group-signature anonynmous-module-signature named-module-signature named-module := module long-ident module-elems anonymous-module := module-elems named-module-signature := module long-ident module-signature-elements anonymous-module-signature := module-signature-elements script-fragment := module-elems -- interactively entered code fragment A sequence of implementation and signature files is checked as follows. 1. Form an initial environment sig-env*0*** and impl-env*0*** by adding all assembly references to the environment in the order in which they are supplied to the compiler. This means that the following procedure is applied for each referenced assembly: • Add the top level types, modules, and namespaces to the environment. • For each AutoOpen attribute in the assembly, find the types, modules, and namespaces that the attribute references and add these to the environment. The resulting environment becomes the active environment for the first file to be processed. 2. For each file: • If the ith file is a signature file file**.fsi**: 1. Check it against the current signature environment sig-env*i-1, which generates the signature Sigfile* for the current file. 2. Add Sig*file*** to sig-env*i-1*** to produce sig-envi to make it available for use in later signature files. The processing of the signature file has no effect on the implementation environment, so impl-env*i*** is identical to impl-env*i-1***. • If the file is an implementation file file**.fs**, check it against the environment impl-env*i-1, which gives elaborated namespace declaration groups Implfile*. 1. If a corresponding signature Sig*file*** exists, check Impl*file*** against Sig*file*** during this process (§11.2). Then add Sig*file*** to impl-env*i-1*** to produce impl-envi. This step makes the signature-constrained view of the implementation file available for use in later implementation files. The processing of the implementation file has no effect on the signature environment, so sig-env*i*** is identical to sig-env*i-1***. 1. If the implementation file has no signature file, add Impl*file*** to both sig-env*i-1*** and impl-env*i-1***, to produce sig-envi and impl-envi. This makes the contents of the implementation available for use in both later signature and implementation files. The signature file for a particular implementation must occur before the implementation file in the compilation order. For every signature file, a corresponding implementation file must occur after the file in the compilation order. Script files may not have signatures. ## Implementation Files Implementation files consist of one or more namespace declaration groups. For example: namespace MyCompany.MyOtherLibrary type MyType() = let x = 1 member v.P = x + 2 module MyInnerModule = let myValue = 1 namespace MyCompany. MyOtherLibrary.Collections type MyCollection(x : int) = member v.P = x An implementation file that begins with a module declaration defines a single namespace declaration group with one module. For example: module MyCompany.MyLibrary.MyModule let x = 1 is equivalent to: namespace MyCompany.MyLibrary module MyModule = let x = 1 The final identifier in the long-ident that follows the module keyword is interpreted as the module name, and the preceding identifiers are interpreted as the namespace. Anonymous implementation files do not have either a leading module or namespace declaration. Only the scripts and the last file within an implementation group for an executable image (.exe) may be anonymous. An anonymous implementation file contains module definitions that are implicitly placed in a module. The name of the module is generated from the name of the source file by capitalizing the first letter and removing the filename extensionIf the filename contains characters that are not valid in an F# identifier, the resulting module name is unusable and a warning occurs. Given an initial environment env*0***, an implementation file is checked as follows: • Create a new constraint solving context. • Check the namespace declaration groups in the file against the existing environment env*i-1*** and incrementally add them to the environment (§10.1) to create a new environment env*i***. • Apply default solutions to any remaining type inference variables that include default constraints. The defaults are applied in the order that the type variables appear in the type-annotated text of the checked namespace declaration groups. • Check the inferred signature of the implementation file against any required signature by using Signature Conformance (§11.2). The resulting signature of an implementation file is the required signature, if it is present; otherwise it is the inferred signature. • Report a “value restriction” error if the resulting signature of any item that is not a member, constructor, function, or type function contains any free inference type variables. • Choose solutions for any remaining type inference variables in the elaborated form of an expression. Process any remaining type variables in the elaborated form from left-to-right to find a minimal type solution that is consistent with constraints on the type variable. If no unique minimal solution exists for a type variable, report an error. The result of checking an implementation file is a set of elaborated namespace declaration groups. ## Signature Files Signature files specify the functionality that is implemented by a corresponding implementation file. Each signature file contains a sequence of namespace-decl-group-signature elements. The inclusion of a signature file in compilation implicitly applies that signature type to the contents of a corresponding implementation file. Anonymous signature files do not have either a leading module or namespace declaration. Anonymous signature files contain module-elems that are implicitly placed in a module. The name of the module is generated from the name of the source file by capitalizing the first letter and removing the filename extension. If the filename contains characters that are not valid in an F# identifier, the resulting module name is unusable and a warning occurs. Given an initial environment env, a signature file is checked as follows: • Create a new constraint solving context. • Check each namespace-decl-group-signature*i*** in env*i-1*** and add the result to that environment to create a new environment env*i***. The result of checking a signature file is a set of elaborated namespace declaration group types. ## Script Files Script files have the**.fsx** or .fsscript filename extension. They are processed in the same way as files that have the .fs extension, with the following exceptions: • Side effects from all scripts are executed at program startup. • For script files, the namespace FSharp.Compiler.Interactive.Settings is opened by default. • F# Interactive references the assembly FSharp.Compiler.Interactive.Settings.dll by default, but the F# compiler does not. If the script uses the script helper fsi object, then the script should explicitly reference FSharp.Compiler.Interactive.Settings.dll. Script files may add to the set of referenced assemblies by using the #r directive (§12.312.4). Script files may add other signature, implementation, and script files to the list of sources by using the #load directive. Files are compiled in the same order that was passed to the compiler, except that each script is searched for #load directives and the loaded files are placed before the script, in the order they appear in the script. If a filename appears in more than one #load directive, the file is placed in the list only once, at the position it first appeared. Script files may have #nowarn directives, which disable a warning for the entire compilation. The F# compiler defines the COMPILED compilation symbol for input files that it has processed. F# Interactive defines the INTERACTIVE symbol. Script files may not have corresponding signature files. ## Compiler Directives Compiler directives are declarations in non-nested modules or namespace declaration groups in the following form: # id string ... string The lexical preprocessor directives #if, #else, #endif and #indent "off" are similar to compiler directives. For details on #if, #else, #endif, see §3.3. The #indent "off" directive is described in §19.4. The following directives are valid in all files: Directive Example Short Description #nowarn #nowarn "54" For signature (.fsi) files and implementation (.fs) files, turns off warnings within this lexical scope. For script (.fsx or .fsscript) files, turns off warnings globally. The following directives are valid in script files: Directive Example Short Description #r #reference #r "System.Core" #r @"Nunit.Core.dll" #r @"c:\NUnit\Nunit.Core.dll" #r "nunit.core, Version=2.2.2.0, Culture=neutral, PublicKeyToken=96d09a1eb7f44a77" References a DLL within this entire script. #I #Include #I @"c:\Projects\Libraries\Bin" Adds a path to the search paths for DLLs that are referenced within this entire script. #load #load "library.fs" #load "core.fsi" "core.fs" Loads a set of signature and implementation files into the script execution engine. #time #time #time "on" #time "off" Enables or disables the display of performance information, including elapsed real time, CPU time, and garbage collection information for each section of code that is interpreted and executed. #help #help Asks the script execution environment for help. #q #quit #q #quit Requests the script execution environment to halt execution and exit. ## Program Execution Execution of F# code occurs in the context of an executing CLI program into which one or more compiled F# assemblies or script fragments is loaded. During execution, the CLI program can use the functions, values, static members, and object constructors that the assemblies and script fragments define. ### Execution of Static Initializers Each implementation file, script file, and script fragment involves a static initializer. The execution of the static initializer is triggered as follows: • For executable (.exe) files that have an explicit entry point function, the static initializer for the last file that appears on the command line is forced immediately as the first action in the execution of the entry point function. • For executable files that have an implicit entry point, the static initializer for the last file that appears on the command line is the body of the implicit entry point function. • For scripts, F# Interactive executes the static initializer for each program fragment immediately. • For all other implementation files, the static initializer for the file is executed on first access of a value that has observable initialization according to the rules that follow, or first access to any member of any type in the file that has at least one “static let” or “static do” declaration. At runtime, the static initializer evaluates, in order, the definitions in the file that have observable initialization according to the rules that follow. Definitions with observable initialization in nested modules and types are included in the static initializer for the overall file. All definitions have observable initialization except for the following definitions in modules: • Function definitions • Type function definitions • Literal definitions • Value definitions that are generalized to have one or more type variables • Non-mutable, non-thread-local values that are bound to an initialization constant expression, which is an expression whose elaborated form is one of the following: • A simple constant expression. • A null expression. • A use of the typeof<_> or sizeof<_> operator from FSharp.Core.Operators, or the defaultof<_> operator from FSharp.Core.Operators.Unchecked. • A let expression where the constituent expressions are initialization constant expressions. • A match expression where the input is an initialization constant expression, each case is a test against a constant, and each target is an initialization constant expression. • A use of one of the unary or binary operators =, <>, <, >, <=, >=, +, -, * , <<<, >>>, |||, &&&, ^^^, ~~~, enum<_>, not, compare, prefix , and prefix + from FSharp.Core.Operators on one or two arguments, respectively. The arguments themselves must be initialization constant expressions, but cannot be operations on decimals or strings. Note that the operators are unchecked for arithmetic operations, and that the operators % and / are not included because their use can raise division-by-zero exceptions. • A use of a [<Literal>] value. • A use of a case from an enumeration type. • A use of a null case from a union type. • A use of a value that is defined in the same assembly and does not have observable initialization, or the use of a value that is defined by a “let” or “match” expression within the expression itself. If the execution environment supports the concurrent execution of multiple threads of F# code, each static initializer runs as a mutual exclusion region. The use of a mutual exclusion region ensures that if another thread attempts to access a value that has observable initialization, that thread pauses until static initialization is complete. A static initializer runs only once, on the first thread that acquires entry to the mutual exclusion region. Values that have observable initialization have implied CLI fields that are private to the assembly. If such a field is accessed by using CLI reflection before the execution of the corresponding initialization code, then the default value for the type of the field will be returned. Within implementation files, generic types that have static value definitions receive a static initializer for each generic instantiation. These initializers are executed immediately before the first dereference of the static fields for the generic type, subject to any limitations present in the specific CLI implementation in used. If the static initializer for the enclosing file is first triggered during execution of the static initializer for a generic instantiation, references to static values definition in the generic class evaluate to the default value. For example, if external code accesses data in this example, the static initializer runs and the program prints “hello”: module LibraryModule printfn "hello" let data = new Dictionary<int,int>() That is, the side effect of printing “hello” is guaranteed to be triggered by an access to the value data. If external code calls id or accesses size in the following example, the execution of the static initializer is not yet triggered. However if external code calls f(),the execution of the static initializer is triggered because the body refers to the value data, which has observable initialization. module LibraryModule printfn "hello" let data = new Dictionary<int,int>() let size = 3 let id x = x let f() = data All of the following represent definitions that do not have observable initialization because they are initialization constant expressions. let x = System.DayOfWeek.Friday let x = 1.0 let x = "two" let x = enum<System.DayOfWeek>(0) let x = 1 + 1 let x : int list = [] let x : int option = None let x = compare 1 1 let x = match true with true -> 1 | false -> 2 let x = true && true let x = 42 >>> 2 let x = typeof<int> let x = Unchecked.defaultof<int> let x = Unchecked.defaultof<string> let x = sizeof<int> ### Explicit Entry Point The last file that is specified in the compilation order for an executable file may contain an explicit entry point. The entry point is indicated by annotating a function in a module with EntryPoint attribute: • The EntryPoint attribute applies only to a “let”-bound function in a module. The function cannot be a member. • This attribute can apply to only one function, and the function must be the last declaration in the last file processed on the command line. The function may be in a nested module. • The function is asserted to have type string[] -> int before type checking. If the assertion fails, an error occurs. • At runtime, the entry point is passed one argument at startup: an array that contains the same entries as System.Environment.GetCommandLineArgs(), minus the first entry in that array. The function becomes the entry point to the program. At startup, F# immediately forces execution of the static initializer for the file in which the function is declared, and then evaluates the body of the function. # Custom Attributes and Reflection CLI languages use metadata inspection and the System.Reflection libraries to make guarantees about how compiled entities appear at runtime. They also allow entities to be attributed by static data, and these attributes may be accessed and read by tools and running programs. This chapter describes these mechanisms for F#. Attributes are given by the following grammar: attribute := attribute-target**:opt** object-construction attribute-set := [< attribute ; ... ; attribute >] attributes := attribute-set ... attribute-set attribute-target := assembly module return field property param type constructor event ## Custom Attributes CLI languages support the notion of custom attributes which can be added to most declarations. These are added to the corresponding elaborated and compiled forms of the constructs to which they apply. Custom attributes can be applied only to certain target language constructs according to the AttributeUsage attribute, which is found on the attribute class itself. An error occurs if an attribute is attached to a language construct that does not allow that attribute. Custom attributes are not permitted on function or value definitions in expressions or computation expressions. Attributes on parameters are given as follows: let foo([<SomeAttribute>] a) = a + 5 If present, the arguments to a custom attribute must be literal constant expressions, or arrays of the same. Custom attributes on return values are given as follows: let foo a : [<SomeAttribute>] = a + 5 Custom attributes on primary constructors are given before the arguments and before any accessibility annotation: type Foo1 [<System.Obsolete("don't use me")>] () = member x.Bar() = 1 type Foo2 [<System.Obsolete("don't use me")>] private () = member x.Bar() = 1 Custom attributes are mapped to compiled CLI metadata as follows: • Custom attributes map to the element that is specified by their target, if a target is given. • A custom attribute on a type type is compiled to a custom attribute on the corresponding CLI type definition, whose System.Type object is returned by typeof<type>. • By default, a custom attribute on a record field F for a type T is compiled to a custom attribute on the CLI property for the fieldthat is named F, unless the target of the attribute is field, in which case it becomes a custom attribute on the underlying backing field for the CLI property that is named _F. • A custom attribute on a union case ABC for a type T is compiled to a custom attribute on a static method on the CLI type definition T. This method is called: • get_ABC if the union case takes no arguments • ABC otherwise • Custom attributes on arguments are propagated only for arguments of member definitions, and not for “let”-bound function definitions. • Custom attributes on generic parameters are not propagated. Custom attributes that appear immediately preceding “do” statements in modules anywhere in an assembly are attached to one of the following: • The main entry point of the program. • The compiled module. • The compiled assembly. Custom attributes are attached to the main entry point if it is valid for them to be attached to a method according to the AttributeUsage attribute that is found on the attribute class itself, and likewise for the assembly. If it is valid for the attribute to be attached to either the main method or the assembly. the main method takes precedence. For example, the STAThread attribute should be placed immediately before a top-level “do” statement. **let main() = let form = new System.Windows.Forms.Form() System.Windows.Forms.Application.Run(form) [<STAThread>] do main()** ### Custom Attributes and Signatures During signature checking, custom attributes attached to items in F# signature files (.fsi files) are combined with custom attributes on the corresponding element from the implementation file according to the following algorithm: • Start with lists AImpl and ASig containing the attributes in the implementation and signature, in declaration order. • Check each attribute in AImpl against the available attributes in ASig. • If ASig contains an attribute that is an exact match after evaluating attribute arguments, then ignore the attribute in the implementation, remove the attribute from ASig, and continue checking; • If ASig contains an attribute that has the same attribute type but is not an exact match, then give a warning and ignore the attribute in the implementation; • Otherwise, keep the attribute in the implementation. The compiled element contains the compiled forms of the attributes from the signature and the retained attributes from the implementation. This means: • When an implementation has an attribute X("abc") and the signature is missing the attribute, then no warning is given and the attribute appears in the compiled assembly. • When a signature has an attribute X("abc") and the implementation is missing the attribute, then no warning is given, and the attribute appears in the compiled assembly. • When an implementation has an attribute X("abc") and the signature has attribute X("def"), then a warning is given, and only X("def") appears in the compiled assembly. ## Reflected Forms of Declaration Elements The typeof and typedefof F# library operators return a System.Type object for an F# type definition. According to typical implementations of the CLI execution environment, the System.Type object in turn can be used to access further information about the compiled form of F# member declarations. If this operation is supported in a particular implementation of F#, then the following rules describe which declaration elements have corresponding System.Reflection objects: • All member declarations are present as corresponding