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

Foldable Levitated

Defined in Algebra.Lattice.Levitated

Methods

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

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

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

Functor Levitated

Defined in Algebra.Lattice.Levitated

Methods

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

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

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

Generic1 Levitated

Defined in Algebra.Lattice.Levitated

Associated Types

type Rep1 Levitated :: k -> Type

Methods

from1 :: forall (a :: k). Levitated a -> Rep1 Levitated a

to1 :: forall (a :: k). Rep1 Levitated a -> Levitated a

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

Function a => Function (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

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

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 :: forall r r'. (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)

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

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

NFData a => NFData (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

rnf :: Levitated a -> ()

Eq a => Eq (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

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

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

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

Hashable a => Hashable (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

hashWithSalt :: Int -> Levitated a -> Int

hash :: Levitated a -> Int

Lattice a => BoundedJoinSemiLattice (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

bottom :: Levitated a

Lattice a => BoundedMeetSemiLattice (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

top :: 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

PartialOrd a => PartialOrd (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

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

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

Finite a => Finite (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

universeF :: [Levitated a]

cardinality :: Tagged (Levitated a) Natural

Universe a => Universe (Levitated a)

Defined in Algebra.Lattice.Levitated

Methods

universe :: [Levitated a]

type Rep1 Levitated

Defined in Algebra.Lattice.Levitated

type Rep1 Levitated = D1 ('MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.2-ExsECSVnOmtEcARHt0Jtvl" '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)))

type Rep (Levitated a)

Defined in Algebra.Lattice.Levitated

type Rep (Levitated a) = D1 ('MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.2-ExsECSVnOmtEcARHt0Jtvl" '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)))

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.