Template:cpp/synopsis/concepts

// all freestanding
namespace std {
  // language-related concepts
  // concept same_as
  template<class T, class U>
  concept same_as = /* see description */;

  // concept derived_from
  template<class Derived, class Base>
  concept derived_from = /* see description */;

  // concept convertible_to
  template<class From, class To>
  concept convertible_to = /* see description */;

  // concept common_reference_with
  template<class T, class U>
  concept common_reference_with = /* see description */;

  // concept common_with
  template<class T, class U>
  concept common_with = /* see description */;

  // arithmetic concepts
  template<class T>
  concept integral = /* see description */;
  template<class T>
  concept signed_integral = /* see description */;
  template<class T>
  concept unsigned_integral = /* see description */;
  template<class T>
  concept floating_point = /* see description */;

  // concept assignable_from
  template<class LHS, class RHS>
  concept assignable_from = /* see description */;

  // concept swappable
  namespace ranges {
    inline namespace /* unspecified */ {
      inline constexpr /* unspecified */ swap = /* unspecified */;
    }
  }
  template<class T>
  concept swappable = /* see description */;
  template<class T, class U>
  concept swappable_with = /* see description */;

  // concept destructible
  template<class T>
  concept destructible = /* see description */;

  // concept constructible_from
  template<class T, class... Args>
  concept constructible_from = /* see description */;

  // concept default_initializable
  template<class T>
  concept default_initializable = /* see description */;

  // concept move_constructible
  template<class T>
  concept move_constructible = /* see description */;

  // concept copy_constructible
  template<class T>
  concept copy_constructible = /* see description */;

  // comparison concepts
  // concept equality_comparable
  template<class T>
  concept equality_comparable = /* see description */;
  template<class T, class U>
  concept equality_comparable_with = /* see description */;

  // concept totally_ordered
  template<class T>
  concept totally_ordered = /* see description */;
  template<class T, class U>
  concept totally_ordered_with = /* see description */;

  // object concepts
  template<class T>
  concept movable = /* see description */;
  template<class T>
  concept copyable = /* see description */;
  template<class T>
  concept semiregular = /* see description */;
  template<class T>
  concept regular = /* see description */;

  // callable concepts
  // concept invocable
  template<class F, class... Args>
  concept invocable = /* see description */;

  // concept regular_invocable
  template<class F, class... Args>
  concept regular_invocable = /* see description */;

  // concept predicate
  template<class F, class... Args>
  concept predicate = /* see description */;

  // concept relation
  template<class R, class T, class U>
  concept relation = /* see description */;

  // concept equivalence_relation
  template<class R, class T, class U>
  concept equivalence_relation = /* see description */;

  // concept strict_weak_order
  template<class R, class T, class U>
  concept strict_weak_order = /* see description */;
}

Helper concept boolean-testable

template<class T>
concept /*boolean-testable-impl*/ = convertible_to<T, bool>; // exposition only;

template<class T>
concept boolean-testable = // exposition only
  /*boolean-testable-impl*/<T> && requires(T&& t) {
    {
      !std::forward<T>(t)
    } -> /*boolean-testable-impl*/;
  };

Concept same_as

template<class T, class U>
concept /*same-as-impl*/ = is_same_v<T, U>; // exposition only

template<class T, class U>
concept same_as = /*same-as-impl*/<T, U> && /*same-as-impl*/<U, T>;

Concept derived_from

template<class Derived, class Base>
concept derived_from = is_base_of_v<Base, Derived> &&
                       is_convertible_v<const volatile Derived*, const volatile Base*>;

Concept convertible_to

template<class From, class To>
concept convertible_to =
  is_convertible_v<From, To> && requires { static_cast<To>(declval<From>()); };

Concept common_reference_with

template<class T, class U>
concept common_reference_with =
  same_as<common_reference_t<T, U>, common_reference_t<U, T>> &&
  convertible_to<T, common_reference_t<T, U>> &&
  convertible_to<U, common_reference_t<T, U>>;

Concept common_with

template<class T, class U>
concept common_with =
  same_as<common_type_t<T, U>, common_type_t<U, T>> &&
  requires {
    static_cast<common_type_t<T, U>>(declval<T>());
    static_cast<common_type_t<T, U>>(declval<U>());
  } &&
  common_reference_with<add_lvalue_reference_t<const T>,
                        add_lvalue_reference_t<const U>> &&
  common_reference_with<
    add_lvalue_reference_t<common_type_t<T, U>>,
    common_reference_t<add_lvalue_reference_t<const T>, add_lvalue_reference_t<const U>>>;

Concept integral

template<class T>
concept integral = is_integral_v<T>;

Concept signed_integral

template<class T>
concept signed_integral = integral<T> && is_signed_v<T>;

Concept unsigned_integral

template<class T>
concept unsigned_integral = integral<T> && !signed_integral<T>;

Concept floating_point

template<class T>
concept floating_point = is_floating_point_v<T>;

Concept assignable_from

template<class LHS, class RHS>
concept assignable_from =
  is_lvalue_reference_v<LHS> &&
  common_reference_with<const remove_reference_t<LHS>&, const remove_reference_t<RHS>&> &&
  requires(LHS lhs, RHS&& rhs) {
    {
      lhs = std::forward<RHS>(rhs)
    } -> same_as<LHS>;
  };

