[concept.stricttotallyordered]

🔗

template<class T>
  concept StrictTotallyOrdered =
    EqualityComparable<T> &&
    requires(const remove_reference_t<T>& a,
             const remove_reference_t<T>& b) {
      a <  b; requires Boolean<decltype(a <  b)>;
      a >  b; requires Boolean<decltype(a >  b)>;
      a <= b; requires Boolean<decltype(a <= b)>;
      a >= b; requires Boolean<decltype(a >= b)>;
    };

Let a, b, and c be lvalues of type const remove_reference_t<T>.

StrictTotallyOrdered<T> is satisfied only if

(1.1)
Exactly one of bool(a < b), bool(a > b), or bool(a == b) is true.
(1.2)
If bool(a < b) and bool(b < c), then bool(a < c).
(1.3)
bool(a > b) == bool(b < a).
(1.4)
bool(a <= b) == !bool(b < a).
(1.5)
bool(a >= b) == !bool(a < b).

🔗

template<class T, class U>
  concept StrictTotallyOrderedWith =
    StrictTotallyOrdered<T> && StrictTotallyOrdered<U> &&
    CommonReference<const remove_reference_t<T>&, const remove_reference_t<U>&> &&
    StrictTotallyOrdered<
      common_reference_t<
        const remove_reference_t<T>&,
        const remove_reference_t<U>&>> &&
    EqualityComparableWith<T, U> &&
    requires(const remove_reference_t<T>& t,
             const remove_reference_t<U>& u) {
      t <  u; requires Boolean<decltype(t <  u)>;
      t >  u; requires Boolean<decltype(t >  u)>;
      t <= u; requires Boolean<decltype(t <= u)>;
      t >= u; requires Boolean<decltype(t >= u)>;
      u <  t; requires Boolean<decltype(u <  t)>;
      u >  t; requires Boolean<decltype(u >  t)>;
      u <= t; requires Boolean<decltype(u <= t)>;
      u >= t; requires Boolean<decltype(u >= t)>;
    };

Let t be an lvalue of type const remove_reference_t<T>, u be an lvalue of type const remove_reference_t<U>, and C be:

common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&>

StrictTotallyOrderedWith<T, U> is satisfied only if

(2.1)
bool(t < u) == bool(C(t) < C(u)).
(2.2)
bool(t > u) == bool(C(t) > C(u)).
(2.3)
bool(t <= u) == bool(C(t) <= C(u)).
(2.4)
bool(t >= u) == bool(C(t) >= C(u)).
(2.5)
bool(u < t) == bool(C(u) < C(t)).
(2.6)
bool(u > t) == bool(C(u) > C(t)).
(2.7)
bool(u <= t) == bool(C(u) <= C(t)).
(2.8)
bool(u >= t) == bool(C(u) >= C(t)).

17 Concepts library [concepts]

17.5 Comparison concepts [concepts.compare]

17.5.4 Concept StrictTotallyOrdered [concept.stricttotallyordered]