Tests for basic composition properties in JS (with Jest)

composition-properties.js

function compose (...fns) {
  function _compose(fnA, fnB) {
    if (fnA === undefined) {
      throw new Error('compose needs at least one argument')
    }
  
    return (...args) => {
      return fnA(fnB(...args));
    }
  }

  return fns.reduce((acc, cur) => {
    return _compose(acc, cur)
  });
}

function id(x) {
  return x;
};

function square(n) {
  return n * n;
}

// f :: A -> B
// g :: B -> C
// h :: C -> D
// h . (g . f) = (h . g) . f = h . g . f
test('ℎ ∘ (𝑔 ∘ 𝑓 ) = (ℎ ∘ 𝑔) ∘ 𝑓 = ℎ ∘ 𝑔 ∘ 𝑓', () => {
  const c = compose;

  const h = (x) => `h(${x})`;
  const g = (x) => `g(${x})`;
  const f = (x) => `f(${x})`;

  const r = c(h, c(g, f))
  const s = c(c(h, g), f)
  const t = c(h, g, f);

  const EXPECTED = 'h(g(f(7)))';

  expect(r(7)).toBe(EXPECTED);
  expect(s(7)).toBe(EXPECTED);
  expect(t(7)).toBe(EXPECTED);
});

// id . f = f
test('id𝐵 ∘ 𝑓 = 𝑓', () => {
  const r = compose(id, square);

  expect(r(4)).toBe(16);
});

// f . id = f
test('𝑓 ∘ id𝐴 = 𝑓', () => {
  const r = compose(square, id);

  expect(r(9)).toBe(81);
});