This functor extends the basic definition of a commutative monoid by adding a convenient operator synonym ( @ ) = combine, as well as derived functions reduce and map_reduce.

The commutative monoid you get with empty = false and combine = ( || ).

The commutative monoid you get with empty = true and combine = ( && ).

The trivial commutative monoid with empty = () and combine () () = ().

The addition monoid with empty = zero and combine = ( + ).

The multiplication monoid with empty = one and combine = ( * ).

The union monoid with empty = M.empty and combine = M.union.

The product of commutative monoids where pairs are combined component-wise.

Same as Product but for 3 commutative monoids.

Functions that return a commutative monoid form the following commutative monoid: