Groups in Perl 6

role Semigroup[::T] {
    method append(T $a, T $b --> T) {!!!}
}

role Monoid[::T] does Semigroup[T] {
    method empty(--> T) {!!!}
}

role Group[::T] does Monoid[T] {
    method inverse(T $a --> T) {!!!}
}

class IntAdd does Group[Int] {
    method append(Int $a, Int $b --> Int) { $a + $b }
    method empty(--> Int) { 0 }
    method inverse(Int $a --> Int) { -$a }
}

class IterableCat does Monoid[Iterable] {
    method append(Iterable $a, Iterable $b --> Iterable) { (|$a, |$b) }
    method empty(--> Iterable) { () }
}

sub concat(Monoid $m, @xs) {
    ($m.empty, |@xs).reduce: {$m.append($^a, $^b)};
}

dd concat(IntAdd, [1, 2, 3]);
dd concat(IntAdd, [1, 2]);
dd concat(IntAdd, [1]);
dd concat(IntAdd, []);

dd concat(IterableCat, [<1 2 3>, <4 5 6>, <7 8 9>]);
dd concat(IterableCat, [<1 2 3>, <4 5 6>]);
dd concat(IterableCat, [<1 2 3>,]);
dd concat(IterableCat, []);