Cheat Sheet For SML

SML_Cheat_Sheet.sml

(* SML notes *)
when writing in editor, semicolon is not required but when typing in terminal we need
semicolon
val negative_number = ~15  (* Yeah, unary minus uses the 'tilde' symbol *)
(*
- Math.e;
val it = 2.71828182846 : real
- Math.cos (Math.pi/2.0);
val it = 0.0 : real
- Math.sqrt (49.01);
val it = 7.00071424927 : real
- Int.min (ceil 3.4, floor 3.4);
val it = 3 : int
*)
(* Optionally, you can explicitly declare types. This is not necessary as
   ML will automatically figure out the types of your values. *)
val e = 2.718 : real
(*
- val a = 0 and b = 1 and c = 7.8;
val a = 0 : int
val b = 1 : int
val c = 7.8 : real
*)
- let
=   val c = 3 and d = 4    (* Two local, independent bindings.  *)
= in
=   (c * d) div 3
= end;
val it = 4 : int
- let val e = 5 and f = e+1 in e+f end;  (* Error! *)
stdIn:24.23 Error: unbound variable or constructor: e
- let
=   val c = 3; val d = c+1;     (* These bindings are dependent *)
= in
=   (c * d) div 3
= end;
val it = 4 : int
- let
=   val c = 3
= in
=   let val d = c+1 in (c * d) div 3 end
= end;
val it = 4 : int
(* Floating-point numbers are called "reals". *)
val tau = 2.0 * pi         (* You can multiply two reals *)
val twice_rent = 2 * rent  (* You can multiply two ints *)
(* val meh = 1.25 * 10 *)  (* But you can't multiply an int and a real *)
val yeh = 1.25 * (Real.fromInt 10) (* ...unless you explicitly convert
                                      one or the other *)
(* +, - and * are overloaded so they work for both int and real. *)
(* The same cannot be said for division which has separate operators: *)
val real_division = 14.0 / 4.0  (* gives 3.5 *)
val int_division  = 14 div 4    (* gives 3, rounding down *)
val int_remainder = 14 mod 4    (* gives 2, since 3*4 = 12 *)
(* ~ is actually sometimes a function (e.g. when put in front of variables) *)
val negative_rent = ~(rent)  (* Would also have worked if rent were a "real" *)
(* andalso is same as && in c, orelse is same as || in c, not is the negation)
(* Many values can be compared using equality operators: = (==) and <> (!=) *)
val pays_same_rent = (rent = 1300)  (* false *)
val is_wrong_phone_no = (phone_no <> 5551337)  (* false *)
(* Actually, most of the parentheses above are unnecessary.  Here are some
   different ways to say some of the things mentioned above: *)
fun is_large x = x > 37  (* The parens above were necessary because of ': int' *)
val is_sad = not has_something
val pays_same_rent = rent = 1300  (* Looks confusing, but works *)
val is_wrong_phone_no = phone_no <> 5551337
val negative_rent = ~rent  (* ~ rent (notice the space) would also work *)
(* Parentheses are mostly necessary when grouping things: *)
val some_answer = is_large (5 + 5)      (* Without parens, this would break! *)
(* val some_answer = is_large 5 + 5 *)  (* Read as: (is_large 5) + 5. Bad! *)
(* Besides booleans, ints and reals, Standard ML also has chars and strings: *)
val foo = "Hello, World!\n"  (* The \n is the escape sequence for linebreaks *)
val one_letter = #"a"        (* That funky syntax is just one character, a *)
val combined = "Hello " ^ "there, " ^ "fellow!\n"  (* Concatenate strings *)
val _ = print foo       (* You can print things. We are not interested in the *)
val _ = print combined  (* result of this computation, so we throw it away. *)
(* val _ = print one_letter *)  (* Only strings can be printed this way *)
val bar = [ #"H", #"e", #"l", #"l", #"o" ]  (* SML also has lists! *)
(* val _ = print bar *)  (* Lists are unfortunately not the same as strings *)
(* Fortunately they can be converted.  String is a library and implode and size
   are functions available in that library that take strings as argument. *)
val bob = String.implode bar          (* gives "Hello" *)
val bob_char_count = String.size bob  (* gives 5 *)
val _ = print (bob ^ "\n")            (* For good measure, add a linebreak *)
(* Lists can only contain one kind of thing... *)
The notation with the square brackets is just a special syntax of building up lists using the constructors :: ("::" is called cons operator) and nil.
