cppdraft_translate/cppdraft/concept/strictweakorder.md

[concept.strictweakorder]

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](#concept:strict_weak_order "18.7.7 Concept strict_­weak_­order [concept.strictweakorder]") = [relation](concept.relation#concept:relation "18.7.5 Concept relation [concept.relation]")<R, T, U>;

1

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A relation models strict_weak_order only if it imposes a strict weak ordering on its arguments.

2

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The termstrict refers to the requirement of an irreflexive relation (!comp(x, x) for all x), and the termweak to requirements that are not as strong as those for a total ordering, but stronger than those for a partial ordering.

If we defineequiv(a, b) as!comp(a, b) && !comp(b, a), then the requirements are thatcomp andequiv both be transitive relations:

• (2.1)

comp(a, b) && comp(b, c) impliescomp(a, c)

• (2.2)

equiv(a, b) && equiv(b, c) impliesequiv(a, c)

3

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[Note 1:

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 byequiv, and

• (3.3)

the induced relation is a strict total ordering.

— end note]