Defining Recursive Functions using a Fixed Point Combinator

FixedFactorial.js

/* A fixed point combinator */
function fix(f) {
  var g = function(x){return f(function(y){return x(x)(y);});}; 
  return g(g);
}

/* An indirectly recursive factorial function. */
function factorial(self) {
  return function(n) {
    if (n == 0) {return 1;}
    return n * self(n - 1); 
  };
};

/* By fixing `factorial` we supply it as an argument
to itself, so that by making calls to `self`, `factorial`
can indirectly call itself. */
var fact = fix(factorial);

/* The behavior is what we would expect. */
fact(3);  //=> 6
fact(5);  //=> 120
fact(9);  //=> 362880