Difference between revisions of "cpp/concepts/totally ordered"
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template <class T> | template <class T> | ||
concept totally_ordered = | concept totally_ordered = | ||
| − | std::equality_comparable<T> && | + | std::equality_comparable<T> && __PartiallyOrderedWith<T, T>; |
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}} | }} | ||
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const std::remove_reference_t<T>&, | const std::remove_reference_t<T>&, | ||
const std::remove_reference_t<U>&>> && | const std::remove_reference_t<U>&>> && | ||
| − | + | __PartiallyOrderedWith<T, U>; | |
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@2@ The concept {{tt|totally_ordered_with<T, U>}} specifies that the comparison operators {{tt|1===,!=,<,>,<=,>=}} on (possibly mixed) {{tt|T}} and {{tt|U}} operands yield results consistent with a strict total order. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type. | @2@ The concept {{tt|totally_ordered_with<T, U>}} specifies that the comparison operators {{tt|1===,!=,<,>,<=,>=}} on (possibly mixed) {{tt|T}} and {{tt|U}} operands yield results consistent with a strict total order. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type. | ||
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| + | In both definitions, {{tt|''__PartiallyOrderedWith''}} is the exposition-only concept described in {{ltt|cpp/utility/compare/three_way_comparable}}. | ||
=== Semantic requirements === | === Semantic requirements === | ||
Revision as of 20:15, 14 December 2020
| Defined in header <concepts>
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| template <class T> concept totally_ordered = |
(1) | (since C++20) |
| template <class T, class U> concept totally_ordered_with = |
(2) | (since C++20) |
1) The concept
totally_ordered<T> specifies that the comparison operators ==,!=,<,>,<=,>= on T yield results consistent with a strict total order on T.2) The concept
totally_ordered_with<T, U> specifies that the comparison operators ==,!=,<,>,<=,>= on (possibly mixed) T and U operands yield results consistent with a strict total order. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type.In both definitions, __PartiallyOrderedWith is the exposition-only concept described in three_way_comparable.
Semantic requirements
1)
totally_ordered<T> is modeled only if, given lvalues a, b and c of type const std::remove_reference_t<T>:
- Exactly one of bool(a < b), bool(a > b) and bool(a == b) is true;
- If bool(a < b) and bool(b < c) are both true, then bool(a < c) is true;
- bool(a > b) == bool(b < a)
- bool(a >= b) == !bool(a < b)
- bool(a <= b) == !bool(b < a)
2)
totally_ordered_with<T, U> is satisfied only if, given any lvalue t of type const std::remove_reference_t<T> and any lvalue u of type const std::remove_reference_t<U>, and let C be std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&> :
- bool(t < u) == bool(C(t) < C(u))
- bool(t > u) == bool(C(t) > C(u))
- bool(t <= u) == bool(C(t) <= C(u))
- bool(t >= u) == bool(C(t) >= C(u))
- bool(u < t) == bool(C(u) < C(t))
- bool(u > t) == bool(C(u) > C(t))
- bool(u <= t) == bool(C(u) <= C(t))
- bool(u >= t) == bool(C(u) >= C(t))
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.
