heyting-algebras-0.0.2.0: Heyting and Boolean algebras

Algebra.Heyting.Layered

Synopsis

# Documentation

data Layered a b Source #

Layer one Heyting algebra on top of the other. Note: this is not a categorical sum.

Constructors

 Lower a Upper b
Instances
 (Eq a, Eq b) => Eq (Layered a b) Source # Instance detailsDefined in Algebra.Heyting.Layered Methods(==) :: Layered a b -> Layered a b -> Bool #(/=) :: Layered a b -> Layered a b -> Bool # (Ord a, Ord b) => Ord (Layered a b) Source # Instance detailsDefined in Algebra.Heyting.Layered Methodscompare :: Layered a b -> Layered a b -> Ordering #(<) :: Layered a b -> Layered a b -> Bool #(<=) :: Layered a b -> Layered a b -> Bool #(>) :: Layered a b -> Layered a b -> Bool #(>=) :: Layered a b -> Layered a b -> Bool #max :: Layered a b -> Layered a b -> Layered a b #min :: Layered a b -> Layered a b -> Layered a b # (Show a, Show b) => Show (Layered a b) Source # Instance detailsDefined in Algebra.Heyting.Layered MethodsshowsPrec :: Int -> Layered a b -> ShowS #show :: Layered a b -> String #showList :: [Layered a b] -> ShowS # (JoinSemiLattice a, JoinSemiLattice b) => JoinSemiLattice (Layered a b) Source # Instance detailsDefined in Algebra.Heyting.Layered Methods(\/) :: Layered a b -> Layered a b -> Layered a b #join :: Layered a b -> Layered a b -> Layered a b # (MeetSemiLattice a, MeetSemiLattice b) => MeetSemiLattice (Layered a b) Source # Instance detailsDefined in Algebra.Heyting.Layered Methods(/\) :: Layered a b -> Layered a b -> Layered a b #meet :: Layered a b -> Layered a b -> Layered a b # (Lattice a, Lattice b) => Lattice (Layered a b) Source # Instance detailsDefined in Algebra.Heyting.Layered Source # Instance detailsDefined in Algebra.Heyting.Layered Methodsbottom :: Layered a b # Source # Instance detailsDefined in Algebra.Heyting.Layered Methodstop :: Layered a b # Source # Instance detailsDefined in Algebra.Heyting.Layered (HeytingAlgebra a, HeytingAlgebra b, Eq a) => HeytingAlgebra (Layered a b) Source # Instance detailsDefined in Algebra.Heyting.Layered Methods(==>) :: Layered a b -> Layered a b -> Layered a b Source #not :: Layered a b -> Layered a b Source #

layer :: (a -> c) -> (b -> c) -> Layered a b -> c Source #