77 lines
1.5 KiB
Swift
77 lines
1.5 KiB
Swift
func succ<A, B, C>(_ n: @escaping (@escaping (A) -> B) -> (C) -> A) -> (@escaping (A) -> B) -> (C) -> B {
|
|
return {f in
|
|
return {x in
|
|
return f(n(f)(x))
|
|
}
|
|
}
|
|
}
|
|
|
|
func zero<A, B>(_ a: A) -> (B) -> B {
|
|
return {b in
|
|
return b
|
|
}
|
|
}
|
|
|
|
func three<A>(_ f: @escaping (A) -> A) -> (A) -> A {
|
|
return {x in
|
|
return succ(succ(succ(zero)))(f)(x)
|
|
}
|
|
}
|
|
|
|
func four<A>(_ f: @escaping (A) -> A) -> (A) -> A {
|
|
return {x in
|
|
return succ(succ(succ(succ(zero))))(f)(x)
|
|
}
|
|
}
|
|
|
|
func add<A, B, C>(_ m: @escaping (B) -> (A) -> C) -> (@escaping (B) -> (C) -> A) -> (B) -> (C) -> C {
|
|
return {n in
|
|
return {f in
|
|
return {x in
|
|
return m(f)(n(f)(x))
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
func mult<A, B, C>(_ m: @escaping (A) -> B) -> (@escaping (C) -> A) -> (C) -> B {
|
|
return {n in
|
|
return {f in
|
|
return m(n(f))
|
|
}
|
|
}
|
|
}
|
|
|
|
func exp<A, B, C>(_ m: A) -> (@escaping (A) -> (B) -> (C) -> C) -> (B) -> (C) -> C {
|
|
return {n in
|
|
return {f in
|
|
return {x in
|
|
return n(m)(f)(x)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
func church<A>(_ x: Int) -> (@escaping (A) -> A) -> (A) -> A {
|
|
guard x != 0 else { return zero }
|
|
|
|
return {f in
|
|
return {a in
|
|
return f(church(x - 1)(f)(a))
|
|
}
|
|
}
|
|
}
|
|
|
|
func unchurch<A>(_ f: (@escaping (Int) -> Int) -> (Int) -> A) -> A {
|
|
return f({i in
|
|
return i + 1
|
|
})(0)
|
|
}
|
|
|
|
let a = unchurch(add(three)(four))
|
|
let b = unchurch(mult(three)(four))
|
|
// We can even compose operations
|
|
let c = unchurch(exp(mult(four)(church(1)))(three))
|
|
let d = unchurch(exp(mult(three)(church(1)))(four))
|
|
|
|
print(a, b, c, d)
|