Function composition in swift

Composition.swift

import Foundation

// identity function
func id<T>(_ x: T) -> T {
    return x
}

// compositing functions
infix operator ∘: MultiplicationPrecedence
func ∘<T, U, V> (_ g: @escaping ((U) -> V), _ f: @escaping ((T) -> U)) -> ((T) -> V) {
    return { (x: T) -> V in g(f(x)) }
}

func f(_ x: Int) -> Int {
    return x + 1
}

func g(_ x: Int) -> Int {
    return x * 4
}

func h(_ x: Int) -> Int {
    return x * x
}

g(f(2)) // 12
(g ∘ f)(2) // 12

h(g(f(2))) // 144
(h ∘ g ∘ f)(2) // 144

(id ∘ f)(2) // 3
(f ∘ id)(2) // 3