Y

index.js

const Y = h => (f => f(f))(f => h(n => f(f)(n)));

/* by steps */

// helpers
const recur = (f) => f(f);
const wrap = h => recur(f => h(n => f(f)(n)));

const fact0 = (n) => n < 2
                       ? 1
                       : n * fact0(n - 1);

const fact1 = (f => n => n < 2
                           ? 1
                           : n * f(f)(n - 1))
              (f => n => n < 2
                           ? 1
                           : n * f(f)(n - 1));

const fact2 = recur(f => n => n < 2 
                                ? 1
                                : n * f(f)(n - 1));

const fact3 = recur(f => {
  const g = n => f(f)(n);
  return n => n < 2
                ? 1
                : n * g(n - 1);
});

const fact4 = wrap(g => n => n < 2
                               ? 1
                               : n * g(n - 1));

const fact5 = Y(g => n => n < 2
                            ? 1
                            : n * g(n - 1));


/* test */
const values = [0,  1,  2,  3,  4,  5,  6,  7,  8,  9];

console.log(values.map(fact0));
console.log(values.map(fact1));
console.log(values.map(fact2));
console.log(values.map(fact3));
console.log(values.map(fact4));
console.log(values.map(fact5));