S Combinator

S.js

/*
S : \x y z -> x z (y z)
*/
// S :: (z -> (a -> b)) -> (z -> a) -> z -> b
function S(x, y, z) {
  return x(z)(y(z));
}

// example:
// add :: a -> a -> a
function add(x) {
  return function(y) {
    return x + y;
  }
}

// mult :: a -> a
function mult3(x) {
  return x * 3;
}

/*
S: x(z)(y(z));
   x(10)(y(10))     // sub 10 for z
   x(10)(mult3(10)) // sub mult3 for y
   add(10)(30);     // eval mult3(10) -> 30; sub add for x
   40               // eval add(10)(30) -> 40
*/
S(add, mult3, 10); // => 40

/*
but what does it mean? why the S combinator? Who cares? How is it useful?
Appears useful mostly for combinatory logic, not so much for real code. At least not directly.
*/

I love it that javascript is inspired by scheme, otherwise I would never, ever, ever understand this. Thank god JS exists.