methods, properties or events. • Private and internal members and types are included. • Type abbreviations are not given corresponding System.Type definitions. In addition: • F# modules are compiled to provide a corresponding compiled CLI type declaration and System.Type object, although the System.Type object is not accessible by using the typeof operator. However: • Internal and private function and value definitions are not guaranteed to be given corresponding compiled CLI metadata definitions. They may be removed by optimization. • Additional internal and private compiled type and member definitions may be present in the compiled CLI assembly as necessary for the correct implementation of F# programs. • The System.Reflection operations return results that are consistent with the erasure of F# type abbreviations and F# unit-of-measure annotations. • The definition of new units of measure results in corresponding compiled CLI type declarations with an associated System.Type. # Inference Procedures ## Name Resolution The following sections describe how F# resolves names in various contexts. ### Name Environments Each point in the interpretation of an F# program is subject to an environment. The environment encompasses: • All referenced external DLLs (assemblies). • ModulesAndNamespaces: a table that maps long-idents to a list of signatures. Each signature is either a namespace declaration group signature or a module signature. For example, System.Collections may map to one namespace declaration group signature for each referenced assembly that contributes to the System.Collections namespace, and to a module signature, if a module called System.Collections is declared or in a referenced assembly. If the program references multiple assemblies, the assemblies are added to the name resolution environment in the order in which the references appear on the command line. The order is important only if ambiguities occur in referencing the contents of assemblies—for example, if two assemblies define the type MyNamespace.C. • ExprItems: a table that maps names to the following items: • A value • A union case for use when constructing data • An active pattern result tag for use when returning results from active patterns • A type name for each class or struct type • FieldLabels: a table that maps names to sets of field references for record types • PatItems: a table that maps names to the following items: • A union case, for use when pattern matching on data • An active pattern case name, for use when specifying active patterns • A literal definition • Types: a table that maps names to type definitions. Two queries are supported on this table: • Find a type by name alone. This query may return multiple types. For example, in the default type-checking environment, the resolution of System.Tuple returns multiple tuple types. • Find a type by name and generic arity n. This query returns at most one type. For example, in the default type-checking environment, the resolution of System.Tuple with n = 2 returns a single type. • ExtensionsInScope: a table that maps type names to one or more member definitions The dot notation is resolved during type checking by consulting these tables. ### Name Resolution in Module and Namespace Paths Given an input long-ident and environment env, Name Resolution in Module and Namespace Paths computes the result of interpreting long-ident as a module or namespace. The procedure returns a list of modules and namespace declaration groups. Name Resolution in Module and Namespace Paths proceeds through the following steps: 1. Consult the ModulesAndNamespaces table to resolve the long-ident prefix to a list of modules and namespace declaration group signatures. 2. If any identifiers remain unresolved, recursively consult the declared modules and sub-modules of these namespace declaration groups. 3. Concatenate all the results. If the long-ident starts with the special pseudo-identifier keyword global, the identifier is resolved by consulting the ModulesAndNamespaces table and ignoring all open directives, including those implied by AutoOpen attributes. For example, if the environment contains two referenced DLLs, and each DLL has namespace declaration groups for the namespaces System, System.Collections, and System.Collections.Generic, Name Resolution in Module and Namespace Paths for System.Collections returns the two namespace declaration groups named System.Collections, one from each assembly. ### Opening Modules and Namespace Declaration Groups When a module or namespace declaration group F is opened, the compiler adds items to the name environment as follows: 1. Add each exception label for each exception type definition (§8.11) in F to the ExprItems and PatItems tables in the original order of declaration in F. 2. Add each type definition in the original order of declaration in F. Adding a type definition involves the following procedure: 1. If the type is a class or struct type (or an abbreviation of such a type), add the type name to the ExprItems table. 1. If the type definition is a record, add the record field labels to the FieldLabels table, unless the type has the RequireQualifiedAccess attribute. 2. If the type is a union, add the union cases to the ExprItems and PatItems tables, unless the type has the RequireQualifiedAccess attribute. 3. Add the type to the TypeNames table. If the type has a CLI-encoded generic name such as List1, add an entry under both List and List`1. 3. Add each value in the original order of declaration in F, as follows: 1. Add the value to the ExprItems table. 1. If any value is an active pattern, add the tags of that active pattern to the PatItems table according to the original order of declaration. 2. If the value is a literal, add it to the PatItems table. 4. Add the member contents of each type extension in F*i*** to the ExtensionsInScope table according to the original order of declaration in F*i***. 5. Add each sub-module or sub-namespace declaration group in F*i*** to the ModulesAndNamespaces table according to the original order of declaration in F*i***. 6. Open any sub-modules that are marked with the FSharp.Core.AutoOpen attribute. ### Name Resolution in Expressions Given an input long-ident, environment env, and an optional count n of the number of subsequent type arguments <_,...,_>, Name Resolution in Expressions computes a result that contains the interpretation of the long-ident**<_,...,_>** prefix as a value or other expression item, and a residue path rest. How Name Resolution in Expressions proceeds depends on whether long-ident is a single identifier or is composed of more than one identifier. If long-ident is a single identifier ident: 1. Look up ident in the ExprItems table. Return the result and empty rest. 2. If ident does not appear in the ExprItems table, look it up in the Types table, with generic arity that matches n if available. Return this type and empty rest. 3. If ident does not appear in either the ExprItems table or the Types table, fail. If long-ident is composed of more than one identifier ident.rest, Name Resolution in Expressions proceeds as follows: 1. If ident exists as a value in the ExprItems table, return the result, with rest as the residue. 2. If ident does not exist as a value in the ExprItems table, perform a backtracking search as follows: 1. Consider each division of long-ident into [namespace-or-module-path]**.ident[.**rest], in which the namespace-or-module-path becomes successively longer. 2. For each such division, consider each module signature or namespace declaration group signature F in the list that is produced by resolving namespace-or-module-path by using Name Resolution in Module and Namespace Paths. 3. For each such F, attempt to resolve ident[**.**rest] in the following order. If any resolution succeeds, then terminate the search: 1. A value in F. Return this item and rest. 2. A union case in F. Return this item and rest. 3. An exception constructor in F. Return this item and rest. 4. A type in F. If rest is empty, then return this type; if not, resolve using Name Resolution for Members. 5. A [sub-]module in F. Recursively resolve rest against the contents of this module. 3. If steps 1 and 2 do not resolve long-ident, look up ident in the Types table. 1. If the generic arity n is available, then look for a type that matches both ident and n. 2. If no generic arity n is available, and rest is not empty: 1. If the Types table contains a type ident that does not have generic arguments, resolve to this type. 2. If the Types table contains a unique type ident that has generic arguments, resolve to this type. However, if the overall result of the Name Resolution in Expressions operation is a member, and the generic arguments do not appear in either the return or argument types of the item, warn that the generic arguments cannot be inferred from the type of the item. 3. If neither of the preceding steps resolves the type, give an error. 1. If rest is empty, return the type, otherwise resolve using Name Resolution for Members. 4. If steps 1-3 do not resolve long-ident, look up ident in the ExprItems table and return the result and residue rest. 5. Otherwise, if ident is a symbolic operator name, resolve to an item that indicates an implicitly resolved symbolic operator. 6. Otherwise, fail. If the expression contains ambiguities, Name Resolution in Expressions returns the first result that the process generates. For example, consider the following cases: **module M = type C = | C of string | D of string member x.Prop1 = 3 type Data = | C of string | E member x.Prop1 = 3 member x.Prop2 = 3 let C = 5 open M let C = 4 let D = 6 let test1 = C // resolves to the value C let test2 = C.ToString() // resolves to the value C with residue ToString let test3 = M.C // resolves to the value M.C let test4 = M.Data.C // resolves to the union case M.Data.C let test5 = M.C.C // error: first part resolves to the value M.C, // and this contains no field or property "C" let test6 = C.Prop1 // error: the value C does not have a property Prop let test7 = M.E.Prop2 // resolves to M.E, and then a property lookup** The following example shows the resolution behavior for type lookups that are ambiguous by generic arity: **module M = type C<'T>() = static member P = 1 type C<'T,'U>() = static member P = 1 let _ = new M.C() // gives an error let _ = new M.C<int>() // no error, resolves to C<'T> let _ = M.C() // gives an error let _ = M.C<int>() // no error, resolves to C<'T> let _ = M.C<int,int>() // no error, resolves to C<'T,'U> let _ = M.C<_>() // no error, resolves to C<'T> let _ = M.C<_,_>() // no error, resolves to C<'T,'U> let _ = M.C.P // gives an error let _ = M.C<_>.P // no error, resolves to C<'T> let _ = M.C<_,_>.P // no error, resolves to C<'T,'U>** The following example shows how the resolution behavior differs slightly if one of the types has no generic arguments. **module M = type C() = static member P = 1 type C<'T>() = static member P = 1 let _ = new M.C() // no error, resolves to C let _ = new M.C<int>() // no error, resolves to C<'T> let _ = M.C() // no error, resolves to C let _ = M.C< >() // no error, resolves to C let _ = M.C<int>() // no error, resolves to C<'T> let _ = M.C< >() // no error, resolves to C let _ = M.C<_>() // no error, resolves to C<'T> let _ = M.C.P // no error, resolves to C let _ = M.C< >.P // no error, resolves to C let _ = M.C<_>.P // no error, resolves to C<'T>** In the following example, the procedure issues a warning for an incomplete type. In this case, the type parameter 'T cannot be inferred from the use M.C.P, because 'T does not appear at all in the type of the resolved element M.C<'T>.P. **module M = type C<'T>() = static member P = 1 let _ = M.C.P // no error, resolves to C<'T>.P, warning given** The effect of these rules is to prefer value names over module names for single identifiers. For example, consider this case: **let Foo = 1 module Foo = let ABC = 2 let x1 = Foo // evaluates to 1** The rules, however, prefer type names over value names for single identifiers, because type names appear in the ExprItems table. For example, consider this case: let Foo = 1 type Foo() = static member ABC = 2 let x1 = Foo.ABC // evaluates to 2 let x2 = Foo() // evaluates to a new Foo() ### Name Resolution for Members Name Resolution for Members is a sub-procedure used to resolve .member-ident[**.**rest] to a member, in the context of a particular type type. Name Resolution for Members proceeds through the following steps: 1. Search the hierarchy of the type from System.Object to type. 2. At each type, try to resolve member-ident to one of the following, in order: 1. A union case of type. 1. A property group of type. 2. A method group of type. 3. A field of type. 4. An event of type. 5. A property group of extension members of type, by consulting the ExtensionsInScope table. 6. A method group of extension members of type, by consulting the ExtensionsInScope table. 7. A nested type type-nested of type. Recursively resolve **.**rest if it is present, otherwise return type-nested. 3. At any type, the existence of a property, event, field, or union case named member-ident causes any methods or other entities of that same name from base types to be hidden. 4. Combine method groups with method groups from base types. For example: **type A() = member this.Foo(i : int) = 0 type B() = inherit A() member this.Foo(s : string) = 1 let b = new B() b.Foo(1) // resolves to method in A b.Foo("abc") // resolves to method in B** ### Name Resolution in Patterns Name Resolution for Patterns is used to resolve long-ident in the context of pattern expressions. The long-ident must resolve to a union case, exception label, literal value, or active pattern case name. If it does not, the long-ident may represent a new variable definition in the pattern. Name Resolution for Patterns follows the same steps to resolve the member-ident as Name Resolution in Expressions (§14.1.4) except that it consults the PatItems table instead of the ExprItems table. As a result, values are not present in the namespace that is used to resolve identifiers in patterns. For example: let C = 3 match 4 with | C -> sprintf "matched, C = %d" C | _ -> sprintf "no match, C = %d" C results in "matched, C = 4", because C is not present in the PatItems table, and hence becomes a value pattern. In contrast, **[<Literal>] let C = 3 match 4 with | C -> sprintf "matched, C = %d" C | _ -> sprintf "no match, C = %d" C** results in "no match, C = 3", because C is a literal and therefore is present in the PatItems table. ### Name Resolution for Types Name Resolution for Types is used to resolve long-ident in the context of a syntactic type. A generic arity that matches n is always available. The result is a type definition and a possible residue rest. Name Resolution for Types proceeds through the following steps: 1. Given ident[.rest], look up ident in the Types table, with generic arity n. Return the result and residue rest. 2. If ident is not present in the Types table: 1. Divide long-ident into [namespace-or-module-path]**.ident[.**rest], in which the namespace-or-module-path becomes successively longer. 1. For each such division, consider each module and namespace declaration group F in the list that results from resolving namespace-or-module-path by using Name Resolution in Module and Namespace Paths (§14.1.2). 2. For each such F, attempt to resolve ident[**.**rest] in the following order. Terminate the search when the expression is successfully resolved. 1. A type in F. Return this type and residue rest. 1. A [sub-]module in F. Recursively resolve rest against the contents of this module. In the following example, the name C on the last line resolves to the named type M.C<_,_> because C is applied to two type arguments: **module M = type C<'T, 'U> = 'T * 'T * 'U module N = type C<'T> = 'T * 'T open M open N let x : C<int, string> = (1, 1, "abc")** ### Name Resolution for Type Variables Whenever the F# compiler processes syntactic types and expressions, it assumes a context that maps identifiers to inference type variables. This mapping ensures that multiple uses of the same type variable name map to the same type inference variable. For example, consider the following function: let f x y = (x:'T), (y:'T) In this case, the compiler assigns the identifiers x and y the same static type—that is, the same type inference variable is associated with the name 'T. The full inferred type of the function is: val f<'T> : 'T -> 'T -> 'T * 'T The map is used throughout the processing of expressions and types in a left-to-right order. It is initially empty for any member or any other top-level construct that contains expressions and types. Entries are eliminated from the map after they are generalized. As a result, the following code checks correctly: let f () = let g1 (x:'T) = x let g2 (y:'T) = (y:string) g1 3, g1 "3", g2 "4" The compiler generalizes g1, which is applied to both integer and string types. The type variable 'T in (y:'T) on the third line refers to a different type inference variable, which is eventually constrained to be type string. ### Field Label Resolution Field Label Resolution specifies how to resolve identifiers such as field1 in { field1 = expr**; ...** fieldN = expr }. Field Label Resolution proceeds through the following steps: 1. Look up all fields in all available types in the Types table and the FieldLabels table (§8.4.2). 2. Return the set of field declarations. ## Resolving Application Expressions Application expressions that use dot notation—such as x.Y<int>.Z(g).H.I.j—are resolved according to a set of rules that take into account the many possible shapes and forms of these expressions and the ambiguities that may occur during their resolution. This section specifies the exact algorithmic process that is used to resolve these expressions. Resolution of application expressions proceeds as follows: 1. Repeatedly decompose the application expression into a leading expression expr and a list of projections projs. Each projection has the following form: • **.**long-ident-or-op is a dot lookup projection. • expr is an application projection. • <types> is a type application projection. For example: • x.y.Z(g).H.I.j decomposes into x.y.Z and projections (g), .H.I.j. • x.M<int>(g) decomposes into x.M and projections <int>, (g). • f x decomposes into f and projection x. Note: In this specification we write sequences of projections by juxtaposition; for example, (expr).long-ident<types>(expr). We also write (.rest + projs**)** to refer to adding a residue long identifier to the front of a list of projections, which results in projs if rest is empty and .rest projs otherwise. 2. After decomposition: • If expr is a long identifier expression long-ident, apply Unqualified Lookup (§14.2.1) on long-ident with projections projs. • If expr is not such an expression, check the expression against an arbitrary initial type ty, to generate an elaborated expression expr. Then process expr, ty, and projs by using Expression-Qualified Lookup (§14.2.3) ### Unqualified Lookup Given an input long-ident and projections projs, Unqualified Lookup computes the result of “looking up” long-ident.projs in an environment env. The first part of this process resolves a prefix of the information in long-ident.projs, and recursive resolutions typically use Expression-Qualified Resolution to resolve the remainder. For example, Unqualified Lookup is used to resolve the vast majority of identifier references in F# code, from simple identifiers such as sin, to complex accesses such as System.Environment.GetCommandLineArgs().Length. Unqualified Lookup proceeds through the following steps: 1. Resolve long-ident by using Name Resolution in Expressions (§14.1). This returns a name resolution item item and a residue long identifier rest. For example, the result of Name Resolution in Expressions for v.X.Y may be a value reference v along with a residue long identifier .X.Y. Likewise, N.X(args).Y may resolve to an overloaded method N.X and a residue long identifier**.Y**. Name Resolution in Expressions also takes as input the presence and count of subsequent type arguments in the first projection. If the first projection in projs is <tyargs>, Unqualified Lookup invokes Name Resolution in Expressions with a known number of type arguments. Otherwise, it is invoked with an unknown number of type arguments. 2. Apply Item-Qualified Lookup for item and (rest + projs). ### Item-Qualified Lookup Given an input item item and projections projs, Item-Qualified Lookup computes the projection item.projs. This computation is often a recursive process: the first resolution uses a prefix of the information in item.projs, and recursive resolutions resolve any remaining projections. Item-Qualified Lookup proceeds as follows: 1. If item is not one of the following, return an error: • A named value • A union case • A group of named types • A group of methods • A group of indexer getter properties • A single non-indexer getter property • A static F# field • A static CLI field • An implicitly resolved symbolic operator name 2. If the first projection is <types>, then we say the resolution has a type application <types> with remaining projections. 3. Otherwise, checking proceeds as shown in the table. If item is: Action A value reference v 1. Instantiate the type scheme of v, which results in a type ty. Apply these rules: • If the first projection is <types>, process the types and use the results as the arguments to instantiate the type scheme. • If the first projection is not <types>, the type scheme is freshly instantiated. • If the value has the RequiresExplicitTypeArguments attribute, the first projection must be <types>. • If the value has type byref<ty2>, add a byref dereference to the elaborated expression. • Insert implicit flexibility for the use of the value (§14.4.3). 