#Monoids

Monoids describe a way to combine two values of a given type. A monoid contains an identity value that when combined with another value doesn't change its value. The combine operation has to be associative meaning combine(a, combine(b, c)) is the same as combine(combine(a, b), c).

A simple monoid is an addition because adding 0 (the identity value) to any other integer won't change the value and add(1, add(2, 3)) is the the same result as add(add(1, 2), 3) (both return 6).

This library comes with a few monoids:

• Innmind\Immutable\Monoid\Concat to append 2 instances of Innmind\Immutable\Str together
• Innmind\Immutable\Monoid\Append to append 2 instances of Innmind\Immutable\Sequence together
• Innmind\Immutable\Monoid\MergeSet to append 2 instances of Innmind\Immutable\Set together
• Innmind\Immutable\Monoid\MergeMap to append 2 instances of Innmind\Immutable\Map together

#Create your own

To make sure your own monoid follows the laws this library comes with properties you can use (via innmind/black-box) in your test like so:

use Innmind\BlackBox\Set;
use Properties\Innmind\Immutable\Monoid;

return static function() {
    $equals = static fn($a, $b) => /* this callable is the way to check that 2 values are equal */;
    // this Set must generate values that are of the type your monoid understands
    $set = /* an instance of Set */;

    yield properties(
        'YourMonoid properties',
        Monoid::properties($set, $equals),
        Set\Elements::of(new YourMonoid),
    );

    foreach (Monoid::list($set, $equals) as $property) {
        yield proof(
            'YourMonoid property',
            given($property),
            static fn($assert, $property) => $property->ensureHeldBy($assert, new YourMonoid),
        );
    }
};