- 1::2::3::4::nil;
val it = [1,2,3,4] : int list
- (8,true)::(5,false)::nil;
val it = [(8,true),(5,false)] : (int * bool) list
- (2::4::6::nil) :: (2::3::5::7::nil) :: (2::4::8::16::32::nil) :: nil;
val it = [[2,4,6],[2,3,5,7],[2,4,8,16,32]] : int list list
- val a = 4;                         (* Global binding to a.    *)
val a = 4 : int
- let val a = 5 in a+6 end;          (* Local binding to a.     *)
val it = 11 : int
- a;                                 (* No change in a.         *)
(* You can have lists of any kind *)
val number_count = List.length numbers     (* gives 7 *)
(* Lists of the same kind can be appended using the @ ("append") operator *)
val guest_list = [ "Mom", "Dad" ] @ [ "Aunt", "Uncle" ]
(* If you have many lists of the same kind, you can concatenate them all *)
val everyone = List.concat groups  (* [ "Alice", "Bob", "Huey", ... ] *)
(* val bad_list = [ 1, "Hello", 3.14159 ] : ??? list *)
 (* We can give new names to types. This is called type aliasing  *)
type vector2d = real * real
val unitx : vector2d = (1.0,0.0)          (* unit vector along x-axis *)
val unity : vector2d = (0.0,1.0)          (* unit vector along y-axis *)
(* Tuples, on the other hand, can contain a fixed number of different things *)
(*
val person1 = ("Simon", 28, 3.14159)  (* : string * int * real *)
- ( 2 );    (* No such thing as a one-tuple *)
val it = 2 : int
- ((()));
val it = () : unit
- ((2,3,4), (true,3.3));
val it = ((2,3,4),(true,3.3)) : (int * int * int) * (bool * real)
*)
(* You can even have tuples inside lists and lists inside tuples *)
val mixup = [ ("Alice", 39),
              ("Bob",   37),
              ("Eve",   41) ]  (* : (string * int) list *)
val good_bad_stuff =
  (["ice cream", "hot dogs", "chocolate"],
   ["liver", "paying the rent" ])           (* : string list * string list *)
(* Records are structrured data types of heterogeneous elements that are labeled.
   The labels allow elements to be written in any order.  *)
val rgb = { r=0.23, g=0.56, b=0.91 } (* : {b:real, g:real, r:real} *)
(* You don't need to declare their slots ahead of time. Records with
   different slot names are considered different types, even if their
   slot value types match up. For instance... *)
val Hsl = { H=310.3, s=0.51, l=0.23 } (* : {H:real, l:real, s:real} *)
val Hsv = { H=310.3, s=0.51, v=0.23 } (* : {H:real, s:real, v:real} *)
(* ...trying to evaluate `Hsv = Hsl` or `rgb = Hsl` would give a type
   error. While they're all three-slot records composed only of `real`s,
   they each have different names for at least some slots. *)
(* You can use hash notation to get values out of tuples. *)
val H = #H Hsv (* : real *)
val s = #s Hsl (* : real *)
(*
- {a = 2.3, b = {a="s",c=45}};
val hi = {a=2.3,b={a="s",c=45}} : {a:real, b:{a:string, c:int}}
#a (#b check); will give s
- {one = (2.3, "string")};
val it = {one=(2.3,"string")} : {one:real * string}
*)
((* Pattern matching is a funky part of functional programming.  It is an
   alternative to if-sentences. A function defined using a list of pattern matching rules "tries" each pattern and gives out the value corresponding to the first case that
matched. *)
(* Pattern matching is also possible on composite types like tuples, lists and
   records. Writing "fun solve2 (a, b, c) = ..." is in fact a pattern match on
   the one three-tuple solve2 takes as argument. Similarly, but less intuitively,
   you can match on a list consisting of elements in it (from the beginning of
   the list only). *)
(* PATTERNS:
- val (a,b,c) = (1,3,6);  (* Matching in declaration *)
val a = 1 : int
val b = 3 : int
val c = 6 : int
- val {1=a, 2=b, 3=c} = {1=1,2=3,3=6};
val a = 1 : int
val b = 3 : int
val c = 6 : int
- val {abscissa=x, ordinate=y} = {ordinate=3.2, abscissa=1.2};
val x = 1.2 : real
val y = 3.2 : real
- val {b=x, ...} = {a=2, b="s", c=3.4, d=[1,2]};
val x = "s" : string
- val (x,_,y) = (1,2,3);                 (* wildcard pattern *)
(* _ is a match everything pattern often called wildcard pattern. *)
val x = 1 : int
val y = 3 : int
- val head :: _ = [1, 2, 3];
stdIn:25.1-25.26 Warning: binding not exhaustive
          head :: _ = ...