1. Apply Expression-Qualified Lookup for type ty and any remaining projections. A type name, where projs begins with <types>.long-ident 1. Process the types and use the results as the arguments to instantiate the named type reference, thus generating a type ty. 1. Apply Name Resolution for Members to ty and long-ident, which generates a new item. 2. Apply Item-Qualified Lookup to the new item and any remaining projections. A group of type names where projs begins with <types> or expr or projs is empty 1. Process the types and use the results as the arguments to instantiate the named type reference, thus generating a type ty. 1. Process the object construction ty(expr) as an object constructor call in the same way as new ty(expr). If projs is empty then process the object construction ty as an object constructor call in the same way as (fun arg -> new ty(arg)), i.e. resolve the object constructor call with no arguments. 2. Apply Expression-Qualified Lookup to item and any remaining projections. A group of method references 1. Apply Method Application Resolution for the method group. Method Application Resolution accepts an optional set of type arguments and a syntactic expression argument. Determine the arguments based on what projs begins with: • <types> expr, then use <types> as the type arguments and expr as the expression argument. • expr, then use expr as the expression argument. • anything else, use no expression argument or type arguments. 1. If the result of Method Application Resolution is labeled with the RequiresExplicitTypeArguments attribute, then explicit type arguments are required. 2. Let fty be the actual return type that results from Method Application Resolution. Apply Expression-Qualified Lookup to fty and any remaining projections. A group of property indexer references 1. Apply Method Application Resolution, and use the underlying getter indexer methods for the method group. 1. Determine the arguments to Method Application Resolution as described for a group of methods. A static field reference 1. Check the field for accessibility and attributes. 1. Let fty be the actual type of the field, taking into account the type ty via which the field was accessed in the case where this is a field in a generic type. 2. Apply Expression-Qualified Lookup to fty and projs. A union case tag, exception tag, or active pattern result element tag 1. Check the tag for accessibility and attributes. 1. If projs begins with expr, use expr as the expression argument. 2. Otherwise, use no expression argument or type arguments. In this case, build a function expression for the union case. 3. Let fty be the actual type of the union case. 4. Apply Expression-Qualified Lookup to fty and remaining projs. A CLI event reference 1. Check the event for accessibility and attributes. 1. Let fty be the actual type of the event. 2. Apply Expression-Qualified Lookup to fty and projs. An implicitly resolved symbolic operator name op 1. If op is a unary, binary or the ternary operator ?<-, resolve to the following expressions, respectively: (fun (x:^a) -> (^a : static member (op) : ^a -> ^b) x) (fun (x:^a) (y:^b) -> ((^a or ^b) : static member (op) : ^a * ^b -> ^c) (x,y)) (fun (x:^a) (y:^b) (z:^c) -> ((^a or ^b or ^c) : static member (op) : ^a * ^b * ^c -> ^d) (x,y,z)) 1. The resulting expressions are static member constraint invocation expressions (§0), which enable the default interpretation of operators by using type-directed member resolution. 2. Recheck the entire expression with additional subsequent projections .projs. ### Expression-Qualified Lookup Given an elaborated expression expr of type ty, and projections projs, Expression-Qualified Lookup computes the “lookups or applications” for expr.projs. Expression-Qualified Lookup proceeds through the following steps: 1. Inspect projs and process according to the following table. projs Action Comments Empty Assert that the type of the overall, original application expression is ty. Checking is complete. Starts with**(expr2)** Apply Function Application Resolution (§14.3). Checking is complete when Function Application Resolution returns. Starts with**<types>** Fail. Type instantiations may not be applied to arbitrary expressions; they can apply only to generic types, generic methods, and generic values. Starts with **.**long-ident Resolve long-ident using Name Resolution for Members (§14.1.4). Return a name resolution item item and a residue long identifier rest. Continue processing at step 2. For example, for ty = string and long-ident = Length , Name Resolution for Members returns a property reference to the CLI instance property System.String.Length. 2. If Step 1 returned an item and rest, report an error if item is not one of the following: • A group of methods. • A group of instance getter property indexers. • A single instance, non-indexer getter property. • A single instance F# field. • A single instance CLI field. 3. Proceed based on item as shown in the table: If item is: Action Group of methods 1. Apply Method Application Resolution for the method group. Method Application Resolution accepts an optional set of type arguments and a syntactic expression argument. If projs begins with: • <types>(arg), then use <types> as the type arguments and arg as the expression argument. • (arg), then use arg as the expression argument. • otherwise, use no expression argument or type arguments. 1. Let fty be the actual return type resulting from Method Application Resolution. Apply Expression-Qualified Lookup to fty and any remaining projections. Group of indexer properties 1. Apply Method Application Resolution and use the underlying getter indexer methods for the method group. 1. Determine the arguments to Method Application Resolution as described for a group of methods. Non-indexer getter property Apply Method Application Resolution for the method group that contains only the getter method for the property, with no type arguments and one () argument. Instance intermediate language (IL) or F# field F 1. Check the field for accessibility and attributes. 1. Let fty be the actual type of the field (taking into account the type ty by which the field was accessed). 2. Assert that ty is a subtype of the actual containing type of the field. 3. Produce an elaborated form for expr.F. If F is a field in a value type then take the address of expr by using the AddressOf (expr , NeverMutates) operation §6.9.4. 4. Apply Expression-Qualified Lookup to fty and projs. ## Function Application Resolution Given expressions f and expr where f has type ty, and given subsequent projections projs, Function Application Resolution does the following: 1. Asserts that f has type ty*1*** -> ty*2*** for new inference variables ty*1*** and ty*2**.* 2. If the assertion succeeds: 1. Check expr with the initial type ty*1**.* 1. Process projs using Expression-Qualified against ty*2***. 3. If the assertion fails, and expr has the form { computation-expr }: 1. Check the expression as the computation expression form f { computation-expr }, giving result type ty*1***. 1. Process projs using Expression-Qualified Lookup against ty*1***. ## Method Application Resolution Given a method group M, optional type arguments <ActualTypeArgs>, an optional syntactic argument obj, an optional syntactic argument arg, and overall initial type ty, Method Application Resolution resolves the overloading based on the partial type information that is available. It also: • Resolves optional and named arguments. • Resolves “out” arguments. • Resolves post-hoc property assignments. • Applies method application resolution. • Inserts ad hoc conversions that are only applied for method calls. If no syntactic argument is supplied, Method Application Resolution tries to resolve the use of the method as a first class value, such as the method call in the following example: List.map System.Environment.GetEnvironmentVariable ["PATH"; "USERNAME"] Method Application Resolution proceeds through the following steps: 1. Restrict the candidate method group M to those methods that are accessible from the point of resolution. 2. If an argument arg is present, determine the sets of unnamed and named actual arguments, UnnamedActualArgs and NamedActualArgs: 1. Decompose arg into a list of arguments: • If arg is a syntactic tuple arg1 ,..., argN, use these arguments. • If arg is a syntactic unit value (),use a zero-length list of arguments. 1. For each argument: • If arg is a binary expression of the form name=expr, it is a named actual argument. • Otherwise, arg is an unnamed actual argument. If there are no named actual arguments, and M has only one candidate method, which accepts only one required argument, ignore the decomposition of arg to tuple form. Instead,arg itself is the only named actual argument. All named arguments must appear after all unnamed arguments. Examples: x.M(1, 2) has two unnamed actual arguments. x.M(1, y = 2) has one unnamed actual argument and one named actual argument. x.M(1, (y = 2)) has two unnamed actual arguments. x.M( printfn "hello"; ()) has one unnamed actual argument. x.M((a, b)) has one unnamed actual argument. x.M(()) has one unnamed actual argument. 3. Determine the named and unnamed prospective actual argument types, called ActualArgTypes. • If an argument arg is present, the prospective actual argument types are fresh type inference variables for each unnamed and named actual argument. • If the argument has the syntactic form of an address-of expression **&**expr after ignoring parentheses around the argument, equate this type with a type byref<ty> for a fresh type ty. • If the argument has the syntactic form of a function expression fun pat*1*** … pat*n*** -> expr after ignoring parentheses around the argument, equate this type with a type ty*1 ->tyn -> rty for fresh types ty1*** … ty*n***. • If no argument arg is present: 1. If the method group contains a single method, the prospective unnamed argument types are one fresh type inference variable for each required, non-“out” parameter that the method accepts. 1. If the method group contains more than one method, the expected overall type of the expression is asserted to be a function type dty -> rty. • If dty is a tuple type (dty1 * .. * dtyN), the prospective argument types are (dty1, .. ,dtyN). • If dty is unit, then the prospective argument types are an empty list. • If dty is any other type, the prospective argument types are dty alone. 1. Subsequently: • The method application is considered to have one unnamed actual argument for each prospective unnamed actual argument type. • The method application is considered to have no named actual arguments. 4. For each candidate method in M, attempt to produce zero, one, or two prospective method calls Mpossible as follows: 1. If the candidate method is generic and has been generalized, generate fresh type inference variables for its generic parameters. This results in the FormalTypeArgs for M*possible***. 1. Determine the named and unnamed formal parameters, called NamedFormalArgs and UnnamedFormalArgs respectively, by splitting the formal parameters for M into parameters that have a matching argument in NamedActualArgs and parameters that do not. 2. If the number of UnnamedFormalArgs exceeds the number of UnnamedActualArgs, then modify UnnamedFormalArgs as follows: • Determine the suffix of UnnamedFormalArgs beyond the number of UnnamedActualArgs. • If all formal parameters in the suffix are “out” arguments with byref type, remove the suffix from UnnamedFormalArgs and call it ImplicitlyReturnedFormalArgs. • If all formal parameters in the suffix are optional arguments, remove the suffix from UnnamedFormalArgs and call it ImplicitlySuppliedFormalArgs. 1. If the last element of UnnamedFormalArgs has the ParamArray attribute and type pty**[]** for some pty, then modify UnnamedActualArgs as follows: • If the number of UnnamedActualArgs exceeds the number of UnnamedFormalArgs-1, produce a prospective method call named ParamArrayActualArgs that has the excess of UnnamedActualArgs removed. • If the number of UnnamedActualArgs equals the number of UnnamedFormalArgs**-1**, produce two prospective method calls: • One has an empty ParamArrayActualArgs. • One has no ParamArrayActualArgs. • If ParamArrayActualArgs has been produced, then Mpossible is said to use ParamArray conversion with type pty. 1. Associate each name**=**arg in NamedActualArgs with a target. A target is a named formal parameter, a settable return property, or a settable return field as follows: • If one of the arguments in NamedFormalArgs has name name, that argument is the target. • If the return type of M, before the application of any type arguments ActualTypeArgs, contains a settable property name,then name is the target. The available properties include any property extension members of type, found by consulting the ExtensionsInScope table. • If the return type of M, before the application of any type arguments ActualTypeArgs, contains a settable field name, then name is the target. 1. No prospective method call is generated if any of the following are true: • A named argument cannot be associated with a target. • The number of UnnamedActualArgs is less than the number of UnnamedFormalArgs after steps 4 a-e. • The number of ActualTypeArgs, if any actual type arguments are present, does not precisely equal the number of FormalTypeArgs for M. • The candidate method is static and the optional syntactic argument obj is present, or the candidate method is an instance method and obj is not present. 5. Attempt to apply initial types before argument checking. If only one prospective method call Mpossible exists, assert Mpossible by performing the following steps: 1. Verify that each ActualTypeArg*i*** is equal to its corresponding FormalTypeArg*i***. 1. Verify that the type of obj is a subtype of the containing type of the method M. 2. For each UnnamedActualArg*i*** and UnnamedFormalArg*i***, verify that the corresponding ActualArgType coerces to the type of the corresponding argument of M. 3. If Mpossible uses ParamArray conversion with type pty, then for each ParamArrayActualArg*i***, verify that the corresponding ActualArgType coerces to pty. 4. For each NamedActualArg*i*** that has an associated formal parameter target, verify that the corresponding ActualArgType coerces to the type of the corresponding argument of M. 5. For each NamedActualArg*i*** that has an associated property or field setter target, verify that the corresponding ActualArgType coerces to the type of the property or field. 6. Verify that the prospective formal return type coerces to the expected actual return type. If the method M has return type rty, the formal return type is defined as follows: • If the prospective method call contains ImplicitlyReturnedFormalArgs with type ty1, ..., tyN, the formal return type is rty * ty1 * ... * tyN. If rty is unit then the formal return type is ty1 * ... * tyN. • Otherwise the formal return type is rty. 6. Check and elaborate argument expressions. If arg is present: • Check and elaborate each unnamed actual argument expression arg*i***. Use the corresponding type in ActualArgTypes as the initial type. • Check and elaborate each named actual argument expression arg*i***. Use the corresponding type in ActualArgTypes as the initial type. 7. Choose a unique Mpossible according to the following rules: • For each Mpossible, determine whether the method is applicable by attempting to assert Mpossible as described in step 4a). If the actions in step 4a detect an inconsistent constraint set (§14.5), the method is not applicable. Regardless, the overall constraint set is left unchanged as a result of determining the applicability of each Mpossible. • If a unique applicable Mpossible exists, choose that method. Otherwise, choose the unique best Mpossible by applying the following criteria, in order: 1. Prefer candidates whose use does not constrain the use of a user-introduced generic type annotation to be equal to another type. 2. Prefer candidates that do not use ParamArray conversion. If two candidates both use ParamArray conversion with types pty*1*** and pty*2, and pty1* feasibly subsumes pty*2***, prefer the second; that is, use the candidate that has the more precise type. 3. Prefer candidates that do not have ImplicitlyReturnedFormalArgs. 4. Prefer candidates that do not have ImplicitlySuppliedFormalArgs. 5. If two candidates have unnamed actual argument types ty*11*** ... ty*1n*** and ty*21*** ... ty*2n, and each ty1i* either 1. feasibly subsumes ty*2i***, or 2. ty*2i*** is a System.Func type and ty*1i*** is some other delegate type, then prefer the second candidate. That is, prefer any candidate that has the more specific actual argument types, and consider any System.Func type to be more specific than any other delegate type. 6. Prefer candidates that are not extension members over candidates that are**.** 7. To choose between two extension members, prefer the one that results from the most recent use of open. 8. Prefer candidates that are not generic over candidates that are generic—that is, prefer candidates that have empty ActualArgTypes. Report an error if steps 1) through 8) do not result in the selection of a unique better method. 8. Once a unique best Mpossible is chosen, commit that method. 9. Apply attribute checks. 10. Build the resulting elaborated expression by following these steps: 1. If the type of obj is a variable type or a value type, take the address of obj by using the AddressOf(obj, PossiblyMutates) operation (§6.9.4). 1. Build the argument list by: • Passing each argument corresponding to an UnamedFormalArgs where the argument is an optional argument as a Some value. • Passing a None value for each argument that corresponds to an ImplicitlySuppliedFormalArgs. • Applying coercion to arguments. 1. Bind ImplicitlyReturnedFormalArgs arguments by introducing mutable temporaries for each argument, passing them as byref parameters, and building a tuple from these mutable temporaries and any method return value as the overall result. 2. For each NamedActualArgs whose target is a settable property or field, assign the value into the property. 3. If arg is not present, return a function expression that represents a first class function value. Two additional rules apply when checking arguments (see §8.13.7 for examples): • If a formal parameter has delegate type D, an actual argument farg has known type ty*1*** -> ... -> ty*n*** -> rty, and the number of arguments of the Invoke method of delegate type D is precisely n, interpret the formal parameter in the same way as the following: new D**(fun** arg*1*** ... arg*n*** -> farg arg*1*** ... arg*n***). For more information on the conversions that are automatically applied to arguments, see §8.13.6. • If a formal parameter is an “out” parameter of type byref<ty>, and an actual argument type is not a byref type, interpret the actual parameter in the same way as type ref<ty>. That is, an F# reference cell can be passed where a byref<ty> is expected. One effect of these additional rules is that a method that is used as a first class function value can resolve even if a method is overloaded and no further information is available. For example: let r = new Random() let roll = r.Next;; Method Application Resolution results in the following, despite the fact that in the standard CLI library, System.Random.Next is overloaded: val roll : int -> int The reason is that if the initial type contains no information about the expected number of arguments, the F# compiler assumes that the method has one argument. ### Additional Propagation of Known Type Information in F# 3.1 In the above descreiption of F# overload resolution, the argument expressions of a call to an overloaded set of methods callerObjArgTy.Method(callerArgExpr1, … callerArgExprN) calling calledObjArgTy.Method(calledArgTy1, … calledArgTyN) In F# 3.1 and subsequently, immediately prior to checking argument expressions, each argument position of the unnamed caller arguments for the method call is analysed to propagate type information extracted from method overloads to the expected types of lambda expressions. The new rule is applied when • the candidates are overloaded • the caller argument at the given unnamed argument position is a syntactic lambda, possible parenthesized • all the corresponding formal called arguments have calledArgTy either of • function type “calledArgDomainTy1 -> … -> calledArgDomainTyN -> calledArgRangeTy“ (after taking into account “function to delegate” adjustments), or • some other type which would cause an overload to be discarded • at least one overload has enough curried lambda arguments for it corresponding expected function type In this case, for each unnamed argument position, then for each overload: • Attempt to solve “callerObjArgTy = calledObjArgTy” for the overload, if the overload is for an instance member. When making this application, only solve type inference variables present in the calledObjArgTy. If any of these conversions fail, then skip the overload for the purposes of this rule • Attempt to solve “callerArgTy = (calledArgDomainTy1 -> … -> calledArgDomainTyN -> ?)”