dedekind::category::IsLatticeLess Concept Reference

The injected total order: a caller-supplied comparator with a static consteval less<X,Y>() returning a logic value in its lattice_less_logic (default Boole, i.e. bool). The reported logic must be a full IsOckhamAlgebra, so ::True (accessed by lattice_definitely_less) is guaranteed present. The reducer canonicalises only on a definitely-True result, so an Unknown (undecidable) comparison leaves the operands in authoring order. Total-ness is the caller's obligation (Jlt: asserted downstream), not checked here. More...

Concept definition

template<typename Less, typename X, typename Y>
concept dedekind::category::IsLatticeLess = 
    IsOckhamAlgebra<lattice_less_logic_t<Less>> && requires {
      {
        Less::template less<X, Y>()
      } -> std::convertible_to<typename lattice_less_logic_t<Less>::Ω>;
      
      
      
      
      typename std::bool_constant<(Less::template less<X, Y>() ==
                                   lattice_less_logic_t<Less>::True)>;
    }

Detailed Description

The injected total order: a caller-supplied comparator with a static consteval less<X,Y>() returning a logic value in its lattice_less_logic (default Boole, i.e. bool). The reported logic must be a full IsOckhamAlgebra, so ::True (accessed by lattice_definitely_less) is guaranteed present. The reducer canonicalises only on a definitely-True result, so an Unknown (undecidable) comparison leaves the operands in authoring order. Total-ness is the caller's obligation (Jlt: asserted downstream), not checked here.