val head = 1 : int
- val x as (fst,snd) = (2, true);        (* layered pattern   *)
val x = (2,true) : int * bool
val fst = 2 : int
val snd = true : bool
- val list as head :: tail = [1, 2, 3];
stdIn:27.1-27.37 Warning: binding not exhaustive
          list as head :: tail = ...
val list = [1,2,3] : int list
val head = 1 : int
val tail = [2,3] : int list
Only certain functions, constructors, can be used in patterns. :: is a constructor,
hence it can be use in a pattern. @ is not. Neither is +.
*)
(* Functions! *)
- (fn x => x+1);       (* A function object: successor function *)
val it = fn : int -> int
- val f = (fn x => x+1);  (* Bind f to the successor function   *)
val f = fn : int -> int
- fun f (n) = n+1;       (* Same function, alternative syntax. *)
val f = fn : int -> int
- f;
val it = fn : int -> int
- f (2);                 (* Function application               *)
val it = 3 : int
- f 2;                   (* Parens not needed, if arg a token. *)
val it = 3 : int
- f 2 * 4;               (* Application binds tightest.        *)
val it = 12 : int
- (fn x => x+1) 8;       (* Name not needed to apply to arg    *)
val it = 9 : int
- [fn n=>n+1, fn m=>2*m, fn n=>n div 2];
val it = [fn,fn,fn] : (int -> int) list
- (fn n=>2*n,fn r=>ceil r);
val it = (fn,fn) : (int -> int) * (real -> int)
- fun h (x) = (f x, g x);  h (4);  h (7);   (* functions and tuples. *)
val h = fn : int -> int * int
val it = (6,12) : int * int
val it = (9,21) : int * int
- fun j (x) = [f x, g x];  j (4);  j (7);   (* functions and lists.  *)
val j = fn : int -> int list
val it = [6,12] : int list
val it = [9,21] : int list
- fun fact (n) = if n=0 then 1 else n*fact(n-1);
- val fact' = (fn n => if n=0 then 1 else n*fact'(n-1));  (* Error! *)
stdIn:15.43-15.48 Error: unbound variable or constructor: fact'
- val rec fact = (fn n => if n=0 then 1 else n*fact(n-1));
val fact = fn : int -> int
- fun                        (* mutually recursive function definitions *)
=   odd (n) = if n=0 then false else even (n-1)
= and
=   even (n) = if n=0 then true else odd (n-1);
val odd = fn : int -> bool
val even = fn : int -> bool
- fun                        (* mutually recursive function definitions *)
=   take nil = nil | take (x::xs) = x::(skip xs)
= and
=   skip nil = nil | skip (x::xs) = take xs;
val take = fn : 'a list -> 'a list
val skip = fn : 'a list -> 'a list
- take [1,2,3];  skip [1,2,3,4];
val it = [1,3] : int list
val it = [2,4] : int list
- fun l (x as (fst,snd)) = (x,fst div snd);     (* layered patterns    *)
val l = fn : int * int -> (int * int) * int
- fun switch (x,y) = (y,x);
val switch = fn : 'a * 'b -> 'b * 'a
- switch (2, "abc");
val it = ("abc",2) : string * int
- nil;
val it = [] : 'a list
(* Important list functions *)
- null;
val it = fn : 'a list -> bool
- hd;
val it = fn : 'a list -> 'a
- rev; (* to reverse the list *)
- tl; (* returns the remaining of the list except the head *)
