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 Rep (Levitated a) Source

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

Interpret Levitated a using the BoundedLattice of a.