#line 1 "monoid/prim_monoids.hpp"
#line 1 "monoid/monoid.hpp"
#include <concepts>
#include <functional>
#include <type_traits>
namespace m1une {
template <typename T, auto operation, auto identity, bool commutative>
struct monoid {
static_assert(std::is_invocable_r_v<T, decltype(operation), T, T>, "operation must work as T(T, T)");
static_assert(std::is_invocable_r_v<T, decltype(identity)>, "identity must work as T()");
using value_type = T;
static constexpr auto op = operation;
static constexpr auto id = identity;
static constexpr bool is_commutative = commutative;
};
template <typename T>
concept Monoid = requires(typename T::value_type v) {
typename T::value_type;
{ T::op(v, v) } -> std::same_as<typename T::value_type>;
{ T::id() } -> std::same_as<typename T::value_type>;
{ T::is_commutative } -> std::convertible_to<bool>;
};
} // namespace m1une
#line 1 "monoid/monoids/add_monoid.hpp"
#line 5 "monoid/monoids/add_monoid.hpp"
namespace m1une {
template <typename T>
using add_monoid = monoid<T, [](T a, T b) { return a + b; }, []() { return T(0); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/mul_monoid.hpp"
#line 5 "monoid/monoids/mul_monoid.hpp"
namespace m1une {
template <typename T>
using mul_monoid = monoid<T, [](T a, T b) { return a * b; }, []() { return T(1); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/min_monoid.hpp"
#include <algorithm>
#include <limits>
#line 8 "monoid/monoids/min_monoid.hpp"
namespace m1une {
template <typename T>
using min_monoid =
monoid<T, [](T a, T b) { return std::min(a, b); }, []() { return std::numeric_limits<T>::max(); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/max_monoid.hpp"
#line 6 "monoid/monoids/max_monoid.hpp"
#line 8 "monoid/monoids/max_monoid.hpp"
namespace m1une {
template <typename T>
using max_monoid =
monoid<T, [](T a, T b) { return std::max(a, b); }, []() { return std::numeric_limits<T>::min(); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/minmax_monoid.hpp"
#line 6 "monoid/monoids/minmax_monoid.hpp"
#include <utility>
#line 9 "monoid/monoids/minmax_monoid.hpp"
namespace m1une {
// Monoid for storing both a minimum and maximum value.
// The operation combines two pairs by taking the component-wise min and max.
template <typename T>
using minmax_monoid =
monoid<std::pair<T, T>,
[](std::pair<T, T> a, std::pair<T, T> b) {
return std::pair<T, T>(std::min(a.first, b.first), std::max(a.second, b.second));
},
[]() { return std::pair<T, T>(std::numeric_limits<T>::max(), std::numeric_limits<T>::lowest()); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/and_monoid.hpp"
#line 5 "monoid/monoids/and_monoid.hpp"
namespace m1une {
template <typename T>
using and_monoid = monoid<T, [](T a, T b) { return a & b; }, []() { return ~T(0); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/or_monoid.hpp"
#line 5 "monoid/monoids/or_monoid.hpp"
namespace m1une {
template <typename T>
using or_monoid = monoid<T, [](T a, T b) { return a | b; }, []() { return T(0); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/xor_monoid.hpp"
#line 5 "monoid/monoids/xor_monoid.hpp"
namespace m1une {
template <typename T>
using xor_monoid = monoid<T, [](T a, T b) { return a ^ b; }, []() { return T(0); }, true>;
} // namespace m1une
#line 1 "monoid/monoids/affine_monoid.hpp"
#line 5 "monoid/monoids/affine_monoid.hpp"
#line 7 "monoid/monoids/affine_monoid.hpp"
namespace m1une {
// Affine transformation f(x) = ax + b is represented as (a, b)
// perform f first, then g
// op(f, g)(x) = g(f(x))
template <typename T>
using affine_monoid = monoid<std::pair<T, T>,
[](std::pair<T, T> f, std::pair<T, T> g) {
return std::pair<T, T>(f.first * g.first, f.second * g.first + g.second);
},
[]() { return std::pair<T, T>(1, 0); }, false>;
} // namespace m1une
#line 1 "monoid/monoids/update_monoid.hpp"
#line 5 "monoid/monoids/update_monoid.hpp"
namespace m1une {
template <typename T, T identity>
using update_monoid = monoid<T,
[](T a, T b) {
if (b == identity) return a;
return b;
},
[]() { return identity; }, false>;
} // namespace m1une
#line 15 "monoid/prim_monoids.hpp"
monoid/prim_monoids.hpp
Monoid
(monoid/monoid.hpp)
monoid/monoids/add_monoid.hpp