var Y = function(proc) {
  return (function(x) {
    return proc(function(y) { return (x(x))(y);});
  })(function(x) {
    return proc(function(y) { return (x(x))(y);});
  });
};

var factgen = function(fact) {
 return function(n) {
  return (n === 0) ? 1 : n * fact(n-1); // calls argument, not self
 };
};

var fibgen = function(fib) {
  // this naive solution has exponential runtime complexity
  return function(n) {
    return (n <= 2) ? 1 : fib(n-1) + fib(n-2);
  };
};

console.log( Y(factgen)(5) ); // returns 120, i.e., 1 * 2 * 3 * 4 * 5 
console.log( Y(fibgen)(7) ); // returns 13, i.e., the 7th fibonacci number

var factorial = Y(factgen); // built entirely with anonymous functions
var fibonacci = Y(fibgen);

console.log( factorial(6) ); // 120
console.log([1,2,3,4,5,6,7,8,9,10].map( fibonacci) ); // the first 10 fibonacci numbers
console.log( fibonacci(35) ); // uh oh, already getting kind of slow due to poor algorithm