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Difference between revisions of "cpp/concepts/equality comparable"

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< cpp‎ | concepts
m (Space added: t != u,u != t -> t != u, u != t)
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{{cpp/title|equality_comparable|equality_comparable_with}}
+
{{cpp/title|equality_comparable {{mark since c++20}}|equality_comparable_with {{mark since c++20}}}}
 
{{cpp/concepts/navbar}}
 
{{cpp/concepts/navbar}}
 
{{dcl begin}}
 
{{dcl begin}}
 
{{dcl header|concepts}}
 
{{dcl header|concepts}}
 
{{dcl|num=1|since=c++20|1=
 
{{dcl|num=1|since=c++20|1=
−
template < class T >
+
template< class T >
 
concept equality_comparable = __WeaklyEqualityComparableWith<T, T>;
 
concept equality_comparable = __WeaklyEqualityComparableWith<T, T>;
 
}}
 
}}
 
{{dcl|num=2|since=c++20|1=
 
{{dcl|num=2|since=c++20|1=
−
template <class T, class U>
+
template< class T, class U >
 
concept equality_comparable_with =
 
concept equality_comparable_with =
−
  std::equality_comparable<T> &&
+
    std::equality_comparable<T> &&
−
  std::equality_comparable<U> &&
+
    std::equality_comparable<U> &&
−
  std::common_reference_with<
+
     __ComparisonCommonTypeWith<T, U> &&
−
     const std::remove_reference_t<T>&,
+
    std::equality_comparable<
−
    const std::remove_reference_t<U>&> &&
+
        std::common_reference_t<
−
  std::equality_comparable<
+
            const std::remove_reference_t<T>&,
−
    std::common_reference_t<
+
            const std::remove_reference_t<U>&>> &&
−
      const std::remove_reference_t<T>&,
+
    __WeaklyEqualityComparableWith<T, U>;
−
      const std::remove_reference_t<U>&>> &&
+
−
  __WeaklyEqualityComparableWith<T, U>;
+
 
}}
 
}}
−
{{dcl|num=3|since=c++20|1=
+
{{dcl h|Helper concepts}}
−
template<class T, class U>
+
{{dcl|num=3|notes={{mark expos}}|1=
−
concept __WeaklyEqualityComparableWith = // exposition only
+
template< class T, class U >
−
  requires(const std::remove_reference_t<T>& t,
+
concept __WeaklyEqualityComparableWith =
−
          const std::remove_reference_t<U>& u) {
+
    requires(const std::remove_reference_t<T>& t,
−
    { t == u } -> boolean-testable;
+
            const std::remove_reference_t<U>& u) {
−
    { t != u } -> boolean-testable;
+
        { t == u } -> boolean-testable;
−
    { u == t } -> boolean-testable;
+
        { t != u } -> boolean-testable;
−
    { u != t } -> boolean-testable;
+
        { u == t } -> boolean-testable;
−
  };
+
        { u != t } -> boolean-testable;
 +
    };
 
}}
 
}}
 +
{{dcl rev begin|num=4}}
 +
{{dcl|until=c++23|notes={{mark expos}}|1=
 +
template< class T, class U >
 +
concept __ComparisonCommonTypeWith =
 +
    std::common_reference_with<
 +
        const std::remove_reference_t<T>&,
 +
        const std::remove_reference_t<U>&>;
 +
}}
 +
{{dcl|since=c++23|notes={{mark expos}}|1=
 +
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>>;
 +
}}
 +
{{dcl rev end}}
 
{{dcl end}}
 
{{dcl end}}
  
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@3@ The exposition-only concept {{tt|''__WeaklyEqualityComparableWith''}} specifies that an object of type {{tt|T}} and an object of type {{tt|U}} can be compared for equality with each other (in either order) using both {{tt|1===}} and {{tt|1=!=}}, and the results of the comparisons are consistent.  
 
@3@ The exposition-only concept {{tt|''__WeaklyEqualityComparableWith''}} specifies that an object of type {{tt|T}} and an object of type {{tt|U}} can be compared for equality with each other (in either order) using both {{tt|1===}} and {{tt|1=!=}}, and the results of the comparisons are consistent.  
  
−
=== Semantic requirements ===
+
@4@ The exposition-only concept {{tt|''__ComparisonCommonTypeWith''}} specifies that two types share a common type, and a const lvalue{{rev inl|since=c++23| or a non-const rvalue}} 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.
 
These concepts are modeled only if they are satisfied and all concepts they subsume are modeled.
  
