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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../concepts/strict_weak_order.html below:

std::strict_weak_order - cppreference.com

template< class R, class T, class U > concept strict_weak_order = std::relation<R, T, U>; (since C++20)

The concept strict_weak_order<R, T, U> specifies that the relation R imposes a strict weak ordering on its arguments.

[edit] Semantic requirements

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 strict_weak_order is purely semantic.

[edit] References

C++23 standard (ISO/IEC 14882:2024):

18.7.7 Concept strict_weak_order [concept.strictweakorder]

C++20 standard (ISO/IEC 14882:2020):

18.7.7 Concept strict_weak_order [concept.strictweakorder]

[edit] See also

LessThanComparable

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