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.Lifted

Description

Synopsis

Documentation

data Lifted a Source

Graft a distinct bottom onto an otherwise unbounded lattice. As a bonus, the bottom will be an absorbing element for the meet.

Constructors

Lift a
Bottom

Instances

Monad Lifted Source
Methods (>>=) :: Lifted a -> (a -> Lifted b) -> Lifted b (>>) :: Lifted a -> Lifted b -> Lifted b return :: a -> Lifted a fail :: String -> Lifted a
Functor Lifted Source
Methods fmap :: (a -> b) -> Lifted a -> Lifted b (<$) :: a -> Lifted b -> Lifted a
Applicative Lifted Source
Methods pure :: a -> Lifted a (<>) :: Lifted (a -> b) -> Lifted a -> Lifted b (>) :: Lifted a -> Lifted b -> Lifted b (<*) :: Lifted a -> Lifted b -> Lifted a
Foldable Lifted Source
Methods fold :: Monoid m => Lifted m -> m foldMap :: Monoid m => (a -> m) -> Lifted a -> m foldr :: (a -> b -> b) -> b -> Lifted a -> b foldr' :: (a -> b -> b) -> b -> Lifted a -> b foldl :: (b -> a -> b) -> b -> Lifted a -> b foldl' :: (b -> a -> b) -> b -> Lifted a -> b foldr1 :: (a -> a -> a) -> Lifted a -> a foldl1 :: (a -> a -> a) -> Lifted a -> a toList :: Lifted a -> [a] null :: Lifted a -> Bool length :: Lifted a -> Int elem :: Eq a => a -> Lifted a -> Bool maximum :: Ord a => Lifted a -> a minimum :: Ord a => Lifted a -> a sum :: Num a => Lifted a -> a product :: Num a => Lifted a -> a
Traversable Lifted Source
Methods traverse :: Applicative f => (a -> f b) -> Lifted a -> f (Lifted b) sequenceA :: Applicative f => Lifted (f a) -> f (Lifted a) mapM :: Monad m => (a -> m b) -> Lifted a -> m (Lifted b) sequence :: Monad m => Lifted (m a) -> m (Lifted a)
Generic1 Lifted Source
Associated Types type Rep1 (Lifted :: * -> ) :: -> * Methods from1 :: Lifted a -> Rep1 Lifted a to1 :: Rep1 Lifted a -> Lifted a
Eq a => Eq (Lifted a) Source
Methods (==) :: Lifted a -> Lifted a -> Bool (/=) :: Lifted a -> Lifted a -> Bool
Data a => Data (Lifted a) Source
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Lifted a -> c (Lifted a) gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Lifted a) toConstr :: Lifted a -> Constr dataTypeOf :: Lifted a -> DataType dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Lifted a)) dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Lifted a)) gmapT :: (forall b. Data b => b -> b) -> Lifted a -> Lifted a gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Lifted a -> r gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Lifted a -> r gmapQ :: (forall d. Data d => d -> u) -> Lifted a -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Lifted a -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a) gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a) gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a)
Ord a => Ord (Lifted a) Source
Methods compare :: Lifted a -> Lifted a -> Ordering (<) :: Lifted a -> Lifted a -> Bool (<=) :: Lifted a -> Lifted a -> Bool (>) :: Lifted a -> Lifted a -> Bool (>=) :: Lifted a -> Lifted a -> Bool max :: Lifted a -> Lifted a -> Lifted a min :: Lifted a -> Lifted a -> Lifted a
Read a => Read (Lifted a) Source
Methods readsPrec :: Int -> ReadS (Lifted a) readList :: ReadS [Lifted a] readPrec :: ReadPrec (Lifted a) readListPrec :: ReadPrec [Lifted a]
Show a => Show (Lifted a) Source
Methods showsPrec :: Int -> Lifted a -> ShowS show :: Lifted a -> String showList :: [Lifted a] -> ShowS
Generic (Lifted a) Source
Associated Types type Rep (Lifted a) :: * -> * Methods from :: Lifted a -> Rep (Lifted a) x to :: Rep (Lifted a) x -> Lifted a
NFData a => NFData (Lifted a) Source
Methods rnf :: Lifted a -> ()
Hashable a => Hashable (Lifted a) Source
Methods hashWithSalt :: Int -> Lifted a -> Int hash :: Lifted a -> Int
BoundedLattice a => BoundedLattice (Lifted a) Source

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Lifted a) Source
Methods top :: Lifted a Source
JoinSemiLattice a => BoundedJoinSemiLattice (Lifted a) Source
Methods bottom :: Lifted a Source
Lattice a => Lattice (Lifted a) Source

MeetSemiLattice a => MeetSemiLattice (Lifted a) Source
Methods (/\) :: Lifted a -> Lifted a -> Lifted a Source meet :: Lifted a -> Lifted a -> Lifted a Source
JoinSemiLattice a => JoinSemiLattice (Lifted a) Source
Methods (\/) :: Lifted a -> Lifted a -> Lifted a Source join :: Lifted a -> Lifted a -> Lifted a Source
type Rep1 Lifted Source
type Rep (Lifted a) Source

retractLifted :: BoundedJoinSemiLattice a => Lifted a -> a Source

Interpret Lifted a using the BoundedJoinSemiLattice of a.