17 Language support library [support]

17.11 Comparisons [cmp]

17.11.4 Concept three_way_comparable [cmp.concept]

template<class T, class Cat> concept compares-as = // exposition only same_as<common_comparison_category_t<T, Cat>, Cat>; template<class T, class U> concept partially-ordered-with = // exposition only requires(const remove_reference_t<T>& t, const remove_reference_t& u) { { t 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; };

Let t and u be lvalues of types const remove_reference_t<T> and const remove_reference_t, respectively.

T and U model partially-ordered-with<T, U> only if:

(1.1)
t < u, t <= u, t > u, t >= u, u < t, u <= t, u > t, and u >= t have the same domain.
(1.2)
bool(t < u) == bool(u > t) is true,
(1.3)
bool(u < t) == bool(t > u) is true,
(1.4)
bool(t <= u) == bool(u >= t) is true, and
(1.5)
bool(u <= t) == bool(t >= u) is true.

template<class T, class Cat = partial_ordering> concept three_way_comparable = weakly-equality-comparable-with<T, T> && partially-ordered-with<T, T> && requires(const remove_reference_t<T>& a, const remove_reference_t<T>& b) { { a <=> b } -> compares-as<Cat>; };

Let a and b be lvalues of type const remove_reference_t<T>.

T and Cat model three_way_comparable<T, Cat> only if:

(2.1)
(a <=> b == 0) == bool(a == b) is true,
(2.2)
(a <=> b != 0) == bool(a != b) is true,
(2.3)
((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
(2.4)
(a <=> b < 0) == bool(a < b) is true,
(2.5)
(a <=> b > 0) == bool(a > b) is true,
(2.6)
(a <=> b <= 0) == bool(a <= b) is true,
(2.7)
(a <=> b >= 0) == bool(a >= b) is true, and
(2.8)
if Cat is convertible to strong_ordering, T models totally_ordered ([concept.totallyordered]).

template<class T, class U, class Cat = partial_ordering> concept three_way_comparable_with = three_way_comparable<T, Cat> && three_way_comparable<U, Cat> && comparison-common-type-with<T, U> && three_way_comparable< common_reference_t<const remove_reference_t<T>&, const remove_reference_t&>, Cat> && weakly-equality-comparable-with<T, U> && partially-ordered-with<T, U> && requires(const remove_reference_t<T>& t, const remove_reference_t& u) { { t <=> u } -> compares-as<Cat>; { u <=> t } -> compares-as<Cat>; };

Let t and t2 be lvalues denoting distinct equal objects of types const remove_reference_t<T> and remove_cvref_t<T>, respectively, and let u and u2 be lvalues denoting distinct equal objects of types const remove_reference_t and remove_cvref_t, respectively.

Let C be common_reference_t<const remove_reference_t<T>&, const remove_reference_t&>.

Let CONVERT_TO_LVALUE<C>(E) be defined as in [concepts.compare.general].

T, U, and Cat model three_way_comparable_with<T, U, Cat> only if:

(3.1)
t <=> u and u <=> t have the same domain,
(3.2)
((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal,
(3.3)
(t <=> u == 0) == bool(t == u) is true,
(3.4)
(t <=> u != 0) == bool(t != u) is true,
(3.5)
Cat(t <=> u) == Cat(CONVERT_TO_LVALUE<C>(t2) <=> CONVERT_TO_LVALUE<C>(u2)) is true,
(3.6)
(t <=> u < 0) == bool(t < u) is true,
(3.7)
(t <=> u > 0) == bool(t > u) is true,
(3.8)
(t <=> u <= 0) == bool(t <= u) is true,
(3.9)
(t <=> u >= 0) == bool(t >= u) is true, and
(3.10)
if Cat is convertible to strong_ordering, T and U model totally_ordered_with<T, U> ([concept.totallyordered]).