val it = fn : 'a list -> 'a list
- fun member (x, nil) = false | member (x, y::ys) = x=y orelse member (x,ys);
val member = fn : ''a * ''a list -> bool
- fun insert (x, nil) = [x]
=   | insert (x,y::ys) = if x<y then x::y::ys else y :: insert (x,ys);
val insert = fn : int * int list -> int list
- fun merge (xs,nil) = xs
=  |  merge (nil,ys) = ys
=  |  merge (x::xs,y::ys) = if x<y then x :: merge(xs,y::ys) else y :: merge(x::xs,ys);
val merge = fn : int list * int list -> int list
- val const7 = (fn x => fn y => 7);  (* Several ways to define the same thing ... *)
val const7 = fn : 'a -> 'b -> int
- fun const7 x = (fn y => 7);
val const7 = fn : 'a -> 'b -> int
- fun const7 x y = 7;
val const7 = fn : 'a -> 'b -> int
- fun const7 _ _ = 7;
val const7 = fn : 'a -> 'b -> int
- fun f (x) = (fn (y,z) => if x=0 then y+z else x*(y+z));
val f = fn : int -> int * int -> int
- fun f (x) (y,z) = if x=0 then y+z else x*(y+z);
val f = fn : int -> int * int -> int
- val times = (fn x => (fn y => x * y));
val times = fn : int -> int -> int
- fun comp (f,g) = (fn x => f (g (x)));
val comp = fn : ('a -> 'b) * ('c -> 'a) -> 'c -> 'b
- fun comp (f,g) (x) = f(g(x));
val comp = fn : ('a -> 'b) * ('c -> 'a) -> 'c -> 'b
- val f = comp (Math.sin, Math.cos);
val f = fn : real -> real
- val g = Math.sin o Math.cos;        (*  Composition "o" is predefined  *)
val g = fn : real -> real
- f(0.25);
val it = 0.824270418114 : real
- g(0.25);
val it = 0.824270418114 : real
- val curry = (fn f => (fn a => fn b => f(a,b)));
val curry = fn : ('a * 'b -> 'c) -> 'a -> 'b -> 'c
- fun curry (f) (a) (b) = f(a,b);
val curry = fn : ('a * 'b -> 'c) -> 'a -> 'b -> 'c
- fun curry f a b = f (a, b)
- fun uncurry f (a,b) = f a b;
val uncurry = fn : ('a -> 'b -> 'c) -> 'a * 'b -> 'c
(* in uncurry "= f a b" means ((f a) b) *)
- fun add (u,v) = u + v
- fun addp u v  = u + v
(* val add : int * int -> int
val addp : int -> (int -> int) *)
- val addp1 = curry  add;
val addp1 = fn : int -> int -> int
- val add1  = uncurry addp;
val add1 = fn : int * int -> int
*)
(* Algebraic Data types *)
- datatype color = Red | Blue | Green;
datatype color = Blue | Green | Red
- Blue;  Red;  Green;
val it = Blue : color
val it = Red : color
val it = Green : color
(* Here is a function that takes one of these as argument *)
fun say(col) =
    if col = Red then "You are red!" else
    if col = Green then "You are green!" else
    if col = Blue then "You are blue!" else
    raise Fail "Unknown color"
(* We did not include the match arm `say _ = raise Fail "Unknown color"`
because after specifying all three colors, the pattern is exhaustive
and redundancy is not permitted in pattern matching *)
val _ = print (say(Red) ^ "\n")
(* Datatypes are very often used in combination with pattern matching *)
fun say Red   = "You are red!"
  | say Green = "You are green!"
  | say Blue  = "You are blue!"
