Data commit

Task/Church-numerals/Swift/church-numerals.swift

@@ -0,0 +1,77 @@
+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)