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.Dropped

Description

Synopsis

Documentation

data Dropped a Source #

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

Constructors

Top
Drop a

Instances

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

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

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

retractDropped :: BoundedMeetSemiLattice a => Dropped a -> a Source #

Interpret Dropped a using the BoundedMeetSemiLattice of a.