Algebra.Lattice.Levitated

Documentation

data Levitated a

Graft a distinct top and bottom onto an otherwise unbounded lattice. The top is the absorbing element for the join, and the bottom is the absorbing element for the meet.

Constructors

Bottom

Levitate a

Top

Instances

Monad Levitated

Defined in Algebra.Lattice.Levitated

Methods

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

(>>) :: Levitated a -> Levitated b -> Levitated b

return :: a -> Levitated a

fail :: String -> Levitated a

Functor Levitated

Defined in Algebra.Lattice.Levitated

Methods

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

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

Applicative Levitated

Defined in Algebra.Lattice.Levitated

Methods

pure :: a -> Levitated a

(<*>) :: Levitated (a -> b) -> Levitated a -> Levitated b

liftA2 :: (a -> b -> c) -> Levitated a -> Levitated b -> Levitated c

(*>) :: Levitated a -> Levitated b -> Levitated b

(<*) :: Levitated a -> Levitated b -> Levitated a

Foldable Levitated

Defined in Algebra.Lattice.Levitated

Methods

fold :: Monoid m => Levitated m -> m

foldMap :: Monoid m => (a -> m) -> Levitated a -> m

foldr :: (a -> b -> b) -> b -> Levitated a -> b

foldr' :: (a -> b -> b) -> b -> Levitated a -> b

foldl :: (b -> a -> b) -> b -> Levitated a -> b

foldl' :: (b -> a -> b) -> b -> Levitated a -> b

foldr1 :: (a -> a -> a) -> Levitated a -> a

foldl1 :: (a -> a -> a) -> Levitated a -> a

toList :: Levitated a -> [a]

null :: Levitated a -> Bool

length :: Levitated a -> Int

elem :: Eq a => a -> Levitated a -> Bool

maximum :: Ord a => Levitated a -> a

minimum :: Ord a => Levitated a -> a

sum :: Num a => Levitated a -> a

product :: Num a => Levitated a -> a

Traversable Levitated

Defined in Algebra.Lattice.Levitated

Methods

traverse :: Applicative f => (a -> f b) -> Levitated a -> f (Levitated b)

sequenceA :: Applicative f => Levitated (f a) -> f (Levitated a)

mapM :: Monad m => (a -> m b) -> Levitated a -> m (Levitated b)

sequence :: Monad m => Levitated (m a) -> m (Levitated a)

Eq a => Eq (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

(==) :: Levitated a -> Levitated a -> Bool

(/=) :: Levitated a -> Levitated a -> Bool

Data a => Data (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Levitated a -> c (Levitated a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Levitated a)

toConstr :: Levitated a -> Constr

dataTypeOf :: Levitated a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Levitated a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Levitated a))

gmapT :: (forall b. Data b => b -> b) -> Levitated a -> Levitated a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Levitated a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Levitated a -> r

gmapQ :: (forall d. Data d => d -> u) -> Levitated a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Levitated a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Levitated a -> m (Levitated a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Levitated a -> m (Levitated a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Levitated a -> m (Levitated a)

Ord a => Ord (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

compare :: Levitated a -> Levitated a -> Ordering

(<) :: Levitated a -> Levitated a -> Bool

(<=) :: Levitated a -> Levitated a -> Bool

(>) :: Levitated a -> Levitated a -> Bool

(>=) :: Levitated a -> Levitated a -> Bool

max :: Levitated a -> Levitated a -> Levitated a

min :: Levitated a -> Levitated a -> Levitated a

Read a => Read (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

readsPrec :: Int -> ReadS (Levitated a)

readList :: ReadS [Levitated a]

readPrec :: ReadPrec (Levitated a)

readListPrec :: ReadPrec [Levitated a]

Show a => Show (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

showsPrec :: Int -> Levitated a -> ShowS

show :: Levitated a -> String

showList :: [Levitated a] -> ShowS

Generic (Levitated a)

Defined in Algebra.Lattice.Levitated

Associated Types

type Rep (Levitated a) :: Type -> Type

Methods

from :: Levitated a -> Rep (Levitated a) x

to :: Rep (Levitated a) x -> Levitated a

Function a => Function (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

function :: (Levitated a -> b) -> Levitated a :-> b

Arbitrary a => Arbitrary (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

arbitrary :: Gen (Levitated a)

shrink :: Levitated a -> [Levitated a]

CoArbitrary a => CoArbitrary (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

coarbitrary :: Levitated a -> Gen b -> Gen b

NFData a => NFData (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

rnf :: Levitated a -> ()

Hashable a => Hashable (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

hashWithSalt :: Int -> Levitated a -> Int

hash :: Levitated a -> Int

Universe a => Universe (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

universe :: [Levitated a]

Finite a => Finite (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

universeF :: [Levitated a]

cardinality :: Tagged (Levitated a) Natural

PartialOrd a => PartialOrd (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

leq :: Levitated a -> Levitated a -> Bool

comparable :: Levitated a -> Levitated a -> Bool

Lattice a => BoundedMeetSemiLattice (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

top :: Levitated a

Lattice a => BoundedJoinSemiLattice (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

bottom :: Levitated a

Lattice a => Lattice (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

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

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

Generic1 Levitated

Defined in Algebra.Lattice.Levitated

Associated Types

type Rep1 Levitated :: k -> Type

Methods

from1 :: Levitated a -> Rep1 Levitated a

to1 :: Rep1 Levitated a -> Levitated a

type Rep (Levitated a)

Defined in Algebra.Lattice.Levitated

type Rep (Levitated a) = D1 (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.0.2-HdMTcqWeXqlAAQvdNaFFrQ" False) (C1 (MetaCons "Bottom" PrefixI False) (U1 :: Type -> Type) :+: (C1 (MetaCons "Levitate" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Top" PrefixI False) (U1 :: Type -> Type)))

type Rep1 Levitated

Defined in Algebra.Lattice.Levitated

type Rep1 Levitated = D1 (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.0.2-HdMTcqWeXqlAAQvdNaFFrQ" False) (C1 (MetaCons "Bottom" PrefixI False) (U1 :: Type -> Type) :+: (C1 (MetaCons "Levitate" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) :+: C1 (MetaCons "Top" PrefixI False) (U1 :: Type -> Type)))

retractLevitated :: (BoundedMeetSemiLattice a, BoundedJoinSemiLattice a) => Levitated a -> a

Interpret Levitated a using the BoundedLattice of a.

foldLevitated :: b -> (a -> b) -> b -> Levitated a -> b

Fold Levitated.