Sage/Y-Combinator/Z-Combinator

Used for fixed-point recursion.

If we implemented the Sage combinator (Y-Combinator) like this:

// WRONG
export const Sage = (x: Fn): Fn => x(Sage(x));

It would cause a stack overflow. So we use the Z-Combinator instead, which is designed for strict/eager languages.

export const Sage = (f: Fn): Fn => {
  return ((x: Fn) => f((y: any) => x(x)(y)))((x: Fn) => f((y: any) => x(x)(y)));
};
export const Y = Sage;
export const Z = Sage;

const factorial = Sage((f: any) => (n: number) => (n <= 1 ? 1 : n * f(n - 1)));
factorial(5); // 120