−
@1@ {{c|std::equality_comparable<T>}} is modeled only if, given objects {{tt|a}} and {{tt|b}} of type {{tt|T}}, {{c|1=bool(a == b)}} is {{c|true}} if and only if {{tt|a}} and {{tt|b}} are equal. Together with the requirement that {{c|1=a == b}} is equality preserving, this implies that {{tt|1===}} is symmetric and transitive, and further that {{tt|1===}} is reflexive for all objects {{tt|a}} that are equal to at least one other object.
+
In the following paragraphs, given an expression {{tt|E}} and a type {{tt|C}}, {{c|CONVERT_TO<C>(E)}} is defined as:
 +
{{rrev multi|rev1=
 +
* {{c|static_cast<C>(std::as_const(E))}}.
 +
|since2=c++23|rev2=
 +
* {{c|static_cast<const C&>(std::as_const(E))}} if that is a valid expression,
 +
* {{c|static_cast<const C&>(std::move(E))}} otherwise.
 +
}}
  
−
@2@ {{c|std::equality_comparable_with<T, U>}} is modeled only if, given any lvalue {{tt|t}} of type {{c|const std::remove_reference_t<T>}} and any lvalue {{tt|u}} of type {{c|const std::remove_reference_t<U>}}, and let {{tt|C}} be {{c|std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&>}}, {{c|1=bool(t == u) == bool(C(t) == C(u))}}.
+
@1@ {{co|std::equality_comparable<T>}} is modeled only if, given objects {{tt|a}} and {{tt|b}} of type {{tt|T}}, {{c|1=bool(a == b)}} is {{c|true}} if and only if {{tt|a}} and {{tt|b}} are equal. Together with the requirement that {{c|1=a == b}} is [[cpp/concepts#Equality preservation|equality-preserving]], this implies that {{tt|1===}} is symmetric and transitive, and further that {{tt|1===}} is reflexive for all objects {{tt|a}} that are equal to at least one other object.
 +
 
 +
@2@ {{co|std::equality_comparable_with<T, U>}} is modeled only if, let
 +
* {{tt|t}} and {{tt|t2}} be lvalues denoting distinct equal objects of types {{c|const std::remove_reference_t<T>}} and {{c|std::remove_cvref_t<T>}} respectively,
 +
* {{tt|u}} and {{tt|u2}} be lvalues denoting distinct equal objects of types {{c|const std::remove_reference_t<U>}} and {{c|std::remove_cvref_t<U>}} respectively,
 +
* {{tt|C}} be {{c|std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&>}},
 +
the following expression is true:
 +
* {{c|1=bool(t == u) == bool(CONVERT_TO<C>(t2) == CONVERT_TO<C>(u2))}}.
  
 
@3@ {{c|__WeaklyEqualityComparableWith<T, U>}} is modeled only if given
 
@3@ {{c|__WeaklyEqualityComparableWith<T, U>}} is modeled only if given
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* {{c|1=bool(t != u) == !bool(t == u)}}; and
 
* {{c|1=bool(t != u) == !bool(t == u)}}; and
 
* {{c|1=bool(u != t) == bool(t != u)}}.
 
* {{c|1=bool(u != t) == bool(t != u)}}.
 +
 +
@4@ {{c|__WeaklyEqualityComparableWith<T, U>}} is modeled only if:
 +
{{rrev multi|rev1=The corresponding {{lconcept|common_reference_with}} concept is modeled.
 +
|since2=c++23|rev2=
 +
Let
 +
* {{tt|C}} be {{c|std::common_reference_t<const T&, const U&>}},
 +
* {{tt|t1}} and {{tt|t2}} be [[cpp/concepts#Equality preservation|equality-preserving]] expressions that are lvalues of type {{c|std::remove_cvref_t<T>}},
 +
* {{tt|u1}} and {{tt|u2}} be [[cpp/concepts#Equality preservation|equality-preserving]] expressions that are lvalues of type {{c|std::remove_cvref_t<U>}},
 +
the following conditions hold:
 +
* {{c|CONVERT_TO<C>(t1)}} equals {{c|CONVERT_TO<C>(t2)}} if and only if {{tt|t1}} equals {{tt|t2}}; and
 +
* {{c|CONVERT_TO<C>(u1)}} equals {{c|CONVERT_TO<C>(u2)}} if and only if {{tt|u1}} equals {{tt|u2}}.
 +
}}
  
 
{{cpp/concepts/equality preservation}}
 
{{cpp/concepts/equality preservation}}
 
{{cpp/concepts/implicit expression variations}}
 
{{cpp/concepts/implicit expression variations}}
 +
 +
===References===
 +
{{ref std c++23}}
 +
{{ref std|section=18.5.4|title=Concept {{tt|equality_comparable}}|id=concept.equalitycomparable}}
 +
{{ref std end}}
 +
{{ref std c++20}}
 +
{{ref std|section=18.5.3|title=Concept {{tt|equality_comparable}}|id=concept.equalitycomparable}}
 +
{{ref std end}}
  
 
{{langlinks|de|es|ja|ru|zh}}
 
{{langlinks|de|es|ja|ru|zh}}

Latest revision as of 10:40, 7 September 2024

 
C++
 
Concepts library
Exposition-only concepts
 (C++20)
 
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)
Helper concepts
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.

Contents

[edit] 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)

[edit] Equality preservation

Expressions declared in requires expressions of the standard library concepts are required to be equality-preserving (except where stated otherwise).

[edit] Implicit expression variations

A requires expression that uses an expression that is non-modifying for some constant lvalue operand also requires implicit expression variations.

[edit] References

  • C++23 standard (ISO/IEC 14882:2024):
  • 18.5.4 Concept equality_comparable [concept.equalitycomparable]
  • C++20 standard (ISO/IEC 14882:2020):
  • 18.5.3 Concept equality_comparable [concept.equalitycomparable]
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