Church Numerals in Swift

church.swift

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

import UIKit

func zero<N>(succ: N -> N) -> N -> N {
    return { (z: N) in
        return z
    }
}

func one<N>(succ: N -> N) -> N -> N {
    return { (z: N) in
        return succ(z)
    }
}

func two<N>(succ: N -> N) -> N -> N {
    return { (z: N) in
        return succ(succ(z))
    }
}

func three<N>(succ: N -> N) -> N -> N {
    return { (z: N) in
        return succ(succ(succ(z)))
    }
}

func int2Church<N>(n: Int) -> (N -> N) -> N -> N {
    if n == 0 {
        return zero
    }
    
    return { (succ: (N -> N)) -> N -> N in
        return { (z: N) -> N in
            return succ(int2Church(n - 1)(succ)(z))
        }
    }
}

func church2Int<N>(n: (Int -> Int) -> Int-> N) -> N {
    return n({$0 + 1})(0)
}

func plus<N>(a: (N -> N) -> N -> N)-> ((N -> N) -> N -> N) -> (N -> N) -> N -> N {
    return { (b: (N -> N) -> N -> N) in
        return { (succ: N -> N) in
            return { (z: N) in
                return a(succ)(b(succ)(z))
            }
        }
    }
}

church2Int(plus(one)(two))

func mult<N>(a: (N -> N) -> N -> N) -> ((N -> N) -> N -> N) -> (N -> N) -> N -> N {
    return { (b: (N -> N) -> N -> N) in
        return { (succ: (N -> N)) -> N -> N in
            return { (z: N) -> N in
                return a(b(succ))(z)
            }
        }
    }
}

church2Int(mult(two)(three))

func pow<A, B, C>(a : A) -> (A -> B -> C -> C) -> B -> C -> C {
    return { (b : (A -> B -> C -> C)) -> B -> C -> C in
        return { (succ : B) -> C -> C in
            return { (z : C) -> C in
                return b(a)(succ)(z)
            }
        }
    }
}

church2Int(pow(two)(three))