lattices-1.7.1: 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.Levitated

Description

 

Synopsis

Documentation

data Levitated a Source #

Graft a distinct top and bottom onto an otherwise unbounded lattice. The top is the absorbing element for the join, and the bottom is the absorbing element for the meet.

Constructors

Top 
Levitate a 
Bottom 

Instances

Monad Levitated Source # 

Methods

(>>=) :: Levitated a -> (a -> Levitated b) -> Levitated b #

(>>) :: Levitated a -> Levitated b -> Levitated b #

return :: a -> Levitated a #

fail :: String -> Levitated a #

Functor Levitated Source # 

Methods

fmap :: (a -> b) -> Levitated a -> Levitated b #

(<$) :: a -> Levitated b -> Levitated a #

Applicative Levitated Source # 

Methods

pure :: a -> Levitated a #

(<*>) :: Levitated (a -> b) -> Levitated a -> Levitated b #

liftA2 :: (a -> b -> c) -> Levitated a -> Levitated b -> Levitated c #

(*>) :: Levitated a -> Levitated b -> Levitated b #

(<*) :: Levitated a -> Levitated b -> Levitated a #

Foldable Levitated Source # 

Methods

fold :: Monoid m => Levitated m -> m #

foldMap :: Monoid m => (a -> m) -> Levitated a -> m #

foldr :: (a -> b -> b) -> b -> Levitated a -> b #

foldr' :: (a -> b -> b) -> b -> Levitated a -> b #

foldl :: (b -> a -> b) -> b -> Levitated a -> b #

foldl' :: (b -> a -> b) -> b -> Levitated a -> b #

foldr1 :: (a -> a -> a) -> Levitated a -> a #

foldl1 :: (a -> a -> a) -> Levitated a -> a #

toList :: Levitated a -> [a] #

null :: Levitated a -> Bool #

length :: Levitated a -> Int #

elem :: Eq a => a -> Levitated a -> Bool #

maximum :: Ord a => Levitated a -> a #

minimum :: Ord a => Levitated a -> a #

sum :: Num a => Levitated a -> a #

product :: Num a => Levitated a -> a #

Traversable Levitated Source # 

Methods

traverse :: Applicative f => (a -> f b) -> Levitated a -> f (Levitated b) #

sequenceA :: Applicative f => Levitated (f a) -> f (Levitated a) #

mapM :: Monad m => (a -> m b) -> Levitated a -> m (Levitated b) #

sequence :: Monad m => Levitated (m a) -> m (Levitated a) #

Eq a => Eq (Levitated a) Source # 

Methods

(==) :: Levitated a -> Levitated a -> Bool #

(/=) :: Levitated a -> Levitated a -> Bool #

Data a => Data (Levitated a) Source # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Levitated a -> c (Levitated a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Levitated a) #

toConstr :: Levitated a -> Constr #

dataTypeOf :: Levitated a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Levitated a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Levitated a)) #

gmapT :: (forall b. Data b => b -> b) -> Levitated a -> Levitated a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Levitated a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Levitated a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Levitated a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Levitated a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Levitated a -> m (Levitated a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Levitated a -> m (Levitated a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Levitated a -> m (Levitated a) #

Ord a => Ord (Levitated a) Source # 
Read a => Read (Levitated a) Source # 
Show a => Show (Levitated a) Source # 
Generic (Levitated a) Source # 

Associated Types

type Rep (Levitated a) :: * -> * #

Methods

from :: Levitated a -> Rep (Levitated a) x #

to :: Rep (Levitated a) x -> Levitated a #

NFData a => NFData (Levitated a) Source # 

Methods

rnf :: Levitated a -> () #

Hashable a => Hashable (Levitated a) Source # 

Methods

hashWithSalt :: Int -> Levitated a -> Int #

hash :: Levitated a -> Int #

Lattice a => BoundedLattice (Levitated a) Source # 
MeetSemiLattice a => BoundedMeetSemiLattice (Levitated a) Source # 

Methods

top :: Levitated a Source #

JoinSemiLattice a => BoundedJoinSemiLattice (Levitated a) Source # 

Methods

bottom :: Levitated a Source #

Lattice a => Lattice (Levitated a) Source # 
MeetSemiLattice a => MeetSemiLattice (Levitated a) Source # 
JoinSemiLattice a => JoinSemiLattice (Levitated a) Source # 
Generic1 * Levitated Source # 

Associated Types

type Rep1 Levitated (f :: Levitated -> *) :: k -> * #

Methods

from1 :: f a -> Rep1 Levitated f a #

to1 :: Rep1 Levitated f a -> f a #

type Rep (Levitated a) Source # 
type Rep (Levitated a) = D1 * (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" False) ((:+:) * (C1 * (MetaCons "Top" PrefixI False) (U1 *)) ((:+:) * (C1 * (MetaCons "Levitate" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a))) (C1 * (MetaCons "Bottom" PrefixI False) (U1 *))))
type Rep1 * Levitated Source # 
type Rep1 * Levitated = D1 * (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" False) ((:+:) * (C1 * (MetaCons "Top" PrefixI False) (U1 *)) ((:+:) * (C1 * (MetaCons "Levitate" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) (C1 * (MetaCons "Bottom" PrefixI False) (U1 *))))

retractLevitated :: BoundedLattice a => Levitated a -> a Source #

Interpret Levitated a using the BoundedLattice of a.