- datatype bool = true | false;
datatype bool = false | true
- fun not (true) = false | not (false) = true;
val not = fn : bool -> bool
- datatype numbs = i of int | r of real;
datatype numbs = i of int | r of real
- [i 3, r 3.4, i 5, i 9, r 5.4];
val it = [i 3,r 3.4,i 5,i 9,r 5.4] : numbs list
- fun isum nil = 0
=   | isum ((i n)::rest) = n+(isum rest) | isum (_::rest) = isum (rest);
val isum = fn : numbs list -> int
- datatype shape = Rectangle of real*real | Circle of real | Line of (real*real)list
=    | Spline of (real*real)list;
datatype shape
  = Circle of real
  | Line of (real * real) list
  | Rectangle of real * real
  | Spline of (real * real) list
- Circle (1.2);  Circle (3.4);
val it = Circle 1.2 : shape
val it = Circle 3.4 : shape
- Rectangle (4.3, 1.9);  Rectangle (40.3, ~8.345);
val it = Rectangle (4.3,1.9) : shape
val it = Rectangle (40.3,~8.345) : shape
- Line [(1.1, 2.2)];  Line [];
val it = Line [(1.1,2.2)] : shape
val it = Line [] : shape
(* End *)
(* Larger functions are usually broken into several lines for readability *)
fun thermometer temp =
    if temp < 37
    then "Cold"
    else if temp > 37
         then "Warm"
         else "Normal"
val test_thermo = thermometer 40  (* gives "Warm" *)
(* if-sentences are actually expressions and not statements/declarations.
   A function body can only contain one expression.  There are some tricks
   for making a function do more than just one thing, though. *)
(* A function cannot change the variables it can refer to.  It can only
   temporarily shadow them with new variables that have the same names.  In this
   sense, variables are really constants and only behave like variables when
   dealing with recursion.  For this reason, variables are also called value
   bindings. An example of this: *)
val x = 42
fun answer(question) =
    if question = "What is the meaning of life, the universe and everything?"
    then x
    else raise Fail "I'm an exception. Also, I don't know what the answer is."
val x = 43
val hmm = answer "What is the meaning of life, the universe and everything?"
(* Now, hmm has the value 42.  This is because the function answer refers to
   the copy of x that was visible before its own function definition. *)
fun first_elem (x::xs) = x
fun second_elem (x::y::xs) = y
fun evenly_positioned_elems (odd::even::xs) = even::evenly_positioned_elems xs
  | evenly_positioned_elems [odd] = []  (* Base case: throw away *)
  | evenly_positioned_elems []    = []  (* Base case *)
(* The case expression can also be used to pattern match and return a value *)
datatype temp =
      C of real
    | F of real
fun temp_to_f t =
    case t of
      C x => x * (9.0 / 5.0) + 32.0
    | F x => x
(* When matching on records, you must use their slot names, and you must bind
   every slot in a record. The order of the slots doesn't matter though. *)
fun rgbToTup {r, g, b} = (r, g, b)    (* fn : {b:'a, g:'b, r:'c} -> 'c * 'b * 'a *)
fun mixRgbToTup {g, b, r} = (r, g, b) (* fn : {b:'a, g:'b, r:'c} -> 'c * 'b * 'a *)
(* If called with {r=0.1, g=0.2, b=0.3}, either of the above functions
   would return (0.1, 0.2, 0.3). But it would be a type error to call them
   with {r=0.1, g=0.2, b=0.3, a=0.4} *)
(* Higher order functions: Functions can take other functions as arguments.
   Functions are just other kinds of values, and functions don't need names
   to exist.  Functions without names are called "anonymous functions" or
   lambda expressions or closures (since they also have a lexical scope). *)
(* Here is a higher-order function that works on lists (a list combinator) *)
(* map f l
       applies f to each element of l from left to right,
       returning the list of results. *)
val readings = [ 34, 39, 37, 38, 35, 36, 37, 37, 37 ]  (* first an int list *)
val opinions = List.map thermometer readings (* gives [ "Cold", "Warm", ... ] *)
(* And here is another one for filtering lists *)
val warm_readings = List.filter is_large readings  (* gives [39, 38] *)
(* You can create your own higher-order functions, too.  Functions can also take
   several arguments by "currying" them. Syntax-wise this means adding spaces
   between function arguments instead of commas and surrounding parentheses. *)
fun map f [] = []  (* We could have replaced [] by nil *)
  | map f (x::xs) = f(x) :: map f xs
(* map has type ('a -> 'b) -> 'a list -> 'b list and is called polymorphic. This kind of polymorphism is called
parametric polymorphism in the sense that map is a generic list maping
function that works no matter what the types 'a and 'b are. *)
(* 'a is called a type variable. *)
(* We can declare functions as infix *)
val plus = add_them   (* plus is now equal to the same function as add_them *)
infix plus            (* plus is now an infix operator *)
val seven = 2 plus 5  (* seven is now bound to 7 *)
(* Functions can also be made infix before they are declared *)
infix minus
fun x minus y = x - y (* It becomes a little hard to see what's the argument *)
val four = 8 minus 4  (* four is now bound to 4 *)
(* An infix function/operator can be made prefix with 'op' *)
val n = op + (5, 5)   (* n is now 10 *)
(* 'op' is useful when combined with high order functions because they expect
   functions and not operators as arguments. Most operators are really just
   infix functions. *)
(* foldl f init [x1, x2, ..., xn]
       returns
       f(xn, ...f(x2, f(x1, init))...)
