18 Concepts library [concepts]

18.5 Comparison concepts [concepts.compare]

18.5.4 Concept totally_­ordered [concept.totallyordered]

template<class T> concept totally_­ordered = equality_comparable<T> && requires(const remove_reference_t<T>& a, const remove_reference_t<T>& b) { { a < b } -> boolean; { a > b } -> boolean; { a <= b } -> boolean; { a >= b } -> boolean; };
For some type T, let a, b, and c be lvalues of type const remove_­reference_­t<T>.
T models totally_­ordered only if
  • Exactly one of bool(a < b), bool(a > b), or bool(a == b) is true.
  • If bool(a < b) and bool(b < c), then bool(a < c).
  • bool(a > b) == bool(b < a).
  • bool(a <= b) == !bool(b < a).
  • bool(a >= b) == !bool(a < b).
template<class T, class U> concept totally_­ordered_­with = totally_ordered<T> && totally_ordered<U> && common_reference_with<const remove_reference_t<T>&, const remove_reference_t<U>&> && totally_ordered< common_reference_t< const remove_reference_t<T>&, const remove_reference_t<U>&>> && equality_comparable_with<T, U> && requires(const remove_reference_t<T>& t, const remove_reference_t<U>& u) { { t < u } -> boolean; { t > u } -> boolean; { t <= u } -> boolean; { t >= u } -> boolean; { u < t } -> boolean; { u > t } -> boolean; { u <= t } -> boolean; { u >= t } -> boolean; };
For some types T and U, 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>&>
T and U model totally_­ordered_­with<T, U> only if
  • 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)).