. If this fails, then skip the overload for the purposes of this rule ### Conditional Compilation of Member Calls If a member definition has the System.Diagnostics.Conditional attribute, then any application of the member is adjusted as follows: • The Conditional("symbol") attribute may apply to methods only. • Methods that have the Conditional attribute must have return type unit. The return type may be checked either on use of the method or definition of the method. • If symbol is not in the current set of conditional compilation symbols, the compiler eliminates application expressions that resolve to calls to members that have the Conditional attribute and ensures that arguments are not evaluated. Elimination of such expressions proceeds first with static members and then with instance members, as follows: • Static members: Type.M(args) () • Instance members: expr.M(args) () ### Implicit Insertion of Flexibility for Uses of Functions and Members At each use of a data constructor, named function, or member that forms an expression, flexibility is implicitly added to the expression. This flexibility is associated with the use of the function or member, according to the inferred type of the expression. The added flexibility allows the item to accept arguments that are statically known to be subtypes of argument types to a function without requiring explicit upcasts The flexibility is added by adjusting each expression expr which represents a use of a function or member as follows: • The type of the function or member is decomposed to the following form: ty11 * ... * ty1n -> ... -> tym1 * ... * tymn -> rty • If the type does not decompose to this form, no flexibility is added. • The positions tyij are called the “parameter positions” for the type. For each parameter position where tyij is not a sealed type, and is not a variable type, the type is replaced by a fresh type variable ty'ij with a coercion constraint ty'ij :> tyij. • After the addition of flexibility, the expression elaborates to an expression of type ty'11 * ... * ty'1n -> ... -> ty'm1 * ... * ty'mn -> rty but otherwise is semantically equivalent to expr by creating an anonymous function expression and inserting appropariate coercions on arguments where necessary. This means that F# functions whose inferred type includes an unsealed type in argument position may be passed subtypes when called, without the need for explicit upcasts. For example: type Base() = member b.X = 1 type Derived(i : int) = inherit Base() member d.Y = i let d = new Derived(7) let f (b : Base) = b.X // Call f: Base -> int with an instance of type Derived let res = f d // Use f as a first-class function value of type : Derived -> int let res2 = (f : Derived -> int) The F# compiler determines whether to insert flexibility after explicit instantiation, but before any arguments are checked. For example, given the following: let M<'b>(c :'b, d :'b) = 1 let obj = new obj() let str = "" these expressions pass type-checking: M<obj>(obj, str) M<obj>(str, obj) M<obj>(obj, obj) M<obj>(str, str) M(obj, obj) M(str, str) These expressions do not, because the target type is a variable type: M(obj, str) M(str, obj) ## Constraint Solving Constraint solving involves processing (“solving”) non-primitive constraints to reduce them to primitive, normalized constraints on type variables. The F# compiler invokes constraint solving every time it adds a constraint to the set of current inference constraints at any point during type checking. Given a type inference environment, the normalized form of constraints is a list of the following primitive constraints where typar is a type inference variable: typar :> type typar : null (type or ... or type) : (member-sig) typar : (new : unit -> 'T) typar : struct typar : unmanaged typar : comparison typar : equality typar : not struct typar : enum<type> typar : delegate<type, type> Each newly introduced constraint is solved as described in the following sections. ### Solving Equational Constraints New equational constraints in the form typar = type or type = typar, where typar is a type inference variable, cause type to replace typar in the constraint problem; typar is eliminated. Other constraints that are associated with typar are then no longer primitive and are solved again. New equational constraints of the form type**<tyarg11,..., tyarg1n> = type<tyarg21,..., tyarg2n> are reduced to a series of constraints tyarg1i** = tyarg*2i*** on identical named types and solved again. ### Solving Subtype Constraints Primitive constraints in the form typar :> obj are discarded. New constraints in the form type1 :> type2, where type2 is a sealed type, are reduced to the constraint type1 = type2 and solved again. New constraints in either of these two forms are reduced to the constraints tyarg*11*** = tyarg*21 ... tyarg1n = tyarg**2n*** and solved again: type**<tyarg11,..., tyarg1n> :> type<tyarg21,..., tyarg2n**> type**<tyarg11,..., tyarg1n> = type<tyarg21,..., tyarg2n**> Note: F# generic types do not support covariance or contravariance. That is, although single-dimensional array types in the CLI are effectively covariant, F# treats these types as invariant during constraint solving. Likewise, F# considers CLI delegate types as invariant and ignores any CLI variance type annotations on generic interface types and generic delegate types. New constraints of the form type*1<tyarg11,...,* tyarg*1n> :> type2<tyarg21,...,* tyarg*2n> where type1* and type*2*** are hierarchically related, are reduced to an equational constraint on two instantiations of type*2 according to the subtype relation between type1* and type*2***, and solved again. For example, if MySubClass<'T> is derived from MyBaseClass<list<'T>>, then the constraint MySubClass<'T> :> MyBaseClass<int> is reduced to the constraint MyBaseClass<list<'T>> :> MyBaseClass<list<int>> and solved again, so that the constraint 'T = int will eventually be derived. Note: Subtype constraints on single-dimensional array types ty[] :> ty are reduced to residual constraints, because these types are considered to be subtypes of System.Array, System.Collections.Generic.IList<'T>, System.Collections.Generic.ICollection<'T>, and System.Collections.Generic.IEnumerable<'T>. Multidimensional array types ty[,…,] are also subtypes of System.Array. Types from other CLI languages may, in theory, support multiple instantiations of the same interface type, such as C : I<int>, I<string>. Consequently, it is more difficult to solve a constraint such as C :> I<'T>. Such constraints are rarely used in practice in F# coding. To solve this constraint, the F# compiler reduces it to a constraint C :> I<'T>, where I<'T> is the first interface type that occurs in the tree of supported interface types, when the tree is ordered from most derived to least derived, and iterated left-to-right in the order of the declarations in the CLI metadata. The F# compiler ignores CLI variance type annotations on interfaces. New constraints of the form type :> 'b are solved again as type = 'b. Note: Such constraints typically occur only in calls to generic code from other CLI languages where a method accepts a parameter of a “naked” variable type—for example, a C# 2.0 function with a signature such as T Choose<'T>(T x, T y). ### Solving Nullness, Struct, and Other Simple Constraints New constraints in any of the following forms, where type is not a variable type, are reduced to further constraints: type : null type : (new : unit -> 'T) type : struct type : not struct type : enum<type> type : delegate<type, type> type : unmanaged The compiler then resolves them according to the requirements for each kind of constraint listed in §5.2 and §5.4.8. ### Solving Member Constraints New constraints in the following form ) are solved as member constraints (§5.2.3): (type1 or ... or typen) : (member-sig) A member constraint is satisfied if one of the types in the support set type*1 ... typen* satisfies the member constraint. A static type type satisfies a member constraint in the form (staticopt member ident : arg-type1 * ... * arg-typen -> ret-type**)** if all of the following are true: • type is a named type whose type definition contains the following member, which takes n arguments: staticopt member ident : formal-arg-type1 * ... * formal-arg-typen -> ret-type • The type and the constraint are both marked static or neither is marked static . • The assertion of type inference constraints on the arguments and return types does not result in a type inference error. As mentioned in §5.2.3, a type variable may not be involved in the support set of more than one member constraint that has the same name, staticness, argument arity, and support set. If a type variable is in the support set of more than one such constraint, the argument and return types are themselves constrained to be equal. #### Simulation of Solutions for Member Constraints Certain types are assumed to implicitly define static members even though the actual CLI metadata for types does not define these operators. This mechanism is used to implement the extensible conversion and math functions of the F# library including sin, cos, int, float, (+), and (-). The following table shows the static members that are implicitly defined for various types. Type Implicitly defined static members Integral types: byte, sbyte, int16, uint16, int32, uint32, int64, uint64, nativeint, unativeint op_BitwiseAnd, op_BitwiseOr, op_ExclusiveOr, op_LeftShift, op_RightShift, op_UnaryPlus, op_UnaryNegation, op_Increment, op_Decrement, op_LogicalNot, op_OnesComplement op_Addition, op_Subtraction, op_Multiply, op_Division, op_Modulus, op_UnaryPlus op_Explicit: takes the type as an argument and returns byte, sbyte, int16, uint16, int32, uint32, int64, uint64, float32, float, decimal, nativeint, or unativeint Signed integral CLI types: sbyte, int16, int32, int64 and nativeint op_UnaryNegation Sign Abs Floating-point CLI types: float32 and float Sin, Cos, Tan, Sinh, Cosh, Tanh, Atan, Acos, Asin, Exp, Ceiling, Floor, Round, Log10, Log, Sqrt, Atan2, Pow op_Addition, op_Subtraction, op_Multiply, op_Division, op_Modulus, op_UnaryPlus op_UnaryNegation Sign Abs op_Explicit: takes the type as an argument and returns byte, sbyte, int16, uint16, int32, uint32, int64, uint64, float32, float, decimal, nativeint, or unativeint decimal type Note: The decimal type is included only for the Sign static member. This is deliberate: in the CLI, System.Decimal includes the definition of static members such as op_Addition and the F# compiler does not need to simulate the existence of these methods. Sign String type string op_Addition op_Explicit: takes the type as an argument and return byte, sbyte, int16, uint16, int32, uint32, int64, uint64, float32, float or decimal. ### Over-constrained User Type Annotations An implementation of F# must give a warning if a type inference variable that results from a user type annotation is constrained to be a type other than another type inference variable. For example, the following results in a warning because 'T has been constrained to be precisely string: let f (x:'T) = (x:string) During the resolution of overloaded methods, resolutions that do not give such a warning are preferred over resolutions that do give such a warning. ## Checking and Elaborating Function, Value, and Member Definitions This section describes how function, value, and member definitions are checked, generalized, and elaborated. These definitions occur in the following contexts: • Module declarations • Class type declarations • Expressions • Computation expressions Recursive definitions can also occur in each of these locations. In addition, member definitions in a mutually recursive group of type declarations are implicitly recursive. Each definition is one of the following: • A function definition : inline***opt*** ident*1** pat**1*** ... pat*n*** :opt return-type*opt*** = rhs-expr • A value definition, which defines one or more values by matching a pattern against an expression: mutable***opt*** pat :opt type*opt*** = rhs-expr • A member definition: staticopt member** ident*opt*** ident pat*1*** ... pat*n*** = expr For a function, value, or member definition in a class: 1. If the definition is an instance function, value or member, checking uses an environment to which both of the following have been added: • The instance variable for the class, if one is present. • All previous function and value definitions for the type, whether static or instance. 2. If the definition is static (that is, a static function, value or member defeinition), checking uses an environment to which all previous static function, value, and member definitions for the type have been added. ### Ambiguities in Function and Value Definitions In one case, an ambiguity exists between the syntax for function and value definitions. In particular, ident pat = expr can be interpreted as either a function or value definition. For example, consider the following: type OneInteger = Id of int let Id x = x In this case, the ambiguity is whether Id x is a pattern that matches values of type OneInteger or is the function name and argument list of a function called Id. In F# this ambiguity is always resolved as a function definition. In this case, to make a value definition, use the following syntax in which the ambiguous pattern is enclosed in parentheses: let v = if 3 = 4 then Id "yes" else Id "no" let (Id answer) = v ### Mutable Value Definitions Value definitions may be marked as mutable. For example: let mutable v = 0 while v < 10 do v <- v + 1 printfn "v = %d" v These variables are implicitly dereferenced when used. ### Processing Value Definitions A value definition pat = rhs-expr with optional pattern type type is processed as follows: 1. The pattern pat is checked against a fresh initial type ty (or type if such a type is present). This check results in zero or more identifiers ident*1** ... ident**m, each of type ty1 ... ty**m***. 2. The expression rhs-expr is checked against initial type ty, resulting in an elaborated form expr. 3. Each ident*i*** (of type ty*i) is then generalized (§14.6.7) and yields generic parameters <typarsj>*. 4. The following rules are checked: • All ident*j*** must be distinct. • Value definitions may not be inline. 5. If pat is a single value pattern, the resulting elaborated definition is: ident <typars1> = expr body-expr 6. Otherwise, the resulting elaborated definitions are the following, where tmp is a fresh identifier and each expr*i*** results from the compilation of the pattern pat (§7) against input tmp. tmp <typars1… typarsn> = expr ident1 <typars1> = expr1 identn <typarsn> = exprn ### Processing Function Definitions A function definition ident*1** pat**1*** ... pat*n*** = rhs-expr is processed as follows: 1. If ident*1*** is an active pattern identifier then active pattern result tags are added to the environment (§10.2.4). 2. The expression (fun pat1 ... pat*n*** : return-type -> rhs-expr**)** is checked against a fresh initial type ty*1*** and reduced to an elaborated form expr1. The return type is omitted if the definition does not specify it. 3. The ident*1*** (of type ty*1) is then generalized (§14.6.7) and yields generic parameters <typars1>*. 4. The following rules are checked: • Function definitions may not be mutable. Mutable function values should be written as follows: let mutable f = (fun args -> ...) • The patterns of functions may not include optional arguments (§8.13.6). 5. The resulting elaborated definition is: ident1 <typars1> = expr1 ### Processing Recursive Groups of Definitions A group of functions and values may be declared recursive through the use of let rec. Groups of members in a recursive set of type definitions are also implicitly recursive. In this case, the defined values are available for use within their own definitions—that is, within all the expressions on the right-hand side of the definitions. For example: let rec twoForward count = printfn "at %d, taking two steps forward" count if count = 1000 then "got there!" else oneBack (count + 2) and oneBack count = printfn "at %d, taking one step back " count twoForward (count – 1) When one or more definitions specifies a value, the recursive expressions are analyzed for safety (§14.6.6). This analysis may result in warnings—including some reported at compile time—and runtime checks. Within recursive groups, each definition in the group is checked (§14.6.7) and then the definitions are generalized incrementally. In addition, any use of an ungeneralized recursive definition results in immediate constraints on the recursively defined construct. For example, consider the following declaration: let rec countDown count x = if count > 0 then let a = countDown (count - 1) 1 // constrains "x" to be of type int let b = countDown (count – 1) "Hello" // constrains "x" to be of type string a + b else 1 In this example, the definition is not valid because the recursive uses of f result in inconsistent constraints on x. If a definition has a full signature, early generalization applies and recursive calls at different types are permitted (§14.6.7). For example: module M = let rec f<'T> (x:'T) : 'T = let a = f 1 let b = f "Hello" x In this example, the definition is valid because f is subject to early generalization, and so the recursive uses of f do not result in inconsistent constraints on x. ### Recursive Safety Analysis A set of recursive definitions may include value definitions. For example: type Reactor = React of (int -> React) * int let rec zero = React((fun c -> zero), 0) let const n = let rec r = React((fun c -> r), n) r Recursive value definitions may result in invalid recursive cycles, such as the following: let rec x = x + 1 The Recursive Safety Analysis process partially checks the safety of these definitions and convert thems to a form that uses lazy initialization, where runtime checks are inserted to check initialization. A right-hand side expression is safe if it is any of the following: • A function expression, including those whose bodies include references to variables that are defined recursively. • An object expression that implements an interface, including interfaces whose member bodies include references to variables that are being defined recursively. • A lazy delayed expression. • A record, tuple, list, or data construction expression whose field initialization expressions are all safe. • A value that is not being recursively bound. • A value that is being recursively bound and appears in one of the following positions: • As a field initializer for a field of a record type where the field is marked mutable. • As a field initializer for an immutable field of a record type that is defined in the current assembly. If record fields contain recursive references to values being bound, the record fields must be initialized in the same order as their declared type, as described later in this section. • Any expression that refers only to earlier variables defined by the sequence of recursive definitions. Other right-hand side expressions are elaborated by adding a new definition. If the original definition is u = expr then a fresh value (say v) is generated with the definition: v = lazy expr and occurrences of the original variable u on the right-hand side are replaced by Lazy.force v. The following definition is then added at the end of the definition list: u = v**.Force()** Note: This specification implies that recursive value definitions are executed as an initialization graph of delayed computations. Some recursive references may be checked at runtime because the computations that are involved in evaluating the definitions might actually execute the delayed computations. The F# compiler gives a warning for recursive value definitions that might involve a runtime check. If runtime self-reference does occur then an exception will be raised. Recursive value definitions that involve computation are useful when defining objects such as forms, controls, and services that respond to various inputs. For example, GUI elements that store and retrieve the state of the GUI elements as part of their specification typically involve recursive value definitions. A simple example is the following menu item, which prints out part of its state when invoked: open System.Windows.Form let rec menuItem : MenuItem = new MenuItem("&Say Hello", new EventHandler(fun sender e -> printfn "Text = %s" menuItem.Text), Shortcut.CtrlH) This code results in a compiler warning because, in theory, the new MenuItem(...) constructor might evaluate the callback as part of the construction process. However, because the System.Windows.Forms library is well designed, in this example this does not happen in practice, and so the warning can be suppressed or ignored by using compiler options. The F# compiler performs a simple approximate static analysis to determine whether immediate cyclic dependencies are certain to occur during the evaluation of a set of recursive value definitions. The compiler creates a graph of definite references and reports an error if such a dependency cycle exists. All references within function expressions, object expressions, or delayed expressions are assumed to be indefinite, which makes the analysis an under-approximation. As a result, this check catches naive and direct immediate recursion dependencies, such as the following: let rec A = B + 1 and B = A + 1 Here, a compile-time error is reported. This check is necessarily approximate because dependencies under function expressions are assumed to be delayed, and in this case the use of a lazy initialization means that runtime checks and forces are inserted. Note: In F# 3.1 this check does not apply to value definitions that are generic through generalization because a generic value definition is not executed immediately, but is instead represented as a generic method. For example, the following value definitions are generic because each right-hand-side is generalizable: let rec a = b and b = a In compiled code they are represented as a pair of generic methods, as if the code had been written as follows: let rec a<'T>() = b<'T>() and b<'T>() = a<'T>() As a result, the definitions are not executed immediately unless the functions are called. Such definitions indicate a programmer error, because executing such generic, immediately recursive definitions results in an infinite loop or an exception. In practice these definitions only occur in pathological examples, because value definitions are generalizable only when the right-hand-side is very simple, such as a single value. Where this issue is a concern, type annotations can be added to existing value definitions to ensure they are not generic. For example: let rec a : int = b and b : int = a In this case, the definitions are not generic. The compiler performs immediate dependency analysis and reports an error. In addition, record fields in recursive data expressions must be initialized in the order they are declared. For example: **type Foo = { x: int y: int parent: Foo option children: Foo list } let rec parent = { x = 0; y = 0; parent = None; children = children } and children = [{ x = 1; y = 1; parent = Some parent; children = [] }] printf "%A" parent** Here, if the order of the fields x and y is swapped, a type-checking error occurs. ### Generalization Generalization is the process of inferring a generic type for a definition where possible, thereby making the construct reusable with multiple different types. Generalization is applied by default at all function, value, and member definitions, except where listed later in this section. Generalization also applies to member definitions that implement generic virtual methods in object expressions. Generalization is applied incrementally to items in a recursive group after each item is checked. Generalization takes a set of ungeneralized but type-checked definitions checked-defns that form part of a recursive group, plus a set of unchecked definitions unchecked-defns that have not yet been checked in the recursive group, and an environment env. Generalization involves the following steps: 1. Choose a subset generalizable-defns of checked-defns to generalize. A definition can be generalized if its inferred type is closed with respect to any inference variables that are present in the types of the unchecked-defns that are in the recursive group and that are not yet checked or which, in turn, cannot be generalized. A greatest-fixed-point computation repeatedly removes definitions from the set of checked-defns until a stable set of generalizable definitions remains. 