lattices-2.0.2: Fine-grained library for constructing and manipulating lattices

Copyright(C) 2010-2015 Maximilian Bolingbroke 2015-2019 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

Drop a 
Top 
Instances
Monad Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

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 # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

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

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

Applicative Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

pure :: a -> Dropped a #

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

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

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

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

Foldable Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

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 # 
Instance details

Defined in Algebra.Lattice.Dropped

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) #

Eq a => Eq (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

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

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

Data a => Data (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

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 # 
Instance details

Defined in Algebra.Lattice.Dropped

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 # 
Instance details

Defined in Algebra.Lattice.Dropped

Show a => Show (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

showsPrec :: Int -> Dropped a -> ShowS #

show :: Dropped a -> String #

showList :: [Dropped a] -> ShowS #

Generic (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Associated Types

type Rep (Dropped a) :: Type -> Type #

Methods

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

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

Function a => Function (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

function :: (Dropped a -> b) -> Dropped a :-> b #

Arbitrary a => Arbitrary (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

arbitrary :: Gen (Dropped a) #

shrink :: Dropped a -> [Dropped a] #

CoArbitrary a => CoArbitrary (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

coarbitrary :: Dropped a -> Gen b -> Gen b #

NFData a => NFData (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

rnf :: Dropped a -> () #

Hashable a => Hashable (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

hashWithSalt :: Int -> Dropped a -> Int #

hash :: Dropped a -> Int #

Universe a => Universe (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

universe :: [Dropped a] #

Finite a => Finite (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

PartialOrd a => PartialOrd (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

leq :: Dropped a -> Dropped a -> Bool Source #

comparable :: Dropped a -> Dropped a -> Bool Source #

Lattice a => BoundedMeetSemiLattice (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

top :: Dropped a Source #

BoundedJoinSemiLattice a => BoundedJoinSemiLattice (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

bottom :: Dropped a Source #

Lattice a => Lattice (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

(\/) :: Dropped a -> Dropped a -> Dropped a Source #

(/\) :: Dropped a -> Dropped a -> Dropped a Source #

Generic1 Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Associated Types

type Rep1 Dropped :: k -> Type #

Methods

from1 :: Dropped a -> Rep1 Dropped a #

to1 :: Rep1 Dropped a -> Dropped a #

type Rep (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

type Rep (Dropped a) = D1 (MetaData "Dropped" "Algebra.Lattice.Dropped" "lattices-2.0.2-HdMTcqWeXqlAAQvdNaFFrQ" False) (C1 (MetaCons "Drop" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Top" PrefixI False) (U1 :: Type -> Type))
type Rep1 Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

type Rep1 Dropped = D1 (MetaData "Dropped" "Algebra.Lattice.Dropped" "lattices-2.0.2-HdMTcqWeXqlAAQvdNaFFrQ" False) (C1 (MetaCons "Drop" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) :+: C1 (MetaCons "Top" PrefixI False) (U1 :: Type -> Type))

foldDropped :: b -> (a -> b) -> Dropped a -> b Source #

Similar to maybe, but for Dropped type.