Copyright	(C) 2010-2015 Maximilian Bolingbroke 2015 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

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

Top
Levitate a
Bottom

Instances

Monad Levitated Source #
Methods (>>=) :: Levitated a -> (a -> Levitated b) -> Levitated b # (>>) :: Levitated a -> Levitated b -> Levitated b # return :: a -> Levitated a # fail :: String -> Levitated a #
Functor Levitated Source #
Methods fmap :: (a -> b) -> Levitated a -> Levitated b # (<$) :: a -> Levitated b -> Levitated a #
Applicative Levitated Source #
Methods pure :: a -> Levitated a # (<>) :: Levitated (a -> b) -> Levitated a -> Levitated b # (>) :: Levitated a -> Levitated b -> Levitated b # (<*) :: Levitated a -> Levitated b -> Levitated a #
Foldable Levitated Source #
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 Source #
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) #
Generic1 Levitated Source #
Associated Types type Rep1 (Levitated :: * -> ) :: -> * # Methods from1 :: Levitated a -> Rep1 Levitated a # to1 :: Rep1 Levitated a -> Levitated a #
Eq a => Eq (Levitated a) Source #
Methods (==) :: Levitated a -> Levitated a -> Bool # (/=) :: Levitated a -> Levitated a -> Bool #
Data a => Data (Levitated a) Source #
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) Source #
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) Source #
Methods readsPrec :: Int -> ReadS (Levitated a) # readList :: ReadS [Levitated a] # readPrec :: ReadPrec (Levitated a) # readListPrec :: ReadPrec [Levitated a] #
Show a => Show (Levitated a) Source #
Methods showsPrec :: Int -> Levitated a -> ShowS # show :: Levitated a -> String # showList :: [Levitated a] -> ShowS #
Generic (Levitated a) Source #
Associated Types type Rep (Levitated a) :: * -> * # Methods from :: Levitated a -> Rep (Levitated a) x # to :: Rep (Levitated a) x -> Levitated a #
NFData a => NFData (Levitated a) Source #
Methods rnf :: Levitated a -> () #
Hashable a => Hashable (Levitated a) Source #
Methods hashWithSalt :: Int -> Levitated a -> Int # hash :: Levitated a -> Int #
Lattice a => BoundedLattice (Levitated a) Source #

MeetSemiLattice a => BoundedMeetSemiLattice (Levitated a) Source #
Methods top :: Levitated a Source #
JoinSemiLattice a => BoundedJoinSemiLattice (Levitated a) Source #
Methods bottom :: Levitated a Source #
Lattice a => Lattice (Levitated a) Source #

MeetSemiLattice a => MeetSemiLattice (Levitated a) Source #
Methods (/\) :: Levitated a -> Levitated a -> Levitated a Source # meet :: Levitated a -> Levitated a -> Levitated a Source #
JoinSemiLattice a => JoinSemiLattice (Levitated a) Source #
Methods (\/) :: Levitated a -> Levitated a -> Levitated a Source # join :: Levitated a -> Levitated a -> Levitated a Source #
type Rep1 Levitated Source #
type Rep1 Levitated = D1 (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" False) ((:+:) (C1 (MetaCons "Top" PrefixI False) U1) ((:+:) (C1 (MetaCons "Levitate" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) (C1 (MetaCons "Bottom" PrefixI False) U1)))
type Rep (Levitated a) Source #
type Rep (Levitated a) = D1 (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" False) ((:+:) (C1 (MetaCons "Top" PrefixI False) U1) ((:+:) (C1 (MetaCons "Levitate" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) (C1 (MetaCons "Bottom" PrefixI False) U1)))

retractLevitated :: BoundedLattice a => Levitated a -> a Source #

Interpret Levitated a using the BoundedLattice of a.