2. Generalize all type inference variables that are not otherwise ungeneralizable and for which any of the following is true: • The variable is present in the inferred types of one or more of generalizable-defns. • The variable is a type parameter copied from the enclosing type definition (for members and “let” definitions in classes). • The variable is explicitly declared as a generic parameter on an item. The following type inference variables cannot be generalized: • A type inference variable ^typar that is part of the inferred or declared type of a definition, unless the definition is marked inline. • A type inference variable in an inferred type in the ExprItems or PatItems tables of env, or in an inferred type of a module in the ModulesAndNamespaces table in env. • A type inference variable that is part of the inferred or declared type of a definition in which the elaborated right-hand side of the definition is not a generalizable expression, as described later in this section. • A type inference variable that appears in a constraint that itself refers to an ungeneralizable type variable. Generalizable type variables are computed by a greatest-fixed-point computation, as follows: 1. Start with all variables that are candidates for generalization. 2. Determine a set of variables U that cannot be generalized because they are free in the environment or present in ungeneralizable definitions. 3. Remove the variables in U from consideration. 4. Add to U any inference variables that have a constraint that involves a variable in U. 5. Repeat steps 2 through 4. Informally, generalizable expressions represent a subset of expressions that can be freely copied and instantiated at multiple types without affecting the typical semantics of an F# program. The following expressions are generalizable: • A function expression • An object expression that implements an interface • A delegate expression • A “let” definition expression in which both the right-hand side of the definition and the body of the expression are generalizable • A “let rec” definition expression in which the right-hand sides of all the definitions and the body of the expression are generalizable • A tuple expression, all of whose elements are generalizable • A record expression, all of whose elements are generalizable, where the record contains no mutable fields • A union case expression, all of whose arguments are generalizable • An exception expression, all of whose arguments are generalizable • An empty array expression • A simple constant expression • An application of a type function that has the GeneralizableValue attribute. Explicit type parameter definitions on value and member definitions can affect the process of type inference and generalization. In particular, a declaration that includes explicit generic parameters will not be generalized beyond those generic parameters. For example, consider this function: let f<'T> (x : 'T) y = x During type inference, this will result in a function of the following type, where '_b is a type inference variable that is yet to be resolved. f<'T> : 'T -> '_b -> '_b To permit generalization at these definitions, either remove the explicit generic parameters (if they can be inferred), or use the required number of parameters, as the following example shows: let throw<'T,'U> (x:'T) (y:'U) = x ### Condensation of Generalized Types After a function or member definition is generalized, its type is condensed by removing generic type parameters that apply subtype constraints to argument positions. (The removed flexibility is implicitly reintroduced at each use of the defined function; see §14.4.3). Condensation decomposes the type of a value or member to the following form: ty11 * ... * ty1n -> ... -> tym1 * ... * tymn -> rty The positions tyij are called the parameter positions for the type. Condensation applies to a type parameter 'a if all of the following are true: • 'a is not an explicit type parameter. • 'a occurs at exactly one tyij parameter position. • 'a has a single coercion constraint 'a :> ty and no other constraints. However, one additional nullness constraint is permitted if ty satisfies the nullness constraint. • 'a does not occur in any other tyij, nor in rty. • 'a does not occur in the constraints of any condensed typar. Condensation is a greatest-fixed-point computation that initially assumes all generalized type parameters are condensed, and then progressively removes type parameters until a minimal set remains that satisfies the above rules. The compiler removes all condensed type parameters and replaces them with their subtype constraint ty. For example: let F x = (x :> System.IComparable).CompareTo(x) After generalization, the function is inferred to have the following type: F : 'a -> int when 'a :> System.IComparable In this case, the actual inferred, generalized type for F is condensed to: F : System.IComparable -> R Condensation does not apply to arguments of unconstrained variable type. For example: let ignore x = () with type ignore: 'a -> unit In particular, this is not condensed to ignore: obj -> unit In rare cases, condensation affects the points at which value types are boxed. In the following example, the value 3 is now boxed at uses of the function: F 3 If a function is not generalized, condensation is not applied. For example, consider the following: let test1 = let ff = Seq.map id >> Seq.length (ff [1], ff [| 1 |]) // error here In this example, ff is not generalized, because it is not defined by using a generalizable expression—computed functions such as Seq.map id >> Seq.length are not generalizable. This means that its inferred type, after processing the definition, is F : '_a -> int when '_a :> seq<'_b> where the type variables are not generalized and are unsolved inference variables. The application of ff to [1] equates 'a with int list, making the following the type of F: F : int list -> int The application of ff to an array type then causes an error. This is similar to the error returned by the following: let test1 = let ff = Seq.map id >> Seq.length (ff [1], ff ["one"]) // error here Again, ff is not generalized, and its use with arguments of type int list and string list is not permitted. ## Dispatch Slot Inference The F# compiler applies Dispatch Slot Inference to object expressions and type definitions before it processes their members. For both object expressions and type definitions, the following are input to Dispatch Slot Inference: • A type ty*0*** that is being implemented. • A set of members override x.M(arg1...argN*)*. • A set of additional interface types ty*1*** ... ty*n.*** • A further set of members override x.M(arg1...argN) for each ty*i***. Dispatch slot inference associates each member with a unique abstract member or interface member that the collected types ty*i*** define or inherit. The types ty*0*** ... ty*n*** together imply a collection of required types R, each of which has a set of required dispatch slots SlotsR of the form abstract M : aty*1...atyN -> atyrty. Each dispatch slot is placed under the most-specific tyi*** relevant to that dispatch slot. If there is no most-specific type for a dispatch slot, an error occurs. For example, assume the following definitions: type IA = interface abstract P : int end type IB = interface inherit IA end type ID = interface inherit IB end With these definitions, the following object expression is legal. Type IB is the most-specific implemented type that encompasses IA, and therefore the implementation mapping for P must be listed under IB: let x = { new ID interface IB with member x.P = 2 } But given: type IA = interface abstract P : int end type IB = interface inherit IA end type IC = interface inherit IB end type ID = interface inherit IB inherit IC end then the following object expression causes an error, because both IB and IC include the interface IA, and consequently the implementation mapping for P is ambiguous. let x = { new ID interface IB with member x.P = 2 interface IC with member x.P = 2 } The ambiguity can be resolved by explicitly implementing interface IA. After dispatch slots are assigned to types, the compiler tries to associate each member with a dispatch slot based on name and number of arguments. This is called dispatch slot inference, and it proceeds as follows: • For each member x.M(arg1...argN) in type ty*i***, attempt to find a single dispatch slot in the form abstract M : aty*1***...atyN -> rty with name M, argument count N, and most-specific implementing type ty*i***. • To determine the argument counts, analyze the syntax of patterns and look specifically for tuple and unit patterns. Thus, the following members have argument count 1, even though the argument type is unit: member obj.ToString(() | ()) = ... member obj.ToString(():unit) = ... member obj.ToString(_:unit) = ... • A member may have a return type, which is ignored when determining argument counts: member obj.ToString() : string = ... For example, given let obj1 = { new System.Collections.Generic.IComparer<int> with member x.Compare(a,b) = compare (a % 7) (b % 7) } the types of a and b are inferred by looking at the signature of the implemented dispatch slot, and are hence both inferred to be int. ## Dispatch Slot Checking Dispatch Slot Checking is applied to object expressions and type definitions to check consistency properties, such as ensuring that all abstract members are implemented. After the compiler checks all bodies of all methods, it checks that a one-to-one mapping exists between dispatch slots and implementing members based on exact signature matching. The interface methods and abstract method slots of a type are collectively known as dispatch slots. Each object expression and type definition results in an elaborated dispatch map. This map is keyed by dispatch slots, which are qualified by the declaring type of the slot. This means that a type that supports two interfaces I and I2, both of which contain the method m, may supply different implementations for I.m() and I2.m(). The construction of the dispatch map for any particular type is as follows: • If the type definition or extension has an implementation of an interface, mappings are added for each member of the interface, • If the type definition or extension has a default or override member, a mapping is added for the associated abstract member slot. ## Byref Safety Analysis Byref arguments are pointers that can be stack-bound and are used to pass values by reference to procedures in CLI languages, often to simulate multiple return values. Byref pointers are not often used in F#; more typically, tuple values are used for multiple return values. However, a byref value can result from calling or overriding a CLI method that has a signature that involves one or more byref values. To ensure the safety of byref arguments, the following checks are made: • Byref types may not be used as generic arguments. • Byref values may not be used in any of the following: • The argument types or body of function expressions (fun … -> …). • The member implementations of object expressions. • The signature or body of let-bound functions in classes. • The signature or body of let-bound functions in expressions. Note that function expressions occur in: • The elaborated form of sequence expressions. • The elaborated form of computation expressions. • The elaborated form of partial applications of module-bound functions and members. In addition: • A generic type cannot be instantiated by a byref type. • An object field cannot have a byref type. • A static field or module-bound value cannot have a byref type. As a result, a byref-typed expression can occur only in these situations: • As an argument to a call to a module-defined function or class-defined function. • On the right-hand-side of a value definition for a byref-typed local. These restrictions also apply to uses of the prefix && operator for generating native pointer values. ## Promotion of Escaping Mutable Locals to Objects Value definitions whose byref address would be subject to the restrictions on byref<_> listed in §14.9 are treated as implicit declarations of reference cells. For example let sumSquares n = let mutable total = 0 [ 1 .. n ] |> Seq.iter (fun x -> total <- total + x*x) total is considered equivalent to the following definition: let sumSquares n = let total = ref 0 [ 1 .. n ] |> Seq.iter (fun x -> total.contents <- total.contents + x*x) total.contents because the following would be subject to byref safety analysis: let sumSquares n = let mutable total = 0 &total ## Arity Inference During checking, members within types and function definitions within modules are inferred to have an arity. An arity includes both of the following: • The number of iterated (curried) arguments n • A tuple length for these arguments [A1;...;An]. A tuple length of zero indicates that the corresponding argument is of type unit. Arities are inferred as follows. A function definition of the following form is given arity [A1;...;An], where each A*i*** is derived from the tuple length for the final inferred types of the patterns: let ident pat*1*** ... pat*n*** = ... For example, the following is given arity [1; 2]: let f x (y,z) = x + y + z Arities are also inferred from function expressions that appear on the immediate right of a value definition. For example, the following has an arity of [1]: let f = fun x -> x + 1 Similarly, the following has an arity of [1;1]: let f x = fun y -> x + y Arity inference is applied partly to help define the elaborated form of a function definition. This is the form that other CLI languages see. In particular: • A function value F in a module that has arity [A1;...;An] and the type ty*1,1*** * ... * ty*1,A1*** -> ... -> ty*n,1*** * ... * ty*n,An*** -> rty elaborates to a CLI static method definition with signature rty F(ty1,1, ..., ty*1,A1, ..., tyn,1, ..., tyn,An***). • F# instance (respectively static) methods that have arity [A1;...;An] and type ty*1,1*** * ... * ty*1,A1*** -> ... -> ty*n,1*** * ... * ty*n,An*** -> rty elaborate to a CLI instance (respectively static) method definition with signature rty F(ty1,1, ..., ty*1,A1***), subject to the syntactic restrictions that result from the patterns that define the member, as described later in this section. For example, consider a function in a module with the following definition: let AddThemUp x (y, z) = x + y + z This function compiles to a CLI static method with the following C# signature: int AddThemUp(int x, int y, int z); Arity inference applies differently to function and member definitions. Arity inference on function definitions is fully type-directed. Arity inference on members is limited if parentheses or other patterns are used to specify the member arguments. For example: module Foo = // compiles as a static method taking 3 arguments let test1 (a1: int, a2: float, a3: string) = () // compiles as a static method taking 3 arguments let test2 (aTuple : int * float * string) = () // compiles as a static method taking 3 arguments let test3 ( (aTuple : int * float * string) ) = () // compiles as a static method taking 3 arguments let test4 ( (a1: int, a2: float, a3: string) ) = () // compiles as a static method taking 3 arguments let test5 (a1, a2, a3 : int * float * string) = () type Bar() = // compiles as a static method taking 3 arguments static member Test1 (a1: int, a2: float, a3: string) = () // compiles as a static method taking 1 tupled argument static member Test2 (aTuple : int * float * string) = () // compiles as a static method taking 1 tupled argument static member Test3 ( (aTuple : int * float * string) ) = () // compiles as a static method taking 1 tupled argument static member Test4 ( (a1: int, a2: float, a3: string) ) = () // compiles as a static method taking 1 tupled argument static member Test5 (a1, a2, a3 : int * float * string) = () ## Additional Constraints on CLI Methods F# treats some CLI methods and types specially, because they are common in F# programming and cause extremely difficult-to-find bugs. For each use of the following constructs, the F# compiler imposes additional ad hoc constraints: x.Equals(yobj) requires type ty : equality for the static type of x x.GetHashCode() requires type ty : equality for the static type of x new Dictionary<A,B>() requires A : equality, for any overload that does not take an IEqualityComparer<T> No constraints are added for the following operations. Consider writing wrappers around these functions to improve the type safety of the operations. System.Array.BinarySearch<T>(array,value) requiring C : comparison, for any overload that does not take an IComparer<T> System.Array.IndexOf requiring C : equality System.Array.LastIndexOf(array,T) requiring C : equality System.Array.Sort<'T>(array) requiring C : comparison, for any overload that does not take an IEqualityComparer<T> new SortedList<A,B>() requiring A : comparison, for any overload that does not take an IEqualityComparer<T> new SortedDictionary<A,B>() requiring C : comparison, for any overload that does not take an IEqualityComparer<_> # Lexical Filtering ## Lightweight Syntax F# supports lightweight syntax, in which whitespace makes indentation significant. The lightweight syntax option is a conservative extension of the explicit language syntax, in the sense that it simply lets you leave out certain tokens such as in and ;; because the parser takes indentation into account. Indentation can make a surprising difference in the readability of code. Compiling your code with the indentation-aware syntax option is useful even if you continue to use explicit tokens, because the compiler reports many indentation problems with your code and ensures a regular, clear formatting style. In the processing of lightweight syntax, comments are considered pure whitespace. This means that the compiler ignores the indentation position of comments. Comments act as if they were replaced by whitespace characters. Tab characters cannot be used in F# files. ### Basic Lightweight Syntax Rules by Example The basic rules that the F# compiler applies when it processes lightweight syntax are shown below, illustrated by example. ;; delimiter When the lightweight syntax option is enabled, top level expressions do not require the ;; delimiter because every construct that starts in the first column is implicitly a new declaration. The ;; delimiter is still required to terminate interactive entries to fsi.exe, but not when using F# Interactive from Visual Studio. Lightweight Syntax printf "Hello" printf "World" Normal Syntax printf "Hello";; printf "World";; in keyword When the lightweight syntax option is enabled, the in keyword is optional. The token after the "=" in a 'let' definition begins a new block, and the pre-parser inserts an implicit separating in token between each definition that begins at the same column as that token. Lightweight Syntax let SimpleSample() = let x = 10 + 12 - 3 let y = x * 2 + 1 let r1,r2 = x/3, x%3 (x,y,r1,r2) Normal Syntax #indent "off" let SimpleSample() = let x = 10 + 12 - 3 in let y = x * 2 + 1 in let r1,r2 = x/3, x%3 in (x,y,r1,r2) done keyword When the lightweight syntax option is enabled, the done keyword is optional. Indentation establishes the scope of structured constructs such as match, for, while and if/then/else. Lightweight Syntax let FunctionSample() = let tick x = printfn "tick %d" x let tock x = printfn "tock %d" x let choose f g h x = if f x then g x else h x for i = 0 to 10 do choose (fun n -> n%2 = 0) tick tock i printfn "done!" Normal Syntax #indent "off" let FunctionSample() = let tick x = printfn "tick %d" x in let tock x = printfn "tock %d" x in let choose f g h x = if f x then g x else h x in for i = 0 to 10 do choose (fun n -> n%2 = 0) tick tock i done; printfn "done!" if/then/else Scope When the lightweight syntax option is enabled, the scope of if/then/else is implicit from indentation. Without the lightweight syntax option, begin/end or parentheses are often required to delimit such constructs. Lightweight Syntax let ArraySample() = let numLetters = 26 let results = Array.create numLetters 0 let data = "The quick brown fox" for i = 0 to data.Length - 1 do let c = data.Chars(i) let c = Char.ToUpper(c) if c >= 'A' && c <= 'Z' then let i = Char.code c - Char.code 'A' results.[i] <- results.[i] + 1 printfn "done!" Normal Syntax #indent "off" let ArraySample() = let numLetters = 26 in let results = Array.create numLetters 0 in let data = "The quick brown fox" in for i = 0 to data.Length - 1 do let c = data.Chars(i) in let c = Char.ToUpper(c) in if c >= 'A' && c <= 'Z' then begin let i = Char.code c - Char.code 'A' in results.[i] <- results.[i] + 1 end done; printfn "done!" ### Inserted Tokens Lexical filtering inserts the following hidden tokens : tokenin // Note: also called ODECLEND

