The set-indexed lift of category::IsSemiring (an exact alias of category::IsRig): the "rig" rung of the tower. More...

Concept definition

template<typename X, typename Add std::plus<typename X::Domain>, typename Mult std::multiplies<typename X::Domain>>
concept dedekind::algebra::IsSemiring = 
    IsAlgebraOnSet<X, Add, Mult> &&
    dedekind::category::IsSemiring<typename X::Domain, Add, Mult>

Detailed Description

The set-indexed lift of category::IsSemiring (an exact alias of category::IsRig): the "rig" rung of the tower.

The faithful lift, matching every other rung: IsAlgebraOnSet supplies the carrier discipline and category::IsSemiring<X::Domain, Add, Mult> supplies the full axioms — commutative additive monoid, multiplicative monoid, and the registered distributive laws. (An earlier composition through a signature-only action concept checked call shapes and was strictly weaker than the category rung it names.)

Template Parameters

X	The set object (`category::IsSet`).
Add	Additive operation witness (defaults to std::plus).
Mult	Multiplicative operation witness (defaults to std::multiplies).