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std::totally_ordered, std::totally_ordered_with

Defined in header <concepts> 
template< class T >
concept totally_ordered =
    std::equality_comparable<T> && __PartiallyOrderedWith<T, T>;
 (1) (since C++20) 
template< class T, class U >
concept totally_ordered_with =
    std::totally_ordered<T> &&
    std::totally_ordered<U> &&
    std::equality_comparable_with<T, U> &&
    std::totally_ordered<
        std::common_reference_t<
            const std::remove_reference_t<T>&,
            const std::remove_reference_t<U>&>> &&
    __PartiallyOrderedWith<T, U>;
 (2) (since C++20) 
template< class T, class U >
concept __PartiallyOrderedWith =
    requires(const std::remove_reference_t<T>& t,
             const std::remove_reference_t<U>& u) {
        { t <  u } -> 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;
    };
 (3) (exposition only*)
1) The concept std::totally_ordered specifies that the comparison operators ==,!=,<,>,<=,>= on a type yield results consistent with a strict total order on the type.
2) The concept std::totally_ordered_with 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.
3) The exposition-only concept __PartiallyOrderedWith specifies that a value of type T and a value of type U can be compared in a partial order with each other (in either order) using <, >, <=, and >=, and the results of the comparisons are consistent.

Semantic requirements

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

1) std::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) std::totally_ordered_with<T, U> is modeled only if, given

let C be std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&>, and, given an expression E and a type C, let CONVERT_TO<C>(E) be:

(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)

the following are true:

  • bool(t < u) == bool(CONVERT_TO<C>(t2) < CONVERT_TO<C>(u2))
  • bool(t > u) == bool(CONVERT_TO<C>(t2) > CONVERT_TO<C>(u2))
  • bool(t <= u) == bool(CONVERT_TO<C>(t2) <= CONVERT_TO<C>(u2))
  • bool(t >= u) == bool(CONVERT_TO<C>(t2) >= CONVERT_TO<C>(u2))
  • bool(u < t) == bool(CONVERT_TO<C>(u2) < CONVERT_TO<C>(t2))
  • bool(u > t) == bool(CONVERT_TO<C>(u2) > CONVERT_TO<C>(t2))
  • bool(u <= t) == bool(CONVERT_TO<C>(u2) <= CONVERT_TO<C>(t2))
  • bool(u >= t) == bool(CONVERT_TO<C>(u2) >= CONVERT_TO<C>(t2))
3) __PartiallyOrderedWith<T, U> is modeled only if given

the following are true:

  • t < u, t <= u, t > u, t >= u, u < t, u <= t, u > t, and u >= t have the same domain;
  • bool(t < u) == bool(u > t);
  • bool(u < t) == bool(t > u);
  • bool(t <= u) == bool(u >= t); and
  • bool(u <= t) == bool(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 requires implicit expression variations.

See also

(C++20)
specifies that operator <=> produces consistent result on given types
(concept)

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