token $done // Note: also called ODECLEND token$begin // Note: also called OBLOCKBEGIN

token $end // Note: also called OEND, OBLOCKEND and ORIGHT_BLOCK_END token$sep // Note: also called OBLOCKSEP

token $app // Note: also called HIGH_PRECEDENCE_APP token$tyapp // Note: also called HIGH_PRECEDENCE_TYAPP

Note: The following tokens are also used in the Microsoft F# implementation. They are translations of the corresponding input tokens and help provide better error messages for lightweight syntax code:

tokens $let$use $let!$use! $do$do! $then$else $with$function $fun ### Grammar Rules Including Inserted Tokens Additional grammar rules take into account the token transformations performed by lexical filtering: expr +:= | let function-defn$in expr

| let value-defn $in expr | let rec function-or-value-defns$in expr

| while expr do expr $done | if expr then$begin expr $end | for pat in expr do expr$done

| for expr to expr do expr $done | try expr$end with expr $done | try expr$end finally expr $done | expr$app expr // equivalent to "expr(expr)"

| expr $sep expr // equivalent to "expr; expr" | expr$tyapp < types > // equivalent to "expr<types>"

| $begin expr$end // equivalent to “expr

elif-branch +:=

| elif expr then $begin expr$end

else-branch +:=

| else $begin expr$end

class-or-struct-type-body +:=

| $begin class-or-struct-type-body$end

// equivalent to class-or-struct-type-body

module-elems +:=

| $begin module-elem ... module-elem$end

module-abbrev +:=

| module ident = $begin long-ident$end

module-defn +:=

| module ident = $begin module-defn-body$end

module-signature-elements +:=

| $begin module-signature-element ... module-signature-element$end

module-signature +:=

| module ident = $begin module-signature-body$end

### Offside Lines

Lightweight syntax is sometimes called the “offside rule”. In F# code, offside lines occur at column positions. For example, an = token associated with let introduces an offside line at the column of the first non-whitespace token after the = token.

Other structured constructs also introduce offside lines at the following places:

• The column of the first token after then in an if/then/else construct.

• The column of the first token after try, else, ->, with (in a match/with or try/with), or with (in a type extension).

• The column of the first token of a (, { or begin token.

• The start of a let, if or module token.

Here are some examples of how the offside rule applies to F# code. In the first example, let and type declarations are not properly aligned, which causes F# to generate a warning.

// "let" and "type" declarations in

// modules must be precisely aligned.

let x = 1

let y = 2 <-- unmatched 'let'

let z = 3 <-- warning FS0058: possible

incorrect indentation: this token is offside of

context at position (2:1)

In the second example, the | markers in the match patterns do not align properly:

// The "|" markers in patterns must align.

// The first "|" should always be inserted.

let f () =

match 1+1 with

| 2 -> printf "ok"

| _ -> failwith "no!" <-- syntax error

### The Pre-Parse Stack

F# implements the lightweight syntax option by preparsing the token stream that results from a lexical analysis of the input text according to the lexical rules in §15.1.3. Pre-parsing for lightweight syntax uses a stack of contexts.

• When a column position becomes an offside line, a context is pushed.

• The closing bracketing tokens ), }, and end terminate offside contexts up to and including the context that the corresponding opening token introduced.

### Full List of Offside Contexts

This section describes the full list of offside contexts that is kept on the pre-parse stack.

The SeqBlock context is the primary context of the analysis.It indicates a sequence of items that must be column-aligned. Where necessary for parsing, the compiler automatically inserts a delimiter that replaces the regular in and ; tokens between the syntax elements. The SeqBlock context is pushed at the following times:

• Immediately after the start of a file, excluding lexical directives such as #if.

• Immediately after an = token is encountered in a Let or Member context.

• Immediately after a Paren, Then, Else, WithAugment, Try, Finally, Do context is pushed.

• Immediately after an infix token is encountered.

• Immediately after a -> token is encountered in a MatchClauses context.

• Immediately after an interface, class, or struct token is encountered in a type declaration.

• Immediately after an = token is encountered in a record expression when the subsequent token either (a) occurs on the next line or (b) is one of try, match, if, let, for, while or use.

• Immediately after a <- token is encoutered when the subsequent token either (a) does not occur on the same line or (b) is one of try, match, if, let, for, while or use.

Here “immediately after” refers to the fact that the column position associated with the SeqBlock is the first token following the significant token.

In the last two rules, a new line is significant. For example, the following do not start a SeqBlock on the right-hand side of the “<-“ token, so it does not parse correctly:

let mutable x = 1

// The subsequent token occurs on the same line.

X <- printfn "hello"

2 + 2

To start a SeqBlock on the right, either parentheses or a new line should be used:

// The subsequent token does not occur on the same line, so a SeqBlock is pushed.

X <-

printfn "hello"

2 + 2

The following contexts are associated with nested constructs that are introduced by the specified keywords:

Context Pushed when the token stream contains…
Let The let keyword
If The if or elif keyword
Try The try keyword
Lazy The lazy keyword
Fun The fun keyword
Function The function keyword
WithLet The with keyword as part of a record expression or an object expression whose members use the syntax{ new Foo with M() = 1 and N() = 2 }
WithAugment The with keyword as part of an extension, interface, or object expression whose members use the syntax { new Foo member x.M() = 1 member x. N() = 2 }
Match the match keyword
For the for keyword
While The while keyword
Then The then keyword
Else The else keyword
Do The do keyword
Type The type keyword
Namespace The namespace keyword
Module The module keyword
Member
• The member, abstract, default, or override keyword, if the Member context is not already active, because multiple tokens may be present.

—or—

• ( is the next token after the new keyword. This distinguishes the member declaration new(x) = ... from the expression new x()

Paren(token) (, begin, struct, sig, {, [, [|, or quote-op-left
MatchClauses The with keyword in a Try or Match context immediately after a function keyword.
Vanilla An otherwise unprocessed keyword in a SeqBlock context.

### Balancing Rules

When the compiler processes certain tokens, it pops contexts off the offside stack until the stack reaches a particular condition. When it pops a context, the compiler may insert extra tokens to indicate the end of the construct. This procedure is called balancing the stack.

The following table lists the contexts that the compiler pops and the balancing condition for each:

Token Contexts Popped and Balancing Conditions:
End

Enclosing context is one of the following:

• WithAugment

• Paren(interface)

• Paren(class)

• Paren(sig)

• Paren(struct)

• Paren(begin)

;; Pop all contexts from stack
else If
elif If
done Do
in For or Let
eith Match, Member, Interface, Try, Type
finally Try
) Paren(()
} Paren({)
] Paren([)
|] Paren([|)
quote-op-right Paren(quote-op-left)

### Offside Tokens, Token Insertions, and Closing Contexts

The offside limit for the current offside stack is the rightmost offside line for the offside contexts on the context stack. The following figure shows the offside limits:

When a token occurs on or before the offside limit for the current offside stack, and a permitted undentation does not apply, enclosing contexts are closed until the token is no longer offside. This may result in the insertion of extra delimiting tokens.

Contexts are closed as follows:

• When a Fun context is closed, the $end token is inserted. • When a SeqBlock, MatchClauses, Let, or Do context is closed, the$end token is inserted, with the exception of the first SeqBlock pushed for the start of the file.

• When a While or For context is closed, and the offside token that forced the close is not done, the $done token is inserted. • When a Member context is closed, the$end token is inserted.

• When a WithAugment context is closed, the $end token is inserted. If a token is offside and a context cannot be closed, then an “undentation” warning or error is issued to indicate that the construct is badly formatted. Tokens are also inserted in the following situations: • When a SeqBlock context is pushed, the$begin token is inserted, with the exception of the first SeqBlock pushed for the start of the file.

• When a token other than and appears directly on the offside line of Let context, and the next surrounding context is a SeqBlock, the $in token is inserted. • When a token occurs directly on the offside line of a SeqBlock on the second or subsequent lines of the block, the$sep token is inserted. This token plays the same role as ; in the grammar rules.

For example, consider this source text:

let x = 1
x

The raw token stream contains let, x, =, 1, x and the end-of-file marker eof. An initial SeqBlock is pushed immediately after the start of the file, at the first token in the file, with an offside line on column 0. The let token pushes a Let context. The = token in a Let context pushes a SeqBlock context and inserts a $begin token. The 1 pushes a Vanilla context. The final token, x, is offside from the Vanilla context, which pops that context. It is also offside from the SeqBlock context, which pops the context and inserts$end. It is also offside from the Let context, which inserts another end token. It is directly aligned with the SeqBlock context, so aseq token is inserted.

### Exceptions to the Offside Rules

The compiler makes some exceptions to the offside rules when it analyzes a token to determine whether it is offside from the current context. The following table summarizes the exceptions and shows examples of each.

Context Exception Example
SeqBlock An infix token may be offside by the size of the token plus one.

let x =

expr + expr

+ expr + expr

let x =

expr

|> f expr

|> f expr

SeqBlock An infix token may align precisely with the offside line of the SeqBlock.

let someFunction(someCollection) =

someCollection

|> List.map (fun x -> x + 1)

SeqBlock

The infix |> token that begins the last line is not considered as a new element in the sequence block on the right-hand side of the definition. The same also applies to end, and, with, then, and right-parenthesis operators.

In the example, the first ) token does not indicate a new element in a sequence of items, even though it aligns precisely with the sequence block that starts at the beginning of the argument list.

new EventHandler(fun _ _ ->

...

))

Let The and token may align precisely with the let keyword.

let rec x = 1

and y = 2

x + y

Type The }, end, and, and | tokens may align precisely with the type keyword.

type X =

| A

| B

with

member x.Seven = 21 / 3

end

and Y = {

x : int

}

and Z() = class

member x.Eight = 4 + 4

end

For The done token may align precisely with the for keyword.

for i = 1 to 3 do

expr

done

SeqBlock; Match On the right-hand side of an arrow for a match expression, a token may align precisely with the match keyword. This exception allows the last expression to align with the match, so that a long series of matches does not increase indentation.

match x with

| Some(_) -> 1

| None ->

match y with

| Some(_) -> 2

| None ->

3

Interface The end token may align precisely with the interface keyword.

interface IDisposable with

member x.Dispose() = printfn disposing!"

end

If The then, elif, and else tokens may align precisely with the if keyword.

if big

then callSomeFunction()

elif small

then callSomeOtherFunction()

else doSomeCleanup()

Try The finally and with tokens may align precisely with the try keyword.

Example 1:

try

callSomeFunction()

finally

doSomeCleanup()

Example 2:

try

callSomeFunction()

with Failure(s) ->

doSomeCleanup()

Do The done token may align precisely with the do keyword.

for i = 1 to 3

do

expr

done

### Permitted Undentations

As a general rule, incremental indentation requires that nested expressions occur at increasing column positions in indentation-aware code. Warnings or syntax errors are issued when this is not the case. However, undentation is permitted for the following constructs:

• Bodies of function expressions

• Branches of if/then/else expressions

• Bodies of modules and module types

#### Undentation of Bodies of Function Expressions

The bodies of functions may be undented from the fun or function symbol. As a result, the compiler ignores the symbol when determining whether the body of the function satisfies the incremental indentation rule. For example, the printf expression in the following example is undented from the fun symbol that delimits the function definition:

let HashSample(tab: Collections.HashTable<_,_>) =

tab.Iterate (fun c v ->

printfn "Entry (%O,%O)" c v)

However, the block must not undent past other offside lines. Thefollowing is not permitted because the second line breaks the offside line established by the = in the first line:

let x = (function (s, n) ->

(fun z ->

s+n+z))

Constructs enclosed in brackets may be undented.

#### Undentation of Branches of If/Then/Else Expressions

The body of a ( ... ) or begin ... end block in an if/then/else expression may be undented when the body of the block follows the then or else keyword but may not undent further than the if keyword. In this example, the parenthesized block follows then, so the body can be undented to the offside line established by if:

let IfSample(day: System.DayOfWeek) =

if day = System.DayOfWeek.Monday then (

printf "I don't like Mondays"

)

#### Undentation of Bodies of Modules and Module Types

The bodies of modules and module types that are delimited by begin and end may be undented. For example, in the following example the two let statements that comprise the module body are undented from the =.

module MyNestedModule = begin
let one = 1
let two = 2
end

Similarly, the bodies of classes, interfaces, and structs delimited by { ... }, class ... end, struct ... end, or interface ... end may be undented to the offside line established by the type keyword. For example:

type MyNestedModule = interface

abstract P : int

end

## High Precedence Application

The entry f x in the precedence table in §4.4.2 refers to a function application in which the function and argument are separated by spaces. The entry "f(x)" indicates that in expressions and patterns, identifiers that are followed immediately by a left parenthesis without intervening whitespace form a “high precedence” application. Such expressions are parsed with higher precedence than prefix and dot-notation operators. Conceptually this means that

Example 1: B(e)

is analyzed lexically as

Example 1: B $app (e) where$app is an internal symbol inserted by lexical analysis. We do not show this symbol in the remainder of this specification and simply show the original source text.

This means that the following two statements

Example 1: B(e).C

Example 2: B (e).C

are parsed as

Example 1: (B(e)).C

Example 2: B ((e).C)

respectively.

Furthermore, arbitrary chains of method applications, property lookups, indexer lookups (.[]), field lookups, and function applications can be used in sequence if the arguments of method applications are parenthesized and immediately follow the method name, with no intervening spaces. For example:

e.Meth1(arg1,arg2).Prop1.[3].Prop2.Meth2()

Although the grammar and these precedence rules technically allow the use of high-precedence application expressions as direct arguments, an additional check prevents such use. Instead, such expressions must be surrounded by parentheses. For example,

f e.Meth1(arg1,arg2) e.Meth2(arg1,arg2)

must be written

f (e.Meth1(arg1,arg2)) (e.Meth2(arg1,arg2))

However, indexer, field, and property dot-notation lookups may be used as arguments without adding parentheses. For example:

f e.Prop1 e.Prop2.[3]

## Lexical Analysis of Type Applications

The entry f<types> x in the precedence table (§4.4.2) refers to any identifier that is followed immediately by a < symbol and a sequence of all of the following:

• _, ,, *, ', [, ], whitespace, or identifier tokens.

• A parentheses ( or < token followed by any tokens until a matching parentheses ) or > is encountered.

• A final > token.

During this analysis, any token that is composed only of the > character (such as >, >>, or >>>) is treated as a series of individual > tokens. Likewise, any token composed only of > characters followed by a period (such as >., >>., or >>>.) is treated as a series of individual > tokens followed by a period.

If such a sequence of tokens follows an identifier, lexical analysis marks the construct as a high precedence type application and subsequent grammar rules ensure that the enclosed text is parsed as a type. Conceptually this means that

Example 1: B<int>.C<int>(e).C

is returned as the following stream of tokens:

Example 1: B $app <int> .C$app <int>(e).C

where \$app is an internal symbol inserted by lexical analysis. We do not show this symbol elsewhere in this specification and simply show the original source text.

