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std::equality_comparable, std::equality_comparable_with

Defined in header <concepts> 
template< class T >
concept equality_comparable = __WeaklyEqualityComparableWith<T, T>;
 (1) (since C++20) 
template< class T, class U >
concept equality_comparable_with =
    std::equality_comparable<T> &&
    std::equality_comparable<U> &&
    __ComparisonCommonTypeWith<T, U> &&
    std::equality_comparable<
        std::common_reference_t<
            const std::remove_reference_t<T>&,
            const std::remove_reference_t<U>&>> &&
    __WeaklyEqualityComparableWith<T, U>;
 (2) (since C++20) 
template< class T, class U >
concept __WeaklyEqualityComparableWith =
    requires(const std::remove_reference_t<T>& t,
             const std::remove_reference_t<U>& u) {
        { t == u } -> boolean-testable;
        { t != u } -> boolean-testable;
        { u == t } -> boolean-testable;
        { u != t } -> boolean-testable;
    };
 (3) (exposition only*)
(4) 
template< class T, class U >
concept __ComparisonCommonTypeWith =
    std::common_reference_with<
        const std::remove_reference_t<T>&,
        const std::remove_reference_t<U>&>;
 (until C++23)
(exposition only*) 
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&>> &&
    requires {
        requires std::convertible_to<const T&, const C&> ||
            std::convertible_to<T, const C&>;
        requires std::convertible_to<const U&, const C&> ||
            std::convertible_to<U, const C&>;
    };
template< class T, class U >
concept __ComparisonCommonTypeWith =
    _ComparisonCommonTypeWithImpl<std::remove_cvref_t<T>, std::remove_cvref_t<U>>;
 (since C++23)
(exposition only*)
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:

(until C++23)
  • static_cast<const C&>(std::as_const(E)) if that is a valid expression,
  • static_cast<const C&>(std::move(E)) otherwise.
(since C++23)
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

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

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

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.
(since C++23)

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.

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