lattices-1.7: Fine-grained library for constructing and manipulating lattices

Copyright(C) 2010-2015 Maximilian Bolingbroke 2015 Oleg Grenrus
LicenseBSD-3-Clause (see the file LICENSE)
MaintainerOleg Grenrus <oleg.grenrus@iki.fi>
Safe HaskellSafe
LanguageHaskell2010

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 # 
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-1.7-LVxdjRPvAj7FxWDUYmNHEJ" 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-1.7-LVxdjRPvAj7FxWDUYmNHEJ" False) ((:+:) (C1 (MetaCons "Top" PrefixI False) U1) (C1 (MetaCons "Drop" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))