std::totally_ordered (since C++20), std::totally_ordered_with (since C++20)

 

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Concepts library

Core language concepts same_as (C++20) derived_from (C++20) convertible_to (C++20) common_reference_with (C++20) common_with (C++20) integral (C++20) signed_integral (C++20) unsigned_integral (C++20) floating_point (C++20) swappableswappable_with (C++20)(C++20) destructible (C++20) constructible_from (C++20) default_initializable (C++20)   move_constructible (C++20) copy_constructible (C++20) assignable_from (C++20)

Comparison concepts equality_comparableequality_comparable_with (C++20)(C++20) totally_orderedtotally_ordered_with (C++20)(C++20) Object concepts movable (C++20) copyable (C++20) semiregular (C++20) regular (C++20) Callable concepts invocableregular_invocable (C++20)(C++20) predicate (C++20) relation (C++20) equivalence_relation (C++20) strict_weak_order (C++20)

Exposition-only concepts boolean-testable  (C++20)

 

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)
Helper concepts
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

• t and t2, lvalues denoting distinct equal objects of types const std::remove_reference_t<T> and std::remove_reference_t<T> respectively, and
• u and u2, lvalues denoting distinct equal objects of types const std::remove_reference_t<U> and std::remove_reference_t<U> respectively,

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:

static_cast<C>(std::as_const(E)).	(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

• any lvalue t of type const std::remove_reference_t<T>, and
• any lvalue u of type const std::remove_reference_t<U>,

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.

References

• C++23 standard (ISO/IEC 14882:2024):

• 18.5.5 Concept totally_ordered [concept.totallyordered]

• C++20 standard (ISO/IEC 14882:2020):

• 18.5.4 Concept totally_ordered [concept.totallyordered]

See also

three_way_comparablethree_way_comparable_with (C++20)

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