module Prelude =>
// ∀a, b ⇒ a → b → a
fun const(x) => \y => x
// ∀a, b, c ⇒ (a → b) → (c → a) → c → b
fun compose(f, g) => \x => f(g(x))
// ∀a, b, c ⇒ (a → b → c) → a → b → c
fun curry(f, a, b) => f((a, b))
// ∀a ⇒ a → a
fun id(x) => x
enum struct Bool { True , False }
// ∀a, b ⇒ a → b → a
fun true(x, y) => x
// ∀a, b ⇒ a → b → b
fun false(x, y) => y

// ∀a, b ⇒ a → b → b
fun zero(f, x) => x
// ∀a, b, c ⇒ ((a → b) → c → a) → (a → b) → c → b
fun succ(n, f, x) => f(n(f, x))
// ∀a, b, c, d ⇒ (a → b → c) → (a → c → d) → a → b → d
fun plus(m, n, f, x) => m(f, n(f, x))
// ∀a, b, c ⇒ (a → b) → (c → a) → c → b
fun mult(m, n, f, x) => m(n(f), x)
// ∀a, b, c, d, e, f, g ⇒
// (((a → b) → (b → c) → c) → (d → d) → (e → f ) → g) → a → f → g
fun pred(n, f, x) => n(\g, h => h(g(f)), \u => x, \v => v)