The lexical analysis of type applications does not apply to the character sequence “<>”. A character sequence such as “< >” with intervening whitespace should be used to indicate an empty list of generic arguments.

type Foo() =

member this.Value = 1

let b = new Foo< >() // valid

let c = new Foo<>() // invalid

# Provided Types

Type providers are extensions provided to an F# compiler or interpreter which provide information about types available in the environment for the F# code being analysed.

The compilation context is augmented with a set of type provider instances. A type provider insance is interrogated for information through type provider invocations (TPI). Type provider invocations are all executed at compile-time. The type provider instance is not required at runtime.

Wherever an operation on a provided namespace, provided type definition or provided member is mentioned in this section, it is assumed to be a compile-time type provider invocation.

The exact protocol used to implement type provider invocations and communicate between an F# compiler/interpreter and type provider instances is implementation dependent.

As of this release of F#,

• a type provider is a .NET 4.x binary component referenced as an imported asssembly reference. The assembly should have a TypeProviderAssemblyAttribute, with at least one component marked with TypeProviderAttribute.

• a type provider instance is an object created for a component marked with TypeProviderAttribute.

• provided type definitions are System.Type objects returned by a type provider instance.

• provided methods are System.Reflection.MethodInfo objects returned by a type provider instance.

• provided constructors are System.Reflection.ConstructorInfo objects returned by a type provider instance.

• provided properties are System.Reflection.PropertyInfo objects returned by a type provider instance.

• provided events are System.Reflection.EventInfo objects returned by a type provider instance.

• provided literal fields are System.Reflection.FieldInfo objects returned by a type provider instance.

• provided parameters are System.Reflection.ParameterInfo objects returned by a type provider instance.

• provided static parameters are System.Reflection.ParameterInfo objects returned by a type provider instance.

• provided attributes are attribute value objects returned by a type provider instance.

## Static Parameters

The syntax of types in F# is expanded to include static parameters, including named static parameters:

type-arg =

static-parameter

static-parameter =

static-parameter-value

id = static-parameter-value

static-parameter-value =

const expr

simple-constant-expression

References to provided types may include static parameters, e.g.

type SomeService = ODataService<"http://some.url.org/service"\>

Static parameters which are constant expressions, but not simple literal constants, may be specified using the const keyword, e.g.

type SomeService = CsvFile<const (__SOURCE_DIRECTORY__ + "/a.csv")>

Parentheses are needed around any simple contanst expressions after “const” that are not simple literal constants, e.g.

type K = N.T< const (+1) >

During checking of a type A<type-args>, where A is a provided type, the TPM GetStaticParameters is invoked to determine the static parameters for the type A if any. If the static parameters exist and are of the correct kinds, the TPM ApplyStaticArguments is invoked to apply the static arguments to the provided type.

During checking of a method M<type-args>, where M is a provided method definition, the TPM GetStaticParametersForMethod is invoked to determine the static parameters if any. If the static parameters exist and are of the correct kinds, the TPM ApplyStaticArgumentsForMethod is invoked to apply the static arguments to the provided method.

In both cases a static parameter value must be given for each non-optional static parameter.

### Mangling of Static Parameter Values

Static parameter values are encoded into the names used for types and methods within F# metadata. The encoding scheme used is

encoding(A<arg1,…,argN>) =

typeOrMethodName,ParamName1=encoding(arg1),…, ParamNameN=encoding(argN)

encoding(v) = "s"

where s is the result applying the F# ‘string’ operator to v (using invariant numeric formatting), and in the result " is replaced by \" and \ by \\

## Provided Namespace

Each type provider instance in the assembly context reports a collection of provided namespaces though the GetNamespaces type provider method. Each provided namespace can in turn report further namespaces through the GetNestedNamespaces type provider method.

## Provided Type Definitions

Each provided namespace reports provided type definitions though the GetTypes and ResolveTypeName type provider methods. The type provider is obliged to ensure that these two methods return consistent results.

Name resolution for unqualified identifiers may return provided type definitions if no other resolution is available.

### Generated v. Erased Types

Each provided type definition may be generated or erased. In this case, the types and method calls are removed entirely during compilation and replaced with other representations. When an erased type is used, the compiler will replace it with the first concrete type in its inheritance chain as returned by the TPM type.BaseType. The erasure of an erased interface type is “object”.

• If it has a type definition under a path D.E.F, and the .Assembly of that type is in a different assembly A to the provider’s assembly, then that type definition is a “generated” type definition. Otherwise it is an erased type definition.

• Erased type definitions must return TypeAttributes with the IsErased flag set, value 0x40000000 and given by the F# literal TypeProviderTypeAttributes.IsErased.

• When a provided type definition is generated, its reported assembly A is treated as an injected assembly which is statically linked into the resulting assembly.

• Concrete type definitions (both provided and F#-authored) and object expressions may not inherit from erased types

• Concrete type definitions (both provided and F#-authored) and object expressions may not implement erased interfaces

• If an erased type definition reports an interface, its erasure must implement the erasure of that interface. The interfaces reported by an erased type definition must be unique up to erasure.

• Erased types may not be used as the target type of a runtime type test of runtime coercion.

• When determining uniqueness for F#-declared methods, uniqueness is determined after erasure of both provided types and units of measure.

• The elaborated form of F# expressions is after erasure of provided types.

• Two generated type definitions are equivalent if and only if they have the same F# path and name in the same assembly, once they are rooted according to their corresponding generative type definition.

• Two erased type definitions are only equivalent if they are provided by the same provider, using the same type name, with the same static arguments.

### Type References

The elements of provided type definitions may reference other provided type definitions, and types from imported assemblies referenced in the compilation context. They may not reference type defined in the F# code currently being compiled.

### Static Parameters

A provided type definition may report a set of static parameters. For such a definition, all other provided contents are ignored.

A provided method definition may also report a set of static parameters. For such a definition, all other provided contents are ignored.

Static parameters may be optional and/or named, indicated by the Attributes property of the static parameter. For a given set of static parameters, no two static parameters may have the same name and named static arguments must come after all other arguments.

### Kind

• Provided type definitions may be classes.

This includes both erased and concrete types. This corresponds to the type.IsClass property returning true for the provided type definition.

• Provided type definitions may be interfaces.

This includes both erased and concrete types. This corresponds to the type.IsInterface property returning true. Only one of IsInterface, IsClass, IsStruct, IsEnum, IsDelegate, IsArray may return true.

• Provided type definitions may be static classes.

This includes both erased and concrete types.

• Provided type definitions may be sealed.

• Provided type definitions may not be arrays. This means the type.IsArray property must always return false. Provided types used in return types and argument positions may be array “symbol” types, see below.

• By default provided type definitions which are reference types are considered to support null literals.

A provided type definition may have the AllowNullLiteralAttribute with value false in which case the type is considered to have null as an abnormal value.

### Inheritance

• Provided type definitions may report base types.

• Provided type definition may report interfaces.

### Members

• Provided type definitions may report methods.

This corresponds to non-null results from the type.GetMethod and type.GetMethods of the provided type definition. The results returned by these methods must be consistent.

• Provided methods may be static, instance and abstract

• Provided methods may not be class constructors (.cctor). By .NET rules these would have to be private anyway.

• Provided methods may be operators such as op_Addition.

• Provided type definitions may report properties.

This corresponds to non-null results from the type.GetProperty and type.GetProperties of the provided type definition. The results returned by these methods must be consistent.

• Provided properties may be static or instance

• Provided properties may be indexers. This corresponds to reporting methods with name Item, or as identified by DefaultMemberAttribute non-null results from the type.GetEvent and type.GetEvents of the provided type definition. The results returned by these methods must be consistent. This include 1D, 2D, 3D and 4D indexer access notation in F# (corresponding to different numbers of parameters to the indexer property).

• Provided type definitions may report constructors.

This corresponds to non-null results from the type.GetConstructor and type.GetConstructors of the provided type definition. The results returned by these methods must be consistent.

• Provided type definitions may report events.

This corresponds to non-null results from the type.GetEvent and type.GetEvents of the provided type definition. The results returned by these methods must be consistent.

• Provided type definitions may report nested types.

This corresponds to non-null results from the type.GetNestedType and type.GetNestedTypes of the provided type definition. The results returned by these methods must be consistent.

• The nested types of an erased type may be generated types in a generated assembly. The type.DeclaringType property of the nested type need not report the erased type.
• Provided type definitions may report literal (constant) fields.

This corresponds to non-null results from the type.GetField and type.GetFields of the provided type definition, and is related to the fact that provided types may be enumerations. The results returned by these methods must be consistent.

• Provided type definitions may not report non-literal (i.e. non-const) fields

This is a deliberate feature limitation, because in .NET, non-literal fields should not appear in public API surface area.

### Attributes

• Provided type definitions, properties, constructors, events and methods may report attributes.

This includes ObsoleteAttribute and ParamArrayAttribute attributes

### Accessibility

• All erased provided type definitions must be public

However, concrete provided types are each in an assembly A that gets statically linked into the resulting F# component. These assemblies may contain private types and methods. These types are not directly “provided” types, since they are not returned to the compiler by the API, but they are part of the closure of the types that are being embedded.

### Elaborated Code

Elaborated uses of provided methods are erased to elaborated expressions returned by the TPM GetInvokerExpression . In the current release of F#, replacement elaborated expressions are specified via F# quotation values composed of quotations constructed with respect to the referenced assemblies in the compilation context according to the following quotation library calls:

• Expr.NewArray

• Expr.NewObject

• Expr.WhileLoop

• Expr.NewDelegate

• Expr.ForIntegerRangeLoop

• Expr.Sequential

• Expr.TryWith

• Expr.TryFinally

• Expr.Lambda

• Expr.Call

• Expr.Constant

• Expr.DefaultValue

• Expr.NewTuple

• Expr.TupleGet

• Expr.TypeAs

• Expr.TypeTest

• Expr.Let

• Expr.VarSet

• Expr.IfThenElse

• Expr.Var

The type of the quotation expression returned by GetInvokerExpression must be an erased type. The type provider is obliged to ensure that this type is equivalent to the erased type of the expression it is replacing.

### Further Restrictions

• If a provided type definition reports a member with ExtensionAttribute, it is not treated as an extension member

• Provided type and method definitions may not be generic

This corresponds to

• GetGenericArguments returning length 0

• For type definitions, IsGenericType and IsGenericTypeDefinition returning false

• For method definitions, IsGenericMethod and IsGenericMethodDefinition returning false

# Special Attributes and Types

This chapter describes attributes and types that have special significance to the F# compiler.

## Custom Attributes Recognized by F#

The following custom attributes have special meanings recognized by the F# compiler. Except where indicated, the attributes may be used in F# code, in referenced assemblies authored in F#, or in assemblies that are authored in other CLI languages.

Attribute Description

System.ObsoleteAttribute

[<Obsolete(...)>]

Indicates that the construct is obsolete and gives a warning or error depending on the settings in the attribute.

This attribute may be used in both F# and imported assemblies.

System.ParamArrayAttribute

[<ParamArray(...)>]

When applied to an argument of a method, indicates that the method can accept a variable number of arguments.

This attribute may be used in both F# and imported assemblies.

Marks a mutable static value in a class as thread static.

This attribute may be used in both F# and imported assemblies.

System.ContextStaticAttribute

[<ContextStatic(...)>]

Marks a mutable static value in a class as context static.

This attribute may be used in both F# and imported assemblies.

System.AttributeUsageAttribute

[<AttributeUsage(...)>]

Specifies the attribute usage targets for an attribute.

This attribute may be used in both F# and imported assemblies.

System.Diagnostics.ConditionalAttribute

[<Conditional(...)>]

Emits code to call the method only if the corresponding conditional compilation symbol is defined.

This attribute may be used in both F# and imported assemblies.

System.Reflection.AssemblyInformationalVersionAttribute

[<AssemblyInformationalVersion(...)>]

This attribute may be used in both F# and imported assemblies.

System.Reflection.AssemblyFileVersionAttribute

[<AssemblyFileVersion(...)>]

Attaches file version metadata to the compiled form of the assembly.

This attribute may be used in both F# and imported assemblies.

System.Reflection.AssemblyDescriptionAttribute

[<AssemblyDescription(...)>]

Attaches descriptive metadata to the compiled form of the assembly, such as the “Comments” attribute in the Win32 version resource for the assembly.

This attribute may be used in both F# and imported assemblies.

System.Reflection.AssemblyTitleAttribute

[<AssemblyTitle(...)>]

Attaches title metadata to the compiled form of the assembly, such as the “ProductName” attribute in the Win32 version resource for the assembly.

This attribute may be used in both F# and imported assemblies.

Attaches copyright metadata to the compiled form of the assembly, such as the “LegalCopyright” attribute in the Win32 version resource for the assembly.

This attribute may be used in both F# and imported assemblies.

Attaches trademark metadata to the compiled form of the assembly, such as the “LegalTrademarks” attribute in the Win32 version resource for the assembly.

This attribute may be used in both F# and imported assemblies.

System.Reflection.AssemblyCompanyAttribute

[<AssemblyCompany(...)>]

Attaches company name metadata to the compiled form of the assembly, such as the “CompanyName” attribute in the Win32 version resource for the assembly.

This attribute may be used in both F# and imported assemblies.

System.Reflection.AssemblyProductAttribute

[<AssemblyProduct(...)>]

Attaches product name metadata to the compiled form of the assembly, such as the “ProductName” attribute in the Win32 version resource for the assembly.

This attribute may be used in both F# and imported assemblies.

System.Reflection.AssemblyKeyFileAttribute

[<AssemblyKeyFile(...)>]

Indicates to the F# compiler how to sign an assembly.

This attribute may be used in both F# and imported assemblies.

System.Reflection.DefaultMemberAttribute

[<DefaultMember(...)>]

When applied to a type, specifies the name of the indexer property for that type.

This attribute may be used in both F# and imported assemblies.

System.Runtime.CompilerServices.InternalsVisibleToAttribute

[<InternalsVisibleTo(...)>]

Directs the F# compiler to permit access to the internals of the assembly.

This attribute may be used in both F# and imported assemblies.

System.Runtime.CompilerServices.TypeForwardedToAttribute

[<TypeForwardedTo(...)>]

Indicates a type redirection.

This attribute may be used only in imported non-F# assemblies. It is not permitted in F# code.

System.Runtime.CompilerServices.ExtensionAttribute

[<Extension(...)>]

Indicates the compiled form of a C# extension member.

This attribute may be used only in imported non-F# assemblies. It is not permitted in F# code.

System.Runtime.InteropServices.DllImportAttribute

[<DllImport(...)>]

When applied to a function definition in a module, causes the F# compiler to ignore the implementation of the definition, and instead compile it as a CLI P/Invoke stub declaration.

This attribute may be used in both F# and imported assemblies.

System.Runtime.InteropServices.MarshalAsAttribute

[<MarshalAs(...)>]

When applied to a parameter or return type, specifies the marshalling attribute for a CLI P/Invoke stub declaration.

This attribute may be used in both F# and imported assemblies. However, F# does not support the specification of "custom" marshallers.

System.Runtime.InteropServices.InAttribute

[<In>]

When applied to a parameter, specifies the CLI In attribute.

This attribute may be used in both F# and imported assemblies. However, in F# its only effect is to change the corresponding attribute in the CLI compiled form.

System.Runtime.InteropServices.OutAttribute

[<Out>]

When applied to a parameter, specifies the CLI Out attribute.

This attribute may be used in both F# and imported assemblies. However, in F# its only effect is to change the corresponding attribute in the CLI compiled form.

System.Runtime.InteropServices.OptionalAttribute

[<Optional(...)>]

When applied to a parameter, specifies the CLI Optional attribute.

This attribute may be used in both F# and imported assemblies. However, in F# its only effect is to change the corresponding attribute in the CLI compiled form.

System.Runtime.InteropServices.FieldOffsetAttribute

[<FieldOffset(...)>]

When applied to a field, specifies the field offset of the underlying CLI field.

This attribute may be used in both F# and imported assemblies.

System.NonSerializedAttribute

[<NonSerialized>]

When applied to a field, sets the "not serialized" bit for the underlying CLI field.

This attribute may be used in both F# and imported assemblies.

System.Runtime.InteropServices.StructLayoutAttribute

[<StructLayout(...)>]

Specifies the layout of a CLI type.

This attribute may be used in both F# and imported assemblies.

FSharp.Core.AutoSerializableAttribute

[<AutoSerializable(false)>]

When added to a type with value false, disables default serialization, so that F# does not make the type serializable.

This attribute should be used only in F# assemblies.

FSharp.Core.CLIMutableAttribute

[<CLIMutable>]

When specified, a record type is compiled to a CLI representation with a default constructor with property getters and setters.

This attribute should be used only in F# assemblies.

FSharp.Core.AutoOpenAttribute

[<AutoOpen>]

When applied to an assembly and given a string argument, causes the namespace or module to be opened automatically when the assembly is referenced.

When applied to a module without a string argument, causes the module to be opened automatically when the enclosing namespace or module is opened.

This attribute should be used only in F# assemblies.

FSharp.Core.
CompilationRepresentationAttribute

[<CompilationRepresentation(...)>]

Adjusts the runtime representation of a type .

This attribute should be used only in F# assemblies.

FSharp.Core.CompiledNameAttribute

[<CompiledName(...)>]

Changes the compiled name of an F# language construct.

