17 Concepts library [concepts]

17.7 Callable concepts [concepts.callable]

17.7.6 Concept StrictWeakOrder [concept.strictweakorder]

template<class R, class T, class U> concept StrictWeakOrder = Relation<R, T, U>;
A Relation satisfies StrictWeakOrder only if it imposes a strict weak ordering on its arguments.
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:
  • comp(a, b) && comp(b, c) implies comp(a, c)
  • equiv(a, b) && equiv(b, c) implies equiv(a, c)
[Note
:
Under these conditions, it can be shown that
  • equiv is an equivalence relation,
  • comp induces a well-defined relation on the equivalence classes determined by equiv, and
  • the induced relation is a strict total ordering.
end note
]