Concept swappable

template<class T>
concept swappable = requires(T& a, T& b) { ranges::swap(a, b); };

Concept swappable_with

template<class T, class U>
concept swappable_with = common_reference_with<T, U> && requires(T&& t, U&& u) {
  ranges::swap(std::forward<T>(t), std::forward<T>(t));
  ranges::swap(std::forward<U>(u), std::forward<U>(u));
  ranges::swap(std::forward<T>(t), std::forward<U>(u));
  ranges::swap(std::forward<U>(u), std::forward<T>(t));
};

Concept destructible

template<class T>
concept destructible = is_nothrow_destructible_v<T>;

Concept constructible_from

template<class T, class... Args>
concept constructible_from = destructible<T> && is_constructible_v<T, Args...>;

Concept default_initializable

template<class T>
constexpr bool /*is-default-initializable*/ = /* see description */; // exposition only

template<class T>
concept default_initializable =
  constructible_from<T> && requires { T{}; } && /*is-default-initializable*/<T>;

Concept move_constructible

template<class T>
concept move_constructible = constructible_from<T, T> && convertible_to<T, T>;

Concept copy_constructible

template<class T>
concept copy_constructible =
  move_constructible<T> && constructible_from<T, T&> && convertible_to<T&, T> &&
  constructible_from<T, const T&> && convertible_to<const T&, T> &&
  constructible_from<T, const T> && convertible_to<const T, T>;

Concept equality_comparable

template<class T, class U>
concept /*weakly-equality-comparable-with*/ = // exposition only
  requires(const remove_reference_t<T>& t, const remove_reference_t<U>& u) {
    { t == u } -> boolean-testable;
    { t != u } -> boolean-testable;
    { u == t } -> boolean-testable;
    { u != t } -> boolean-testable;
  };

template<class T>
concept equality_comparable = /*weakly-equality-comparable-with*/<T, T>;

Concept equality_comparable_with

template<class T, class U, class C = common_reference_t<const T&, const U&>>
concept /*comparison-common-type-with-impl*/ = // exposition only
  same_as<common_reference_t<const T&, const U&>,
          common_reference_t<const U&, const T&>> &&
  requires {
    requires convertible_to<const T&, const C&> || convertible_to<T, const C&>;
    requires convertible_to<const U&, const C&> || convertible_to<U, const C&>;
  };

template<class T, class U>
concept /*comparison-common-type-with*/ = // exposition only
  /*comparison-common-type-with-impl*/<remove_cvref_t<T>, remove_cvref_t<U>>;

template<class T, class U>
concept equality_comparable_with =
  equality_comparable<T> && equality_comparable<U> &&
  /*comparison-common-type-with*/<T, U> &&
  equality_comparable<
    common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&>> &&
  /*weakly-equality-comparable-with*/<T, U>;

Helper concept partially-ordered-with

Defined in header <compare>

template<class T, class U>
concept /*partially-ordered-with*/ = // exposition only
  requires(const remove_reference_t<T>& t, const remove_reference_t<U>& u) {
    { t <  u } -> boolean-testable;
    { t >  u } -> boolean-testable;
    { t <= u } -> boolean-testable;
    { t >= u } -> boolean-testable;
    { u <  t } -> boolean-testable;
    { u >  t } -> boolean-testable;
    { u <= t } -> boolean-testable;
    { u >= t } -> boolean-testable;
  };

Concept totally_ordered

template<class T>
concept totally_ordered = equality_comparable<T> && /*partially-ordered-with*/<T, T>;

Concept totally_ordered_with

template<class T, class U>
concept totally_ordered_with =
  totally_ordered<T> && totally_ordered<U> && equality_comparable_with<T, U> &&
  totally_ordered<
    common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&>> &&
  /*partially-ordered-with*/<T, U>;

Concept movable

template<class T>
concept movable =
  is_object_v<T> && move_constructible<T> && assignable_from<T&, T> && swappable<T>;

Concept copyable

template<class T>
concept copyable = copy_constructible<T> && movable<T> && assignable_from<T&, T&> &&
                   assignable_from<T&, const T&> && assignable_from<T&, const T>;

Concept semiregular

template<class T>
concept semiregular = copyable<T> && default_initializable<T>;

Concept regular

template<class T>
concept regular = semiregular<T> && equality_comparable<T>;

Concept invocable

template<class F, class... Args>
concept invocable = requires(F&& f, Args&&... args) {
  invoke(std::forward<F>(f),
         std::forward<Args>(args)...); // not required to be equality-preserving
};

Concept regular_invocable

template<class F, class... Args>
  concept regular_invocable = invocable<F, Args...>;

Concept predicate

template<class F, class... Args>
concept predicate =
  regular_invocable<F, Args...> && boolean-testable<invoke_result_t<F, Args...>>;

Concept relation

template<class R, class T, class U>
concept relation =
  predicate<R, T, T> && predicate<R, U, U> && predicate<R, T, U> && predicate<R, U, T>;

Concept equivalence_relation

template<class R, class T, class U>
concept equivalence_relation = relation<R, T, U>;

Concept strict_weak_order

template<class R, class T, class U>
concept strict_weak_order = relation<R, T, U>;