std::equality_comparable,std::equality_comparable_with(3)

NAME
std::equality_comparable,std::equality_comparable_with - std::equality_comparable,std::equality_comparable_with

Synopsis
   Defined in header <concepts>
   template< class T > (since
   concept equality_comparable = (1) C++20)
   __WeaklyEqualityComparableWith<T, T>;
   template< class T, class U >
   concept equality_comparable_with =
       std::equality_comparable<T> &&
       std::equality_comparable<U> &&
       __ComparisonCommonTypeWith<T, U> && (2) (since
       std::equality_comparable< C++20)
           std::common_reference_t<
               const std::remove_reference_t<T>&,
               const std::remove_reference_t<U>&>> &&
       __WeaklyEqualityComparableWith<T, U>;
   template< class T, class U >
   concept __WeaklyEqualityComparableWith =
       requires(const std::remove_reference_t<T>& t,
                const std::remove_reference_t<U>& u) { (exposition
           { t == u } -> boolean-testable; (3) only*)
           { t != u } -> boolean-testable;
           { u == t } -> boolean-testable;
           { u != t } -> boolean-testable;
       };
   template< class T, class U >
                        (until
   concept __ComparisonCommonTypeWith = C++23)
       std::common_reference_with< (exposition
           const std::remove_reference_t<T>&, only*)
           const std::remove_reference_t<U>&>;
   template< class T, class U, class C =
   std::common_reference_t<const T&, const U&> >
   concept _ComparisonCommonTypeWithImpl =
       std::same_as<std::common_reference_t<const T&, const
   U&>,
                    std::common_reference_t<const U&, const
   T&>> && (4)
       requires {
           requires std::convertible_to<const T&, const C&> (since
   || C++23)
               std::convertible_to<T, const C&>; (exposition
           requires std::convertible_to<const U&, const C&> only*)
   ||
               std::convertible_to<U, const C&>;
       };
   template< class T, class U >
   concept __ComparisonCommonTypeWith =
   _ComparisonCommonTypeWithImpl<std::remove_cvref_t<T>,
   std::remove_cvref_t<U>>;
   1) The concept std::equality_comparable specifies that the comparison operators ==
   and != on T reflects equality: == yields true if and only if the operands are equal.
   2) The concept std::equality_comparable_with specifies that the comparison operators
   == and != on (possibly mixed) T and U operands yield results consistent with
   equality. Comparing mixed operands yields results equivalent to comparing the
   operands converted to their common type.
   3) The exposition-only concept __WeaklyEqualityComparableWith specifies that an
   object of type T and an object of type U can be compared for equality with each
   other (in either order) using both == and !=, and the results of the comparisons are
   consistent.
   4) The exposition-only concept __ComparisonCommonTypeWith specifies that two types
   share a common type, and a const lvalue
   or a non-const rvalue
   (since C++23) of either type is convertible to that common type.
   Semantic requirements
   These concepts are modeled only if they are satisfied and all concepts they subsume
   are modeled.
   In the following paragraphs, given an expression E and a type C, CONVERT_TO<C>(E) is
   defined as:
     * static_cast<C>(std::as_const(E)). (until C++23)
     * static_cast<const C&>(std::as_const(E)) if that is a valid
       expression, (since C++23)
     * static_cast<const C&>(std::move(E)) otherwise.
   1) std::equality_comparable<T> is modeled only if, given objects a and b of type T,
   bool(a == b) is true if and only if a and b are equal. Together with the requirement
   that a == b is equality-preserving, this implies that == is symmetric and
   transitive, and further that == is reflexive for all objects a that are equal to at
   least one other object.
   2) std::equality_comparable_with<T, U> is modeled only if, let
     * t and t2 be lvalues denoting distinct equal objects of types const
       std::remove_reference_t<T> and std::remove_cvref_t<T> respectively,
     * u and u2 be lvalues denoting distinct equal objects of types const
       std::remove_reference_t<U> and std::remove_cvref_t<U> respectively,
     * C be std::common_reference_t<const std::remove_reference_t<T>&, const
       std::remove_reference_t<U>&>,
   the following expression is true:
     * bool(t == u) == bool(CONVERT_TO<C>(t2) == CONVERT_TO<C>(u2)).
   3) __WeaklyEqualityComparableWith<T, U> is modeled only if given
     * t, an lvalue of type const std::remove_reference_t<T> and
     * u, an lvalue of type const std::remove_reference_t<U>,
   the following are true:
     * t == u, u == t, t != u, u != t have the same domain;
     * bool(u == t) == bool(t == u);
     * bool(t != u) == !bool(t == u); and
     * bool(u != t) == bool(t != u).
   4) __WeaklyEqualityComparableWith<T, U> is modeled only if:
   The corresponding common_reference_with concept is modeled. (until C++23)
   Let
     * C be std::common_reference_t<const T&, const U&>,
     * t1 and t2 be equality-preserving expressions that are lvalues of
       type std::remove_cvref_t<T>,
     * u1 and u2 be equality-preserving expressions that are lvalues of
       type std::remove_cvref_t<U>, (since C++23)
   the following conditions hold:
     * CONVERT_TO<C>(t1) equals CONVERT_TO<C>(t2) if and only if t1
       equals t2; and
     * CONVERT_TO<C>(u1) equals CONVERT_TO<C>(u2) if and only if u1
       equals u2.
   Equality preservation
   Expressions declared in requires expressions of the standard library concepts are
   required to be equality-preserving (except where stated otherwise).
   Implicit expression variations
   A requires expression that uses an expression that is non-modifying for some
   constant lvalue operand also requires implicit expression variations.