       or init if the list is empty. *)
fun fold f init [] = init
 |  fold f init (x :: xs) = f (x, fold f init xs)
(* if we wanted an order from left to right, then *)
fun fold f init [] = init
 |  fold f init (x :: xs) = fold f (f (x, init)) xs; (* uncurried function *)
(* if fold f a [b0, b1 , b2, b3 ...] = f (f a b0) b1 .... then we have *)
fun fold f init [] = init
 |  fold f init (x :: xs) = fold f (f x init) xs; (* curried function *)
val sum_of_numbers = foldl op+ 0 [1, 2, 3, 4, 5]
 (* val sum_of_numbers = 15 : int *)
(* Here is a binary tree datatype *)
datatype 'a tree = Nil
                | Node of 'a tree * 'a * 'a tree;
fun inorder (Nil) = []
    | inorder (Node (left, x, right)) = inorder (left) @ (x :: nil) @ inorder (right);
fun rotate (Nil) = Nil
 | rotate (Node (Nil, x, t)) = Node (Nil, x, t)
 | rotate (Node (Node (t1, b, t2), a, t3)) = Node (t1, b, Node (t2, a, t3));
The option type is a useful datatype defined in standard library that
is used to signal optional result. They capture a lot of logic that
involves the use of the unsafe null values (null pointer in C, null in
Java). They are defined as
datatype 'a option = SOME of 'a | NONE
We use this to define the head and tail of a list.
fun head []         = NONE
  | head (x::_)     = SOME x
fun tail []         = NONE
  | tail (_ :: xs)  = SOME xs
  =====================*************************=========================
=================-- Signatures, Structures, Functors --==================
A structure is defined as follows:
structure Name = struct
  Definitions
end
Example:
structure foo = struct
    type t = string
    val say = fn x => TextIO.print x
end
foo.say "Hi!\n"; (* Will print Hi! *)
Signatures Give the interface of a structure.
signature NAME = sig
    DECLARATIONS
end
Signatures, example
signature bar = sig
    type t
    val say : t -> unit
end
To say that the structure foo implements the signature bar:
structure foo:bar = struct
    type t = string
    val say = fn x => TextIO.print x
    val hello = fn ()
    => TextIO.print "hello/n"
end
foo.say "hej"
is OK,
but not foo.hello() as it is not the part of the signature
Functors
Build structures from structures.
   functor FunctorName (ParamName : SigName)
     = struct
         ...
       end;
To make a structure, we do as follows:
   structure ResultStructure
        = FunctorName (ArgumentStructure)
see ordering2.sml. (mail me if you need this file)

The following are available (among other)
open_in 	string -> instream	Create an input stream
input_line 	instream -> string	Get one line
end_of_stream 	instream -> boolean	Check for more
can_input 	instream -> int	Check for more
input 	instream * int -> string	Get loads
close_in 	instream -> unit	
Handling input & output efficiently can be tricky. So don't bother, use one of the following to load an entire file into either a single string or a list of strings - let the operating system do the work.

fun fileToString fileName = let
  val stream = open_in fileName
  val str = input(stream, can_input stream)
  val _ = close_in stream
in str end;

fun fileToList fileName = let
  fun f fh = if end_of_stream fh then
    let val _ = close_in fh in nil end
    else (input_line fh)::(f fh)
in f(open_in fileName) end;


(* Exceptions *)
exception constructorName of arguments
(* The "of arguments" clause is optional *)
- exception Foo of int;
exception Foo of int
- Foo;
val it = fn : int -> exn
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