BasicMonad.swift

//: Playground - noun: a place where people can play

import Foundation

/*
Basic Monad according to definition in: http://stackoverflow.com/questions/27750046/is-a-collection-with-flatmap-a-monad

The requirements for being a monad

- A monad has to be a type constructor F[_] that takes one type argument. For example, F could be List, Function0, Option, etc.

- A monadic unit. This is a function that takes a value of any type A and produces a value of type F[A].

- A monadic composition operation. It's an operation that takes a function of type A => F[B], and a function of type B => F[C] and produces a composite function of type A => F[C].
*/

struct A<T> {
  var content: T
}

func monadicUnit<T>(p:T) -> A<T> {
  return A(content: p)
}

func monadicComposition<T, U, V>(t1: T -> A<U>, t2: U -> A<V>) -> T -> A<V> {
  return { x in
    t2(t1(x).content)
  }
}

A(content: 3)

let z = monadicComposition({ (x:Int) -> A<Int> in A(content: x * 2)}, {(y:Int) -> A<Int> in A(content: y * 4)})

z(5)