lambda.js

console.log('Lambda calculus with ES6 syntax');

console.log(
  // (\(x,y).x+y)(1,2) => 1+2 => 3
  ((x, y) => x + y) (1, 2)
);

console.log(
  // ((\x.\y.x+y) 1) 2 => (\y.1+y) 2 => 3
  (x => y => x + y) (1) (2)
);

console.log(
  // (\x.x 1) => fn (N->A) -> B
  (x => x(1))
);

console.log(
  // (\x.(\y.x y)) => fn (A->B) -> (B->A)
  (x => y => x(y))
);

console.log(
  // (\x.x 1) (\x.x+1) => (\x.x+1) 1 => 1+1 => 2
  (x => x(1)) (x => x+1)
);

console.log(
  // (\x.(\y.x y)) (\x.x+1) 2 => (\y.(\x.x+1) y) 2 => (\x.x+1) 2 => 2+1 => 3
  (x => y => x(y)) (x => x+1) (2)
);

ycombinator.js

// Y combinator
// \f.(\x.f (x x)) (\x.f (x x))
// Translated from https://gist.github.com/logicmason/0722b5b159a45f7a81b6

var Y = fn => 
  (x => fn(y => x(x)(y)))
  (x => fn(y => x(x)(y)))
;

var factgen = (fact) =>
  n => (n === 0) ? 1 : n * fact(n-1)
;

var factorial = Y(factgen);
console.log(factorial(5));