Concept for commutative monoid (tools/commutative_monoid.hpp)

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Last update: 2025-12-07 12:31:51+09:00
Include: #include "tools/commutative_monoid.hpp"

template <typename M>
concept commutative_monoid = tools::monoid<M>;

It is a concept that represents a commutative monoid. Note that semantic constraints must be guaranteed by the user.

Semantically, you can define that the result of M::op is undefined depending on the arguments. For example, you can define that integer addition is not defined for overflowing pairs.

Constraints

When a user declares that a type <M> satisfies the concept of tools::commutative_monoid, the following conditions must also be satisfied.
- Semantic constraints of tools::monoid<M> hold.
- For any $x$ and $y$ such that M::op(x, y) and M::op(y, x) are defined, M::op(x, y) $=$ M::op(y, x).

Time Complexity

Not applicable

License

Author

anqooqie

Depends on

Concept for monoid (tools/monoid.hpp)

Required by

Verified with

Code

#ifndef TOOLS_COMMUTATIVE_MONOID_HPP
#define TOOLS_COMMUTATIVE_MONOID_HPP

#include "tools/monoid.hpp"

namespace tools {
  template <typename M>
  concept commutative_monoid = tools::monoid<M>;
}

#endif

#line 1 "tools/commutative_monoid.hpp"



#line 1 "tools/monoid.hpp"



#include <concepts>

namespace tools {
  template <typename M>
  concept monoid = requires(typename M::T x, typename M::T y) {
    { M::op(x, y) } -> std::same_as<typename M::T>;
    { M::e() } -> std::same_as<typename M::T>;
  };
}


#line 5 "tools/commutative_monoid.hpp"

namespace tools {
  template <typename M>
  concept commutative_monoid = tools::monoid<M>;
}