dedekind::category::IsSymmetric Concept Reference

Formal verification: Rel(a, b) ⇔ Rel(b, a). More...

Concept definition

template<typename T, typename Rel, typename Ω bool>
concept dedekind::category::IsSymmetric = 
    IsTruthObject<Ω> &&
    requires(const std::remove_cvref_t<Rel>& rel, const T& a, const T& b) {
      { rel(a, b) } -> std::convertible_to<Ω>;
      { rel(b, a) } -> std::convertible_to<Ω>;
    } && requires { requires is_symmetric_v<T, std::remove_cvref_t<Rel>>; }

Detailed Description

Formal verification: Rel(a, b) ⇔ Rel(b, a).

Mirrors IsReflexive / IsTransitive in :mereology: structural shape (rel is callable on the symmetric pair, answering in Ω) plus the engineer-supplied trait declaration.