7 Concepts library [concepts.lib]

7.6 Callable concepts [concepts.lib.callable]

7.6.6 Concept StrictWeakOrder [concepts.lib.callable.strictweakorder]

template <class R, class T, class U> concept bool StrictWeakOrder = Relation<R, T, U>;

1

A Relation satisfies StrictWeakOrder only if it imposes a strict weak ordering on its arguments.

2

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) [ Note: Under these conditions, it can be shown that

    • (2.2.1)

      equiv is an equivalence relation

    • (2.2.2)

      comp induces a well-defined relation on the equivalence classes determined by equiv

    • (2.2.3)

      The induced relation is a strict total ordering.  — end note ]