Y Combinator

readme.txt

In Lambda Calculus, the Y combinator is 

	Y = (λf . (λx . f (x x)) (λx . f (x x)))

Thus Y(g) would break down like so:

	{(x) -> g (x x)} {(x) -> g (x x)}
	g( {(x) -> g (x x)} {(x) -> g (x x)} )
	g( g ({(x) -> g (x x)} {(x) -> g (x x)}) )
	etc...

The Y Combinator finds fixed points, points where f(x) = x. Once found:

	f({(v) -> x(x)(v)}) becomes f({(v) -> f(f)(v)}) = f(f)

index.js

Y = function(f) {	
	var f_xx = function(x) {
		return f(function(v) { return x(x)(v); });
	};
	return f_xx(f_xx);
};
var factorial = Y(function(self) {
	return function(n) {
		return n == 0 ? 1 : n*self(n - 1);
	};
});
console.log(factorial(3));