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 Rep1 Lifted = D1 (MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" False) ((:+:) (C1 (MetaCons "Lift" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) (C1 (MetaCons "Bottom" PrefixI False) U1))
type Rep (Lifted a) Source #
type Rep (Lifted a) = D1 (MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-1.6.0-2oKxOcsrwg99Rpe11Qz7rb" False) ((:+:) (C1 (MetaCons "Lift" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) (C1 (MetaCons "Bottom" PrefixI False) U1))

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

Interpret Lifted a using the BoundedJoinSemiLattice of a.