This attribute should be used only in F# assemblies.

FSharp.Core.CustomComparisonAttribute

[<CustomComparison>]

When applied to an F# structural type, indicates that the type has a user-specified comparison implementation.

This attribute should be used only in F# assemblies.

FSharp.Core.CustomEqualityAttribute

[<CustomEquality>]

When applied to an F# structural type, indicates that the type has a user-defined equality implementation.

This attribute should be used only in F# assemblies.

FSharp.Core.DefaultAugmentationAttribute

[<DefaultAugmentation(...)>]

When applied to an F# discriminated union type with value false, turns off the generation of standard helper member tester, constructor and accessor members for the generated CLI class for that type.

This attribute should be used only in F# assemblies.

FSharp.Core.DefaultValueAttribute

[<DefaultValue(...)>]

When added to a field declaration, specifies that the field is not initialized. During type checking, a constraint is asserted that the field type supports null. If the argument to the attribute is false, the constraint is not asserted.

This attribute should be used only in F# assemblies.

FSharp.Core.GeneralizableValueAttribute

[<GeneralizableValue>]

When applied to an F# value, indicates that uses of the attribute can result in generic code through the process of type inference. For example, Set.empty. The value must typically be a type function whose implementation has no observable side effects.

This attribute should be used only in F# assemblies.

FSharp.Core.LiteralAttribute

[<Literal>]

When applied to a value, compiles the value as a CLI literal.

This attribute should be used only in F# assemblies.

FSharp.Core.NoDynamicInvocationAttribute

[<NoDynamicInvocation>]

When applied to an inline function or member definition, replaces the generated code with a stub that throws an exception at runtime. This attribute is used to replace the default generated implementation of unverifiable inline members with a verifiable stub.

This attribute should be used only in F# assemblies.

FSharp.Core.CompilerMessageAttribute

[<CompilerMessage(...)>]

When applied to an F# construct, indicates that the F# compiler should report a message when the construct is used.

This attribute should be used only in F# assemblies.

FSharp.Core.StructAttribute

[<Struct>]

Indicates that a type is a struct type.

This attribute should be used only in F# assemblies.

FSharp.Core.ClassAttribute

[<Class>]

Indicates that a type is a class type.

This attribute should be used only in F# assemblies.

FSharp.Core.InterfaceAttribute

[<Interface>]

Indicates that a type is an interface type.

This attribute should be used only in F# assemblies.

FSharp.Core.MeasureAttribute

[<Measure>]

Indicates that a type or generic parameter is a unit of measure definition or annotation.

This attribute should be used only in F# assemblies.

FSharp.Core.ReferenceEqualityAttribute

[<ReferenceEquality>]

When applied to an F# record or union type, indicates that the type should use reference equality for its default equality implementation.

This attribute should be used only in F# assemblies.

FSharp.Core.ReflectedDefinitionAttribute

[<ReflectedDefinition>]

Makes the quotation form of a definition available at runtime through the FSharp.Quotations.
Expr.GetReflectedDefinition
method.

This attribute should be used only in F# assemblies.

FSharp.Core.
RequireQualifiedAccessAttribute

[<RequireQualifiedAccess>]

When applied to an F# module, warns if an attempt is made to open the module name.

When applied to an F# union or record type, indicates that the field labels or union cases must be referenced by using a qualified path that includes the type name.

This attribute should be used only in F# assemblies.

FSharp.Core.
RequiresExplicitTypeArgumentsAttribute

[<RequiresExplicitTypeArguments>]

When applied to an F# function or method, indicates that the function or method must be invoked with explicit type arguments, such as typeof<int>.

This attribute should be used only in F# assemblies.

FSharp.Core.StructuralComparisonAttribute

[<StructuralComparison>]

When added to a record, union, exception, or structure type, confirms the automatic generation of implementations for IComparable for the type.

This attribute should only be used in F# assemblies.

FSharp.Core.StructuralEqualityAttribute

[<StructuralEquality>]

When added to a record, union, or struct type, confirms the automatic generation of overrides for Equals and GetHashCode for the type.

This attribute should be used only in F# assemblies.

FSharp.Core.VolatileFieldAttribute

[<VolatileField>]

When applied to an F# field or mutable value definition, controls whether the CLI volatile prefix is emitted before accesses to the field.

This attribute should be used only in F# assemblies.

FSharp.Core.TypeProviderXmlDocAttribute Specifies documentation for provided type definitions and provided members
FSharp.Core.TypeProviderDefinitionLocationAttribute Specifies location information for provided type definitions and provided members

## Custom Attributes Emitted by F#

The F# compiler can emit the following custom attributes:

Attribute Description
System.Diagnostics.DebuggableAttribute Improves debuggability of F# code.
System.Diagnostics.DebuggerHiddenAttribute Improves debuggability of F# code.
System.Diagnostics.DebuggerDisplayAttribute Improves debuggability of F# code.
System.Diagnostics.DebuggerBrowsableAttribute Improves debuggability of F# code.
System.Runtime.CompilerServices.
CompilationRelaxationsAttribute
Enables extra JIT optimizations.
System.Runtime.CompilerServices.
CompilerGeneratedAttribute
Indicates that a method, type, or property is generated by the F# compiler, and does not correspond directly to user source code.
System.Reflection.DefaultMemberAttribute Specifies the name of the indexer property for a class.
FSharp.Core.CompilationMappingAttribute Indicates how a CLI construct corresponds to an F# source language construct.
FSharp.Core.FSharpInterfaceDataVersionAttribute Defines the schema number for the embedded binary resource for F#-specific interface and optimization data.
FSharp.Core.OptionalArgumentAttribute Indicates optional arguments to F# members.

## Custom Attributes Not Recognized by F#

The following custom attributes are defined in some CLI implementations and may appear to be relevant to F#. However, they either do not affect the behavior of the F# compiler, or result in an error when used in in F# code.

Attribute Description
System.Runtime.CompilerServices.DecimalConstantAttribute The F# compiler ignores this attribute. However, if used in F# code, it can cause some other CLI languages to interpret a decimal constant as a compile-time literal.
System.Runtime.CompilerServices.RequiredAttributeAttribute Do not use this attribute in F# code. The F# compiler ignores it or returns an error.
System.Runtime.InteropServices.
DefaultParameterValueAttribute
Do not use this attribute in F# code. The F# compiler ignores it or returns an error.
System.Runtime.InteropServices.
UnmanagedFunctionPointerAttribute
Do not use this attribute in F# code. The F# compiler ignores it or returns an error.
System.Runtime.CompilerServices.FixedBufferAttribute Do not use this attribute in F# code. The F# compiler ignores it or returns an error.
System.Runtime.CompilerServices.UnsafeValueTypeAttribute Do not use this attribute in F# code. The F# compiler ignores it or returns an error.
System.Runtime.CompilerServices.SpecialNameAttribute Do not use this attribute in F# code. The F# compiler ignores it or returns an error.

## Exceptions Thrown by F# Language Primitives

Certain F# language and primitive library operations throw the following exceptions.

Attribute Description
System.ArithmeticException An arithmetic operation failed. This is the base class for exceptions such as System.DivideByZeroException and System.OverflowException.
System.ArrayTypeMismatchException An attempt to store an element in an array failed because the runtime type of the stored element is incompatible with the runtime type of the array.
System.DivideByZeroException An attempt to divide an integral value by zero occurred.
System.IndexOutOfRangeException An attempt to index an array failed because the index is less than zero or outside the bounds of the array.
System.InvalidCastException An explicit conversion from a base type or interface to a derived type failed at run time.
System.NullReferenceException A null reference was used in a way that caused the referenced object to be required.
System.OutOfMemoryException An attempt to use new to allocate memory failed.
System.OverflowException An arithmetic operation in a checked context overflowed.
System.StackOverflowException The execution stack was exhausted because of too many pending method calls, which typically indicates deep or unbounded recursion.
System.TypeInitializationException F# initialization code for a type threw an exception that was not caught.

# The F# Library FSharp.Core.dll

All compilations reference the following two base libraries:

• The CLI base library mscorlib.dll.

• The F# base library FSharp.Core.dll

The following namespaces are automatically opened for all F# code:

open FSharp

open FSharp.Core

open FSharp.Core.LanguagePrimitives

open FSharp.Core.Operators

open FSharp.Text

open FSharp.Collections

open FSharp.Core.ExtraTopLevelOperators

A compilation may open additional namespaces may be opened if the referenced F# DLLs contain AutoOpenAttribute declarations.

## Basic Types (FSharp.Core)

This section provides details about the basic types that are defined in FSharp.Core.

### Basic Type Abbreviations

Type Name Description
obj System.Object
exn System.Exception
nativeint System.IntPtr
unativeint System.UIntPtr
string System.String
float32, single System.Single
float, double System.Double
sbyte, int8 System.SByte
byte, uint8 System.Byte
int16 System.Int16
uint16 System.UInt16
int32, int System.Int32
uint32 System.UInt32
int64 System.Int64
uint64 System.UInt64
char System.Char
bool System.Boolean
decimal System.Decimal

### Basic Types that Accept Unit of Measure Annotations

Type Name Description
sbyte<_> Underlying representation System.SByte, but accepts a unit of measure.
int16<_> Underlying representation System.Int16, but accepts a unit of measure.
int32<_> Underlying representation System.Int32, but accepts a unit of measure.
int64<_> Underlying representation System.Int64, but accepts a unit of measure.
float32<_> Underlying representation System.Single, but accepts a unit of measure.
float<_> Underlying representation System.Double, but accepts a unit of measure.
decimal<_> Underlying representation System.Decimal, but accepts a unit of measure.

### The nativeptr<_> Type

When the nativeptr<type> is used in method argument or return position, it is represented in compiled CIL code as either:

• A CLI pointer type type*****, if type does not contain any generic type parameters.

• T CLI type System.IntPtr otherwise.

Note: CLI pointer types are rarely used. In CLI metadata, pointer types sometimes appear in CLI metadata unsafe object constructors for the CLI type System.String.

You can convert between System.UIntPtr and nativeptr<'T> by using the inlined unverifiable functions in FSharp.NativeInterop.NativePtr.

nativeptr<_> compiles in different ways because CLI restricts where pointer types can appear.

## Basic Operators and Functions (FSharp.Core.Operators)

### Basic Arithmetic Operators

The following operators are defined in FSharp.Core.Operators:

Operator or Function Name Expression Form Description
(-) x - y Overloaded subtraction.
(*) x * y Overloaded multiplication.
(/) x / y

For negative numbers, the behavior of this operator follows the definition of the corresponding operator in the C# specification.

(%) x % y

For integer types, the result of x % y is the value produced by x – (x / y) * y. If y is zero, System.DivideByZeroException is thrown. The remainder operator never causes an overflow. This follows the definition of the remainder operator in the C# specification.

For floating-point types, the behavior of this operator also follows the definition of the remainder operator in the C# specification.

not not x Boolean negation.

### Generic Equality and Comparison Operators

The following operators are defined in FSharp.Core.Operators:

Operator or Function Name Expression Form Description
(<) x < y Generic less-than
(<=) x <= y Generic less-than-or-equal
(>) x > y Generic greater-than
(>=) x >= y Generic greater-than-or-equal
(=) x = y Generic equality
(<>) x <> y Generic disequality
max max x y Generic maximum
min min x y Generic minimum

### Bitwise Operators

The following operators are defined in FSharp.Core.Operators:

Operator or Function Name Expression Form Description
(<<<) x <<< y Overloaded bitwise left-shift
(>>>) x >>> y Overloaded bitwise arithmetic right-shift
(^^^) x ^^^ y Overloaded bitwise exclusive or (XOR)
(&&&) x &&& y Overloaded bitwise and
**(

### Math Operators

The following operators are defined in FSharp.Core.Operators:

Operator or Function Name Expression Form Description
abs abs x Overloaded absolute value
acos acos x Overloaded inverse cosine
asin asin x Overloaded inverse sine
atan atan x Overloaded inverse tangent
atan2 atan2 x y Overloaded inverse tangent of x/y
ceil ceil x Overloaded floating-point ceiling
cosh cosh x Overloaded hyperbolic cosine
floor floor x Overloaded floating-point floor
log log x Overloaded natural logarithm
log10 log10 x Overloaded base-10 logarithm
(**) x ** y Overloaded exponential
pown pown x y Overloaded integer exponential
sign sign x Overloaded sign function
sin sin x Overloaded sine function
sinh sinh x Overloaded hyperbolic sine function
sqrt sqrt x Overloaded square root function
tan tan x Overloaded tangent function
tanh tanh x Overloaded hyperbolic tangent function

### Function Pipelining and Composition Operators

The following operators are defined in FSharp.Core.Operators:

Operator/Function Name Expression Form Description
**( >)** **x
(>>) f >> g Composes two functions, so that they are applied in order from left to right
**(< )** **f <
(<<) g << f Composes two functions, so that they are applied in order from right to left (backward function composition)
ignore ignore x Computes and discards a value

### Object Transformation Operators

The following operators are defined in FSharp.Core.Operators:

Operator/Function Name Expression Form Description
box box x Converts to object representation.
hash hash x Generates a hash value.
sizeof sizeof<type> Computes the size of a value of the given type.
typeof typeof<type> Computes the System.Type representation of the given type.
typedefof typedefof<type> Computes the System.Type representation of type and calls GetGenericTypeDefinition if it is a generic type.
unbox unbox x Converts from object representation.
ref ref x Allocates a mutable reference cell.
(!) !x Reads a mutable reference cell.

### Pair Operators

The following operators are defined in FSharp.Core.Operators:

Operator or Function Name Expression Form Description
fst fst p Returns the first element of a pair.
snd snd p Returns the second element of a pair

### Exception Operators

The following operators are defined in FSharp.Core.Operators:

Operator/Function Name Expression Form Description
failwith failwith x Raises a FailureException exception.
invalidArg invalidArg x Raises an ArgumentException exception.
raise raise x Raises an exception.
reraise reraise() Rethrows the current exception.

### Input/Output Handles

The following operators are defined in FSharp.Core.Operators:

Operator or Function Name Expression Form Description
stdin Stdin Computes System.Console.In.
stdout Stdout Computes System.Console.Out.
stderr Stderr Computes System.Console.Error.

The following operators are defined in FSharp.Core.Operators:

Operator or Function Name Expression Form Description
byte byte x Overloaded conversion to a byte
sbyte sbyte x Overloaded conversion to a signed byte
int16 int16 x Overloaded conversion to a 16-bit integer
uint16 uint16 x Overloaded conversion to an unsigned 16-bit integer
int32, int

int32 x

int x

Overloaded conversion to a 32-bit integer
uint32 uint32 x Overloaded conversion to an unsigned 32-bit integer
int64 int64 x Overloaded conversion to a 64-bit integer
uint64 uint64 x Overloaded conversion to an unsigned 64-bit integer
nativeint nativeint x Overloaded conversion to an native integer
unativeint unativeint x Overloaded conversion to an unsigned native integer
float, double

float x

double x

Overloaded conversion to a 64-bit IEEE floating-point number
float32, single

float32 x

single x

Overloaded conversion to a 32-bit IEEE floating-point number
decimal decimal x Overloaded conversion to a System.Decimal number
char char x Overloaded conversion to a System.Char value
enum enum x Overloaded conversion to a typed enumeration value

## Checked Arithmetic Operators

The module FSharp.Core.Operators.Checked defines runtime-overflow-checked versions of the following operators:

Operator or Function Name Expression Form Description
(-) x – y Checked overloaded subtraction
(*) x * y Checked overloaded multiplication
(~-) -x Checked overloaded unary negation
byte byte x Checked overloaded conversion to a byte
sbyte sbyte x Checked overloaded conversion to a signed byte
int16 int16 x Checked overloaded conversion to a 16-bit integer
uint16 uint16 x Checked overloaded conversion to an unsigned 16-bit integer
int32, int

int32 x

int x

Checked overloaded conversion to a 32-bit integer
uint32 uint32 x Checked overloaded conversion to an unsigned 32-bit integer
int64 int64 x Checked overloaded conversion to a 64-bit integer
uint64 uint64 x Checked overloaded conversion to an unsigned 64-bit integer
nativeint nativeint x Checked overloaded conversion to an native integer
unativeint unativeint x Checked overloaded conversion to an unsigned native integer
char char x Checked overloaded conversion to a System.Char value

## List and Option Types

### The List Type

The following shows the elements of the F# type FSharp.Collections.list referred to in this specification:

type 'T list =

| ([])

| (::) of 'T * 'T list

static member Empty : 'T list

member Length : int

member IsEmpty : bool

member Tail : 'T list

member Item :int -> 'T with get

static member Cons : 'T * 'T list -> 'T list

interface System.Collections.Generic.IEnumerable<'T>

interface System.Collections.IEnumerable

### The Option Type

The following shows the elements of the F# type FSharp.Core.option referred to in this specification:

[<DefaultAugmentation(false)>]

[<CompilationRepresentation(CompilationRepresentationFlags.UseNullAsTrueValue)>] type 'T option =

| None

| Some of 'T

static member None : 'T option

static member Some : 'T -> 'T option

[<CompilationRepresentation(CompilationRepresentationFlags.Instance)>]

member Value : 'T

member IsSome : bool

member IsNone : bool