< cpp‎ | experimental‎ | ranges
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URNG concept
template< class R, class T, class U >
concept bool StrictWeakOrder = Relation<R, T, U>;
(1) (ranges TS)

The concept StrictWeakOrder<R, T, U> specifies that the Relation R imposes a strict weak ordering on its arguments. A relation r is a strict weak ordering if

  • it is irreflexive: for all x, r(x, x) is false;
  • it is transitive: for all a, b and c, if r(a, b) and r(b, c) are both true then r(a, c) is true;
  • let e(a, b) be !r(a, b) && !r(b, a), then e is transitive: e(a, b) && e(b, c) implies e(a, c).

Under these conditions, it can be shown that e is an equivalence relation, and r induces a strict total ordering on the equivalence classes determined by e.

[edit] Notes

The distinction between Relation and StrictWeakOrder is purely semantic.