NAME¶

std::totally_ordered,std::totally_ordered_with - std::totally_ordered,std::totally_ordered_with

Synopsis¶

Defined in header <concepts>
template<class T>

concept totally_ordered = (1) (since C++20)

std::equality_comparable<T> && __PartiallyOrderedWith<T, T>;
template<class T, class U>

concept totally_ordered_with =
std::totally_ordered<T> &&
std::totally_ordered<U> &&
std::equality_comparable_with<T, U> && (2) (since C++20)
std::totally_ordered<
std::common_reference_t<
const std::remove_reference_t<T>&,
const std::remove_reference_t<U>&>> &&

__PartiallyOrderedWith<T, U>;
template<class T, class U>

concept __PartiallyOrderedWith = // exposition only
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; (3) (since C++20)
{ t >= u } -> boolean-testable;
{ u < t } -> boolean-testable;
{ u > t } -> boolean-testable;
{ u <= t } -> boolean-testable;
{ u >= t } -> boolean-testable;

};

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 satisified 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

* 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))

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

An expression is equality preserving if it results in equal outputs given equal
inputs.

* The inputs to an expression consist of its operands.
* The outputs of an expression consist of its result and all operands modified by
the expression (if any).

In specification of standard concepts, operands are defined as the largest
subexpressions that include only:

* an id-expression, and
* invocations of std::move, std::forward, and std::declval.

The cv-qualification and value category of each operand is determined by assuming
that each template type parameter denotes a cv-unqualified complete non-array object
type.

Every expression required to be equality preserving is further required to be
stable: two evaluations of such an expression with the same input objects must have
equal outputs absent any explicit intervening modification of those input objects.

Unless noted otherwise, every expression used in a requires-expression is required
to be equality preserving and stable, and the evaluation of the expression may
modify only its non-constant operands. Operands that are constant must not be
modified.

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.