18 Concepts library [concepts]

18.5 Comparison concepts [concepts.compare]

18.5.4 Concept totally_­ordered [concept.totallyordered]

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template<class T> concept totally_­ordered = equality_­comparable<T> && partially-ordered-with<T, T>;
1
#
Given a type T, let a, b, and c be lvalues of type const remove_­reference_­t<T>.
T models totally_­ordered 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(a < b).
🔗
template<class T, class U> concept totally_­ordered_­with = totally_­ordered<T> && totally_­ordered<U> && equality_­comparable_­with<T, U> && totally_­ordered< common_reference_t< const remove_reference_t<T>&, const remove_reference_t<U>&>> && partially-ordered-with<T, U>;
2
#
Given 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
  • (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)).