dedekind::category::SupInfLattice Concept Reference

A carrier on which max / min (and Sup / Inf) are honest lattice ops: usable (SupInfOperand) and carrying a certified order. More...

Concept definition

template<typename T>
concept dedekind::category::SupInfLattice = 
    SupInfOperand<T> &&
    ((IsReflexive<T, std::less_equal<T>> &&
      IsTransitive<T, std::less_equal<T>> &&
      IsAntisymmetric<T, std::less_equal<T>> &&
      IsConnex<T, std::less_equal<T>>) ||
     (IsReflexive<T, std::less_equal<>> && IsTransitive<T, std::less_equal<>> &&
      IsAntisymmetric<T, std::less_equal<>> && IsConnex<T, std::less_equal<>>))

Detailed Description

A carrier on which max / min (and Sup / Inf) are honest lattice ops: usable (SupInfOperand) and carrying a certified order.

Requires a complete total-order certificate (reflexive, transitive, antisymmetric, connex) under one std::less_equal spelling — typed std::less_equal<T> or transparent std::less_equal<> (see mereology__Lattice_Op_Gate for why the legs are grouped per relation).

Template Parameters

T	The candidate carrier type.