Copyright	(C) 2010-2015 Maximilian Bolingbroke 2015-2019 Oleg Grenrus
License	BSD-3-Clause (see the file LICENSE)
Maintainer	Oleg Grenrus <oleg.grenrus@iki.fi>
Safe Haskell	Safe
Language	Haskell2010

Algebra.Lattice.Levitated

Description

Synopsis

data Levitated a
- = Bottom
- | Levitate a
- | Top
retractLevitated :: (BoundedMeetSemiLattice a, BoundedJoinSemiLattice a) => Levitated a -> a
foldLevitated :: b -> (a -> b) -> b -> Levitated a -> b

Documentation

data Levitated a Source #

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

Instances details

Foldable Levitated Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details Defined in Algebra.Lattice.Levitated Methods fmap :: (a -> b) -> Levitated a -> Levitated b # (<$) :: a -> Levitated b -> Levitated a #
Monad Levitated Source #
Instance details 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 Source #
Instance details 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) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods arbitrary :: Gen (Levitated a) # shrink :: Levitated a -> [Levitated a] #
CoArbitrary a => CoArbitrary (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods coarbitrary :: Levitated a -> Gen b -> Gen b #
Function a => Function (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods function :: (Levitated a -> b) -> Levitated a :-> b #
Data a => Data (Levitated a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods showsPrec :: Int -> Levitated a -> ShowS # show :: Levitated a -> String # showList :: [Levitated a] -> ShowS #
NFData a => NFData (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods rnf :: Levitated a -> () #
Eq a => Eq (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods (==) :: Levitated a -> Levitated a -> Bool # (/=) :: Levitated a -> Levitated a -> Bool #
Ord a => Ord (Levitated a) Source #
Instance details 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) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods hashWithSalt :: Int -> Levitated a -> Int # hash :: Levitated a -> Int #
Lattice a => BoundedJoinSemiLattice (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods bottom :: Levitated a Source #
Lattice a => BoundedMeetSemiLattice (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods top :: Levitated a Source #
Lattice a => Lattice (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods (\/) :: Levitated a -> Levitated a -> Levitated a Source # (/\) :: Levitated a -> Levitated a -> Levitated a Source #
PartialOrd a => PartialOrd (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods leq :: Levitated a -> Levitated a -> Bool Source # comparable :: Levitated a -> Levitated a -> Bool Source #
Finite a => Finite (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods universeF :: [Levitated a] # cardinality :: Tagged (Levitated a) Natural #
Universe a => Universe (Levitated a) Source #
Instance details Defined in Algebra.Lattice.Levitated Methods universe :: [Levitated a] #
type Rep1 Levitated Source #
Instance details Defined in Algebra.Lattice.Levitated type Rep1 Levitated = D1 ('MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.1-FTYhZPoI65oIdMkyt1I5F1" '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) Source #
Instance details Defined in Algebra.Lattice.Levitated type Rep (Levitated a) = D1 ('MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-2.1-FTYhZPoI65oIdMkyt1I5F1" '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 Source #

Interpret Levitated a using the BoundedLattice of a.

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

Fold Levitated.