std::totally_ordered, std::totally_ordered_with
Defined in header <concepts>


template <class T> concept totally_ordered = 
(1)  (since C++20) 
template <class T, class U> concept totally_ordered_with = 
(2)  (since C++20) 
totally_ordered<T>
specifies that the comparison operators ==,!=,<,>,<=,>=
on T
yield results consistent with a strict total order on T
.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 expositiononly concept described in three_way_comparable.
[edit] Semantic requirements
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)
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))
[edit] 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 idexpression, and
 invocations of std::move, std::forward, and std::declval.
The cvqualification and value category of each operand is determined by assuming that each template type parameter denotes a cvunqualified complete nonarray 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 requiresexpression is required to be equality preserving and stable, and the evaluation of the expression may only modify its nonconstant operands. Operands that are constant must not be modified.
[edit] Implicit expression variations
A requiresexpression that uses an expression that is nonmodifying for some constant lvalue operand also implicitly requires additional variations of that expression that accept a nonconstant 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.