spica/monad/sequence.test.ts

Supervisor, Coroutine, Channel, select, AtomicPromise, Cancellation, Cache, List, Queue, Stack, and some utils.

import { Sequence } from './sequence';

export const nat = new Sequence<number, number>((n = 0, cons) => cons(n, n + 1));

describe('Unit: lib/monad/sequence', () => {
  describe('Iterable', () => {
    it('idempotence', () => {
      const s = Sequence.from([0, 1, 2]);
      assert.deepStrictEqual([...s], [0, 1, 2]);
      assert.deepStrictEqual([...s], [0, 1, 2]);
      assert.deepStrictEqual(Sequence.from(s).extract(), [0, 1, 2]);
      assert.deepStrictEqual(Sequence.from(s).extract(), [0, 1, 2]);
      assert.deepStrictEqual([...s], [0, 1, 2]);
      assert.deepStrictEqual(Sequence.from(s).extract(), [0, 1, 2]);
    });

    it('to Sequence', () => {
      assert.deepStrictEqual(Sequence.from(Sequence.from([])).extract(), []);
      assert.deepStrictEqual(Sequence.from(Sequence.from([0])).extract(), [0]);
      assert.deepStrictEqual(Sequence.from(Sequence.from([0, 1])).extract(), [0, 1]);
      assert.deepStrictEqual(Sequence.from(Sequence.from([0, 1, 2])).extract(), [0, 1, 2]);
    });

    it('to Array', () => {
      assert.deepStrictEqual([...Sequence.from([])], []);
      assert.deepStrictEqual([...Sequence.from([0])], [0]);
      assert.deepStrictEqual([...Sequence.from([0, 1])], [0, 1]);
      assert.deepStrictEqual([...Sequence.from([0, 1, 2])], [0, 1, 2]);
    });

  });

  describe('Monoid', () => {
    it('Monoid law 1', () => {
      const x = Sequence.Return(0);
      const ma = Sequence.mappend(Sequence.mempty, x);
      assert.deepStrictEqual(ma.extract(), x.extract());
    });

    it('Monoid law 2', () => {
      const x = Sequence.Return(0);
      const ma = Sequence.mappend(x, Sequence.mempty);
      assert.deepStrictEqual(ma.extract(), x.extract());
    });

    it('Monoid law 3', () => {
      const x = Sequence.Return(0);
      const y = Sequence.Return(1);
      const z = Sequence.Return(2);
      const ma = Sequence.mappend(Sequence.mappend(x, y), z);
      const mb = Sequence.mappend(x, Sequence.mappend(y, z));
      assert.deepStrictEqual(ma.extract(), mb.extract());
    });

  });

  describe('Functor', () => {
    it('fmap', () => {
      assert.deepStrictEqual(Sequence.fmap(n => n + 1, Sequence.Return(0)).extract(), [1]);
    });

    it('Functor law 1', () => {
      const f = <T>(n: T) => n;
      const x = 0;
      const fa = Sequence.Return(x).fmap(f);
      const fb = f(Sequence.Return(x));
      assert.deepStrictEqual(fa.extract(), fb.extract());
    });

    it('Functor law 2', () => {
      const f = (n: number) => n + 2;
      const g = (n: number) => n * 3;
      const x = 1;
      const fa = Sequence.Return(x).fmap(n => g(f(n)));
      const fb = Sequence.Return(x).fmap(f).fmap(g);
      assert.deepStrictEqual(fa.extract(), fb.extract());
    });

  });

  describe('Applicative', () => {
    it('ap 1', () => {
      assert.deepStrictEqual(
        Sequence.pure((a: number) => a)
          .ap(Sequence.pure(1))
          .extract(),
        [1]);
      assert.deepStrictEqual(
        Sequence.pure((a: number) => a)
          .ap(Sequence.pure(1))
          .extract(),
        [1]);
    });

    it('ap 2', () => {
      assert.deepStrictEqual(
        Sequence.pure((a: number, b: number) => a + b)
          .ap(Sequence.pure(1))
          .ap(Sequence.pure(2))
          .extract(),
        [3]);
    });

    it('ap 3', () => {
      assert.deepStrictEqual(
        Sequence.pure((a: number, b: number, c: number) => a + b + c)
          .ap(Sequence.pure(1))
          .ap(Sequence.pure(2))
          .ap(Sequence.pure(3))
          .extract(),
        [6]);
    });

    it('combination 1', () => {
      assert.deepStrictEqual(
        Sequence.from([(n: number) => n, (n: number) => -n])
          .ap(Sequence.from([1, 2]))
          .extract(),
        [1, 2, -1, -2]);
    });

    it('combination 2', () => {
      assert.deepStrictEqual(
        Sequence.from([(n: number, m: number) => n + m, (n: number, m: number) => n * m])
          .ap(Sequence.from([1, 2]))
          .ap(Sequence.from([3, 4]))
          .extract(),
        [4, 5, 5, 6, 3, 4, 6, 8]);
    });

  });

  describe('Monad', () => {
    it('bind', () => {
      assert.deepStrictEqual(Sequence.bind(n => Sequence.Return(n + 1), Sequence.Return(0)).extract(), [1]);
    });

    it('Monad law 1', () => {
      const f = (n: number) => Sequence.Return(n + 1);
      const x = 0;
      const ma = Sequence.Return(x).bind(f);
      const mb = f(x);
      assert.deepStrictEqual(ma.extract(), mb.extract());
    });

    it('Monad law 2', () => {
      const x = 0;
      const ma = Sequence.Return(x);
      const mb = ma.bind(Sequence.Return);
      assert.deepStrictEqual(ma.extract(), mb.extract());
    });

    it('Monad law 3', () => {
      const f = (n: number) => Sequence.Return(n + 2);
      const g = (n: number) => Sequence.Return(n * 3);
      const x = 1;
      const ma = Sequence.Return(x)
        .bind(f)
        .bind(g);
      const mb = Sequence.Return(x)
        .bind(x =>
          f(x)
            .bind(g));
      assert.deepStrictEqual(ma.extract(), mb.extract());
    });

  });

});