Factorial and Fibonacci using Church-encoded numbers

church.js

// Can we write programs without control flow, variables, or even recursion?
// Well, of course we can! Church did that with pen and paper! :)

const to_num = (n) => n((x) => x + 1)(0)

const ZERO = (f) => (x) => x
const ONE = (f) => (x) => f(x)
const TWO = (f) => (x) => f(f(x))
const THREE = (f) => (x) => f(f(f(x)))
const FOUR = (f) => (x) => f(f(f(f(x))))

console.log(to_num(ZERO))
console.log(to_num(ONE))
console.log(to_num(FOUR))

const SUCC = (n) => (f) => (x) => f(n(f)(x))

const FIVE = SUCC(FOUR)
const SIX = SUCC(FIVE)
const SEVEN = SUCC(SIX)
const EIGHT = SUCC(SEVEN)

console.log(to_num(EIGHT))

const PLUS = (n) => (m) => (f) => (x) =>
  n(f)(m(f)(x))

console.log(to_num(PLUS(EIGHT)(FIVE)))

const MULT = (n) => (m) => (f) => (x) =>
  n(m(f))(x)

console.log(to_num(MULT(EIGHT)(FIVE)))

const PRED = (n) => (f) => (x) =>
  n((g) => (h) => h(g(f)))((u) => x) ((u) => u)

console.log(to_num(PRED(MULT(EIGHT)(FIVE))))

const MINUS = (n) => (m) =>
  m(PRED)(n)

console.log(to_num(MINUS(EIGHT)(FIVE)))

const PAIR = (a) => (b) => (f) =>
  f(a)(b)

const FIRST = (p) =>
  p((a) => (b) => a)

const SECOND = (p) =>
  p((a) => (b) => b)

// 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

const FIB = (n) =>
  // Corecursion
  FIRST(
    // Step
    n(p =>
      PAIR(SECOND(p))(PLUS(FIRST(p))(SECOND(p)))
    // Seed
    )(PAIR(ZERO)(ONE)))

console.log(to_num(FIB(EIGHT)))

// 1, 1, 2, 6, 24, 120, ...

const FAT = (n) =>
  // Corecursion again
  SECOND(
    // Step
    n(p =>
      PAIR(SUCC(FIRST(p)))( MULT(FIRST(p))(SECOND(p)))
    // Seed
    )(PAIR(ONE)(ONE)))

console.log(to_num(FAT(FIVE)))