My take in explaining to myself the Y Combinator

Describing Y Combinator

// the original Y Combinator is here: https://leanpub.com/javascript-allonge/read#y
// have a look at that soup of function and return
// I refactored it down to the below version
// I hope is correct, too tired now.

// used like this
var factorial = Y(
  // next
  function(fac) {    
    return function(n) {
      return n == 0 ? 1 : n * fac(n - 1); 
    };
  }
);

function Y(next) {
  
  function self() {
    return next(function(arg1) {
      return self()(arg1);
    });
  }

  return self();
}

// * Y is called
// * self is called
// * next is applied on the function representing the 
//   recursive step 
// * so we obtain the function representing the actual 
//   instruction, in this this case a factorial 
// * this function is assigned to factorial on line 2
// * when factorial is called we are calling the function
//   from line 5 to line 7
// * on the recursive step at the end of line 6 we are
//   calling the function from line 14 to line 16
// * at each recursive step it all resolves at line 15 where
//   where we pass execute the next call passing the new
//   integer (arg1)
// * arg1 is the integer that is being passed through each 
//   recursive call

var assert = require('assert');
assert.equal(factorial(1), 1);
assert.equal(factorial(3), 6);
assert.equal(factorial(5), 120);
console.log('ok');