std::three_way_comparable, std::three_way_comparable_with

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Defined in header <compare>
template< class T, class Cat = std::partial_ordering >

concept three_way_comparable =
    __WeaklyEqualityComparableWith<T, T> &&
    __PartiallyOrderedWith<T, T> &&
    requires(const std::remove_reference_t<T>& a,
             const std::remove_reference_t<T>& b) {
        { a <=> b } -> __ComparesAs<Cat>;

    };
 (1) (since C++20)
template< class T, class U, class Cat = std::partial_ordering >

concept three_way_comparable_with =
    std::three_way_comparable<T, Cat> &&
    std::three_way_comparable<U, Cat> &&
    std::common_reference_with<
        const std::remove_reference_t<T>&,
        const std::remove_reference_t<U>&> &&
    std::three_way_comparable<
        std::common_reference_t<
            const std::remove_reference_t<T>&,
            const std::remove_reference_t<U>&>, Cat> &&
    __WeaklyEqualityComparableWith<T, U> &&
    __PartiallyOrderedWith<T, U> &&
    requires(const std::remove_reference_t<T>& t,
             const std::remove_reference_t<U>& u) {
        { t <=> u } -> __ComparesAs<Cat>;
        { u <=> t } -> __ComparesAs<Cat>;

    };
 (2) (since C++20)
template< class T, class Cat >

concept __ComparesAs =

    std::same_as<std::common_comparison_category_t<T, Cat>, Cat>;
 (3) (exposition only*)
1) The concept std::three_way_comparable specifies that the three way comparison operator <=> on T yield results consistent with the comparison category implied by Cat.
2) The concept std::three_way_comparable_with specifies that the three way comparison operator <=> on (possibly mixed) T and U operands yield results consistent with the comparison category implied by Cat. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type.

In both definitions, __WeaklyEqualityComparableWith and __PartiallyOrderedWith are exposition-only concepts also used by equality_comparable and totally_ordered, respectively.

Semantic requirements

These concepts are modeled only if they are satisfied and all concepts they subsume are modeled.

1) T and Cat model std::three_way_comparable<T, Cat> only if, given lvalues a and b of type const std::remove_reference_t<T>, following are true:
  • (a <=> b == 0) == bool(a == b),
  • (a <=> b != 0) == bool(a != b),
  • ((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
  • bool(a > b) == bool(b < a),
  • bool(a >= b) == !bool(a < b),
  • bool(a <= b) == !bool(b < a),
  • (a <=> b < 0) == bool(a < b),
  • (a <=> b > 0) == bool(a > b),
  • (a <=> b <= 0) == bool(a <= b), and
  • (a <=> b >= 0) == bool(a >= b), and
  • if Cat is convertible to std::strong_ordering, T models totally_ordered.
2) T, U, and Cat model std::three_way_comparable_with<T, U, Cat> only if given

Let C be std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&>, the following are true:

  • t <=> u and u <=> t have the same domain,
  • ((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal,
  • (t <=> u == 0) == bool(t == u),
  • (t <=> u != 0) == bool(t != u),
  • Cat(t <=> u) == Cat(C(t) <=> C(u)),
  • (t <=> u < 0) == bool(t < u),
  • (t <=> u > 0) == bool(t > u),
  • (t <=> u <= 0) == bool(t <= u),
  • (t <=> u >= 0) == bool(t >= u), and
  • if Cat is convertible to std::strong_ordering, T and U model std::totally_ordered_with<T, U>.

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 implicitly requires additional variations of that expression that accept a non-constant lvalue or (possibly constant) rvalue for the given operand unless such an expression variation is explicitly required with differing semantics. These implicit expression variations must meet the same semantic requirements of the declared expression. The extent to which an implementation validates the syntax of the variations is unspecified.

See also

(C++20)
 specifies that operator == is an equivalence relation
(concept)
(C++20)
 specifies that the comparison operators on the type yield a total order
(concept)
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