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 Rep (Dropped a) Source

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

Interpret Dropped a using the BoundedMeetSemiLattice of a.