// `fix` is an Y-combinator implementation (recursive calls in lambda calculus):
// Y = \f -> (\x -> f (x x))(\x -> f (x x))

// fix :: (a -> a) -> a
const fix = f => (x => f(y => (x(x))(y)))(x => f(y => (x(x))(y)));

// Generator function. Inner signature should correspond to actual function interface.
// mapgen :: ((a -> b) -> [a] -> [b]) -> (a -> b) -> [a] -> [b]
const mapgen = map => f => list => list.length === 0 ? [] : [f(list[0])].concat(map(f)(list.slice(1)));

// Memoization of a function of 1 argument. For functions of more arguments explicit work with `arguments` needed.
// memoize :: (a -> b) -> a -> b
const memoize = fn => x => {
  const hash = x === Object(x) ? JSON.stringify(x) : x.toString();
  fn.memoize || (fn.memoize = {});
  return (hash in fn.memoize) ? fn.memoize[hash] : (fn.memoize[hash] = fn(x));
};

// map :: (a -> b) -> [a] -> [b]
const map = fix(memoize(mapgen));