medium_monoid_example.ts

function assertNumber(x: any): asserts x is number {
    if (typeof x !== 'number') {
        throw new Error('x has to be a number type');
    }
}

function assertTrue(b: boolean): asserts b is true {
    if (typeof b !== 'boolean') {
        throw new Error('must be a boolean type');
    }
    if (b !== true) {
        throw new Error('must be true');
    }
}

class Monoid<T extends number> {
    constructor(private s: T[]) { }

    concat(x: T, y: T): T { 
        return (x + y) as T;
    }

    identity(x: T): T {
        return x + 0;
    }

    pick(count: T): T[] {
        const items: T[] = [];
        while (items.length < count) {
            const randomIndex = Math.trunc(Math.random() * (this.s.length - 1));
            const randomItem = this.s[randomIndex];

            if (!items.includes(randomItem)) {
                items.push(randomItem);
            }
        }

        return items;
    }
}

const set = new Monoid([1, 2, 3, 4, 5]);

// Magma 
const [a, b] = set.pick(2);
assertNumber(a);
assertNumber(b);
assertNumber(a + b);

// Semigroup - Associativity
const [x, y, z] = set.pick(3);
assertNumber(set.concat(set.concat(x, y), z));
assertNumber(set.concat(x, set.concat(y, z)));
assertTrue(set.concat(set.concat(x, y), z) === set.concat(x, set.concat(y, z)));

// Monoid - Identity
const [r] = set.pick(1);
assertNumber(r);
assertNumber(set.identity(r));
assertTrue(set.identity(r) === r);