Algebra.Lattice.Free

Free join-semilattices

data FreeJoinSemiLattice a

Instances

Functor FreeJoinSemiLattice

Methods

fmap :: (a -> b) -> FreeJoinSemiLattice a -> FreeJoinSemiLattice b

(<$) :: a -> FreeJoinSemiLattice b -> FreeJoinSemiLattice a

Universe a => Universe (FreeJoinSemiLattice a)

Methods

universe :: [FreeJoinSemiLattice a]

Finite a => Finite (FreeJoinSemiLattice a)

Methods

universeF :: [FreeJoinSemiLattice a]

BoundedJoinSemiLattice a => BoundedJoinSemiLattice (FreeJoinSemiLattice a)

Methods

bottom :: FreeJoinSemiLattice a

JoinSemiLattice (FreeJoinSemiLattice a)

Methods

(\/) :: FreeJoinSemiLattice a -> FreeJoinSemiLattice a -> FreeJoinSemiLattice a

join :: FreeJoinSemiLattice a -> FreeJoinSemiLattice a -> FreeJoinSemiLattice a

liftFreeJoinSemiLattice :: a -> FreeJoinSemiLattice a

lowerFreeJoinSemiLattice :: FreeJoinSemiLattice a -> forall b. JoinSemiLattice b => (a -> b) -> b

retractFreeJoinSemiLattice :: JoinSemiLattice a => FreeJoinSemiLattice a -> a

Free meet-semilattices

data FreeMeetSemiLattice a

Instances

Functor FreeMeetSemiLattice

Methods

fmap :: (a -> b) -> FreeMeetSemiLattice a -> FreeMeetSemiLattice b

(<$) :: a -> FreeMeetSemiLattice b -> FreeMeetSemiLattice a

Universe a => Universe (FreeMeetSemiLattice a)

Methods

universe :: [FreeMeetSemiLattice a]

Finite a => Finite (FreeMeetSemiLattice a)

Methods

universeF :: [FreeMeetSemiLattice a]

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (FreeMeetSemiLattice a)

Methods

top :: FreeMeetSemiLattice a

MeetSemiLattice (FreeMeetSemiLattice a)

Methods

(/\) :: FreeMeetSemiLattice a -> FreeMeetSemiLattice a -> FreeMeetSemiLattice a

meet :: FreeMeetSemiLattice a -> FreeMeetSemiLattice a -> FreeMeetSemiLattice a

liftFreeMeetSemiLattice :: a -> FreeMeetSemiLattice a

lowerFreeMeetSemiLattice :: FreeMeetSemiLattice a -> forall b. MeetSemiLattice b => (a -> b) -> b

retractFreeMeetSemiLattice :: MeetSemiLattice a => FreeMeetSemiLattice a -> a

Free lattices

data FreeLattice a

Instances

Functor FreeLattice

Methods

fmap :: (a -> b) -> FreeLattice a -> FreeLattice b

(<$) :: a -> FreeLattice b -> FreeLattice a

Universe a => Universe (FreeLattice a)

Methods

universe :: [FreeLattice a]

Finite a => Finite (FreeLattice a)

Methods

universeF :: [FreeLattice a]

BoundedLattice a => BoundedLattice (FreeLattice a)

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (FreeLattice a)

Methods

top :: FreeLattice a

BoundedJoinSemiLattice a => BoundedJoinSemiLattice (FreeLattice a)

Methods

bottom :: FreeLattice a

Lattice (FreeLattice a)

MeetSemiLattice (FreeLattice a)

Methods

(/\) :: FreeLattice a -> FreeLattice a -> FreeLattice a

meet :: FreeLattice a -> FreeLattice a -> FreeLattice a

JoinSemiLattice (FreeLattice a)

Methods

(\/) :: FreeLattice a -> FreeLattice a -> FreeLattice a

join :: FreeLattice a -> FreeLattice a -> FreeLattice a

liftFreeLattice :: a -> FreeLattice a

lowerFreeLattice :: FreeLattice a -> forall b. Lattice b => (a -> b) -> b

retractFreeLattice :: Lattice a => FreeLattice a -> a