18 Concepts library [concepts]

18.7 Callable concepts [concepts.callable]

18.7.7 Concept strict_­weak_­order [concept.strictweakorder]

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template<class R, class T, class U> concept strict_­weak_­order = relation<R, T, U>;
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A relation models strict_­weak_­order only if it imposes a strict weak ordering on its arguments.
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The term strict refers to the requirement of an irreflexive relation (!comp(x, x) for all x), and the term weak to requirements that are not as strong as those for a total ordering, but stronger than those for a partial ordering.
If we define equiv(a, b) as !comp(a, b) && !comp(b, a), then the requirements are that comp and equiv both be transitive relations:
  • (2.1)
    comp(a, b) && comp(b, c) implies comp(a, c)
  • (2.2)
    equiv(a, b) && equiv(b, c) implies equiv(a, c)
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[ Note
:
Under these conditions, it can be shown that
  • (3.1)
    equiv is an equivalence relation,
  • (3.2)
    comp induces a well-defined relation on the equivalence classes determined by equiv, and
  • (3.3)
    the induced relation is a strict total ordering.
— end note
 ]