y-comb.js

'use strict'

function factorial(n) {
  return n === 0 ? 1 : n * factorial(n - 1)
}

const almostFactorial = f => n => n === 0 ? 1 : n * f(n - 1)

function tagY(fn) {
  const z = _ => fn(y)(_)
  const y = _ => fn(z)(_)
  return z
}

function Y(f) {
  function callsFunctionWithItself(x) { return x(x) }
  function appliesSelfCallingLambda(x) { return f(y => x(x)(y)) }

  return callsFunctionWithItself(appliesSelfCallingLambda)
}

factorial(3)

tagY(almostFactorial)(3)

Y(almostFactorial)(3)