Dedekind 0.0.0
A structuralist C++23 Module Library
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dedekind::category::IsOrderLatticeOperations Concept Referenceexport
module dedekind.category

Order-theoretic lattice operations as commutative + absorptive refinement over upstream mereological lattice operations. More...

Concept definition

template<typename T, typename Join Sup, typename Meet Inf>
concept dedekind::category::IsOrderLatticeOperations =
IsMereologicalLatticeOperations<T, Join, Meet> &&
IsOrderJoinSemilattice<T, Join> && IsOrderMeetSemilattice<T, Meet> &&
IsAbsorptive<T, Join, Meet>
dedekind::category::IsAbsorptive
Mutual absorption and internal idempotency for a pair of operations.
Definition mereology.cppm:982
dedekind::category::IsMereologicalLatticeOperations
Compatibility lattice alias over the skew core + absorption.
Definition mereology.cppm:1020
dedekind::category::IsOrderJoinSemilattice
Order-theoretic join-semilattice as a commutative refinement.
Definition posetal.cppm:152
dedekind::category::IsOrderLatticeOperations
Order-theoretic lattice operations as commutative + absorptive refinement over upstream mereological ...
Definition posetal.cppm:179
dedekind::category::IsOrderMeetSemilattice
Order-theoretic meet-semilattice as a commutative refinement.
Definition posetal.cppm:124

Detailed Description

Order-theoretic lattice operations as commutative + absorptive refinement over upstream mereological lattice operations.

Note
Naming history: this concept previously bundled an IsOrderLatticeOperationsSignature signature mixin alongside the semantic clauses, mixing syntax (operator surface check) with semantics (axiomatic lattice claims). The signature mixin was removed (and the now-unused signature concept retired) because IsOrderJoinSemilattice / IsOrderMeetSemilattice already imply the operator surface through their upstream mereological magma concepts (IsMereologicalJoinMagma / IsMereologicalMeetMagma). The bundled concept here is purely semantic.