std::three_way_comparable, std::three_way_comparable_with
Defined in header <compare>


template<class T, class Cat = std::partial_ordering> concept three_way_comparable = 
(1)  (since C++20) 
template<class T, class U, class Cat = std::partial_ordering> concept three_way_comparable_with = 
(2)  (since C++20) 
template<class T, class Cat> concept __ComparesAs = // exposition only 
(3)  (since C++20) 
std::three_way_comparable
specifies that the three way comparison operator <=>
on T
yield results consistent with the comparison category implied by Cat
.std::three_way_comparable_with
specifies that the three way comparison operator <=>
on (possibly mixed) T
and U
operands yield results consistent with the comparison category implied by Cat
. Comparing mixed operands yields results equivalent to comparing the operands converted to their common type.In both definitions, __WeaklyEqualityComparableWith and __PartiallyOrderedWith are expositiononly concepts also used by equality_comparable
and totally_ordered
, respectively.
Semantic requirements
These concepts are modeled only if they are satisified and all concepts they subsume are modeled.
T
and Cat
model std::three_way_comparable<T, Cat> only if, given lvalues a
and b
of type const std::remove_reference_t<T>, following are true:
 (a <=> b == 0) == bool(a == b),
 (a <=> b != 0) == bool(a != b),
 ((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
 bool(a > b) == bool(b < a),
 bool(a >= b) == !bool(a < b),
 bool(a <= b) == !bool(b < a),
 (a <=> b < 0) == bool(a < b),
 (a <=> b > 0) == bool(a > b),
 (a <=> b <= 0) == bool(a <= b), and
 (a <=> b >= 0) == bool(a >= b); and
 if
Cat
is convertible to std::strong_ordering,T
modelstotally_ordered
.
T
, U
, and Cat
model std::three_way_comparable_with<T, U, Cat> only if given

t
, an lvalue of type const std::remove_reference_t<T> and 
u
, an lvalue of type const std::remove_reference_t<U>,
Let C
be std::common_reference_t<const std::remove_reference_t<T>&, const std::remove_reference_t<U>&>, the following are true:
 t <=> u and u <=> t have the same domain;
 ((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal;
 (t <=> u == 0) == bool(t == u),
 (t <=> u != 0) == bool(t != u),
 Cat(t <=> u) == Cat(C(t) <=> C(u)),
 (t <=> u < 0) == bool(t < u),
 (t <=> u > 0) == bool(t > u),
 (t <=> u <= 0) == bool(t <= u),
 (t <=> u >= 0) == bool(t >= u); and
 if
Cat
is convertible to std::strong_ordering,T
andU
model std::totally_ordered_with<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 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 modify only its nonconstant operands. Operands that are constant must not be modified.
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.
See also
specifies that operator == is an equivalence relation (concept)  
specifies that the comparison operators on the type yield a total order (concept) 