cppdraft_translate/cppdraft/concept/totallyordered.md

[concept.totallyordered]

18 Concepts library [concepts]

18.5 Comparison concepts [concepts.compare]

18.5.5 Concept totally_ordered [concept.totallyordered]

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template<class T> concept [totally_ordered](#concept:totally_ordered "18.5.5 Concept totally_­ordered [concept.totallyordered]") = [equality_comparable](concept.equalitycomparable#concept:equality_comparable "18.5.4 Concept equality_­comparable [concept.equalitycomparable]")<T> && [partially-ordered-with](cmp.concept#concept:partially-ordered-with "17.12.4 Concept three_­way_­comparable [cmp.concept]")<T, T>;

1

#

Given a type T, let a, b, and c be lvalues of type const remove_reference_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).

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template<class T, class U> concept [totally_ordered_with](#concept:totally_ordered_with "18.5.5 Concept totally_­ordered [concept.totallyordered]") = [totally_ordered](#concept:totally_ordered "18.5.5 Concept totally_­ordered [concept.totallyordered]")<T> && [totally_ordered](#concept:totally_ordered "18.5.5 Concept totally_­ordered [concept.totallyordered]")<U> && [equality_comparable_with](concept.equalitycomparable#concept:equality_comparable_with "18.5.4 Concept equality_­comparable [concept.equalitycomparable]")<T, U> && [totally_ordered](#concept:totally_ordered "18.5.5 Concept totally_­ordered [concept.totallyordered]")< common_reference_t< const remove_reference_t<T>&, const remove_reference_t<U>&>> && [partially-ordered-with](cmp.concept#concept:partially-ordered-with "17.12.4 Concept three_­way_­comparable [cmp.concept]")<T, U>;

2

#

Given types T and U, let t and t2 be lvalues denoting distinct equal objects of types const remove_reference_t andremove_cvref_t, respectively, let u and u2 be lvalues denoting distinct equal objects of types const remove_reference_t andremove_cvref_t, respectively, and let C be:common_reference_t<const remove_reference_t&, const remove_reference_t&>T and U modeltotally_ordered_with<T, U> only if

• (2.1)

  bool(t < u) == bool(CONVERT_TO_LVALUE(t2) < CONVERT_TO_LVALUE(u2)).

• (2.2)

  bool(t > u) == bool(CONVERT_TO_LVALUE(t2) > CONVERT_TO_LVALUE(u2)).

• (2.3)

  bool(t <= u) == bool(CONVERT_TO_LVALUE(t2) <= CONVERT_TO_LVALUE(u2)).

• (2.4)

  bool(t >= u) == bool(CONVERT_TO_LVALUE(t2) >= CONVERT_TO_LVALUE(u2)).

• (2.5)

  bool(u < t) == bool(CONVERT_TO_LVALUE(u2) < CONVERT_TO_LVALUE(t2)).

• (2.6)

  bool(u > t) == bool(CONVERT_TO_LVALUE(u2) > CONVERT_TO_LVALUE(t2)).

• (2.7)

  bool(u <= t) == bool(CONVERT_TO_LVALUE(u2) <= CONVERT_TO_LVALUE(t2)).

• (2.8)

  bool(u >= t) == bool(CONVERT_TO_LVALUE(u2) >= CONVERT_TO_LVALUE(t2)).