Algebra.Heyting.Layered

Documentation

data Layered a b

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)

Defined 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)

Defined in Algebra.Heyting.Layered

Methods

compare :: 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)

Defined in Algebra.Heyting.Layered

Methods

showsPrec :: Int -> Layered a b -> ShowS

show :: Layered a b -> String

showList :: [Layered a b] -> ShowS

(JoinSemiLattice a, JoinSemiLattice b) => JoinSemiLattice (Layered a b)

Defined 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)

Defined 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)

Defined in Algebra.Heyting.Layered

(BoundedJoinSemiLattice a, JoinSemiLattice b) => BoundedJoinSemiLattice (Layered a b)

Defined in Algebra.Heyting.Layered

Methods

bottom :: Layered a b

(MeetSemiLattice a, BoundedMeetSemiLattice b) => BoundedMeetSemiLattice (Layered a b)

Defined in Algebra.Heyting.Layered

Methods

top :: Layered a b

(Lattice a, Lattice b, BoundedJoinSemiLattice a, BoundedMeetSemiLattice b) => BoundedLattice (Layered a b)

Defined in Algebra.Heyting.Layered

(HeytingAlgebra a, HeytingAlgebra b, Eq a) => HeytingAlgebra (Layered a b)

Defined in Algebra.Heyting.Layered

Methods

(==>) :: Layered a b -> Layered a b -> Layered a b

not :: Layered a b -> Layered a b

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