proconlib

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:heavy_check_mark: Concept for semiring (tools/semiring.hpp) 

template <typename R>
concept semiring = tools::commutative_monoid<typename R::add> && tools::monoid<typename R::mul> && std::same_as<typename R::add::T, typename R::mul::T>;

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

Semantically, you can define that the results of R::add::op and R::mul::op are undefined depending on the arguments. For example, you can define that integer addition is not defined for overflowing pairs.

Constraints

Time Complexity

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Code

#ifndef TOOLS_SEMIRING_HPP
#define TOOLS_SEMIRING_HPP

#include "tools/commutative_monoid.hpp"
#include "tools/monoid.hpp"

namespace tools {
  template <typename R>
  concept semiring = tools::commutative_monoid<typename R::add> && tools::monoid<typename R::mul> && std::same_as<typename R::add::T, typename R::mul::T>;
}

#endif

#line 1 "tools/semiring.hpp"



#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>;
}


#line 6 "tools/semiring.hpp"

namespace tools {
  template <typename R>
  concept semiring = tools::commutative_monoid<typename R::add> && tools::monoid<typename R::mul> && std::same_as<typename R::add::T, typename R::mul::T>;
}
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