Dedekind 0.0.0
A structuralist C++23 Module Library
Loading...
Searching...
No Matches
dedekind::category::IsLattice Concept Referenceexport
module dedekind.category

compatibility alias for order-lattice refinement. More...

Concept definition

template<typename T, typename Join std::bit_or<>, typename Meet std::bit_and<>>
concept dedekind::category::IsLattice = IsTotal<T, Join> && IsTotal<T, Meet> &&
IsOrderLatticeOperations<T, Join, Meet>
dedekind::category::IsLattice
compatibility alias for order-lattice refinement.
Definition total.cppm:893
dedekind::category::IsOrderLatticeOperations
Order-theoretic lattice operations as commutative + absorptive refinement over upstream mereological ...
Definition posetal.cppm:179
dedekind::category::IsTotal
The Master Safety Certificate for Level 0: is_total, as a concept.
Definition total.cppm:395

Detailed Description

compatibility alias for order-lattice refinement.

Combines a JoinSemilattice and a MeetSemilattice with the absorption identities: a ∨ (a ∧ b) = a and a ∧ (a ∨ b) = a. bool with (OR, AND) and int with (max, min) are Lattices.

This alias now delegates order laws to :posetal (IsOrderLatticeOperations) and keeps :total totality guards on the selected operators.

The defaults are the operator surface, | and & (std::bit_or<> / std::bit_and<>): the lattice as it is spelled. A chain's (max, min) is named explicitly (Sup, Inf); on int the defaults are the bit lattice 2³², not the order.