dedekind::category::IsOrderMeetSemilattice Concept Reference

Order-theoretic meet-semilattice as a commutative refinement. More...

Concept definition

template<typename T, typename Meet Inf>
concept dedekind::category::IsOrderMeetSemilattice = 
    IsMereologicalMeetBand<T, Meet> && IsCommutative<T, Meet>

Detailed Description

Order-theoretic meet-semilattice as a commutative refinement.

In the module hierarchy, :mereology provides the upstream associative + idempotent meet band. :posetal refines that structure with commutativity, yielding the order-theoretic meet-semilattice notion.

Note

Naming history: an IsOrderMeetSemilatticeSignature shape mixin was previously bundled into this concept's body; it was retired because IsMereologicalMeetBand transitively requires IsMereologicalMeetMagma, which already checks the operator surface (meet(a, b) -> convertible_to<T>). Callsites that need just the operator-surface check use the magma concept directly.