Functional Programming Concepts

functional-programming-concepts.md

Algebraic structures groups

Monoids

Function that operates on a data type (or set)

Laws:

• Associative, eg. 2 + 3 <=> 3 + 2
• Binary Operations, eg. public static Foo Op(Foo x, Foo y)
• With a neutral element (identity), eg. 2 + 3 + 0 <=> 3 + 2 + 0

Examples:

• Maybe
• Endomorphism
• Tuple
• Either

Semigroups

Laws:

• Binary Operation
• Associative
• No identity required

Examples:

• Min / Max
• First / Last
• Aggregation

Quasigroup

Laws:

• Inversion
• No associativity required
• No identity required

Example: substraction

Magmas

Law: binary operation with no constraints on its behaviour

Examples:

• Rock, paper, scissors
• Colour Mixing

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Category Theory

Category

Collection of objects / points with morphisms (ie. functions, transformations) between them:

• f: a -> b
• g: b -> c
• g.f: a -> c

Btw, composition is associative: h.(g.f) = (h.g).f

Functors

A functor F is a mapping between 2 categories, not only between their objects but also between their morphisms.

Laws:

• f: a -> b
• F(f): F(a) -> F(b)

Endofunctors

Functor from a category to itself.

Monad

Monoids in the category of endofunctors

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Ok cool but what does it mean for C#?

Basically a monad in the C# context, is a type that gives some additional features to an 1-ary generic type T.

Examples:

• IEnumerable<T>: gives T non-determinism (multiple values)
• Nullable<T>: gives T nullability
• Task<T>: gives T asynchronicity

To resp. play with them and get the inner value:

• LINQ
• ?? or GetValue
• await

In other languages like F# or Haskell, you could define two methods to create a new monad, in C# it would look like:

• public static Monad<T> Return<T>(T value)
• public static Monad<U> Bind<T, U>(Monad<T> value, Func<T, Monad<U>> operation)