lattices-2.2.1.1: 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

Instances details
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

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)

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

Functor Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Methods

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

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

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

Generic1 Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Associated Types

type Rep1 Dropped 
Instance details

Defined in Algebra.Lattice.Dropped

type Rep1 Dropped = D1 ('MetaData "Dropped" "Algebra.Lattice.Dropped" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) (C1 ('MetaCons "Drop" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type))

Methods

from1 :: Dropped a -> Rep1 Dropped a

to1 :: Rep1 Dropped a -> Dropped a

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

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

Defined in Algebra.Lattice.Dropped

Methods

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

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 :: forall r r'. (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)

Generic (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

Associated Types

type Rep (Dropped a) 
Instance details

Defined in Algebra.Lattice.Dropped

type Rep (Dropped a) = D1 ('MetaData "Dropped" "Algebra.Lattice.Dropped" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) (C1 ('MetaCons "Drop" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type))

Methods

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

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

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

Defined in Algebra.Lattice.Dropped

Methods

readsPrec :: Int -> ReadS (Dropped a)

readList :: ReadS [Dropped a]

readPrec :: ReadPrec (Dropped a)

readListPrec :: ReadPrec [Dropped a]

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

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

Defined in Algebra.Lattice.Dropped

Methods

rnf :: 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

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

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

Defined in Algebra.Lattice.Dropped

Methods

hashWithSalt :: Int -> Dropped a -> Int

hash :: Dropped a -> Int

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

Defined in Algebra.Lattice.Dropped

Methods

bottom :: Dropped a Source #

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

Defined in Algebra.Lattice.Dropped

Methods

top :: 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 #

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 #

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

Defined in Algebra.Lattice.Dropped

Methods

universeF :: [Dropped a]

cardinality :: Tagged (Dropped a) Natural

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

Defined in Algebra.Lattice.Dropped

Methods

universe :: [Dropped a]

type Rep1 Dropped Source # 
Instance details

Defined in Algebra.Lattice.Dropped

type Rep1 Dropped = D1 ('MetaData "Dropped" "Algebra.Lattice.Dropped" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) (C1 ('MetaCons "Drop" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type))
type Rep (Dropped a) Source # 
Instance details

Defined in Algebra.Lattice.Dropped

type Rep (Dropped a) = D1 ('MetaData "Dropped" "Algebra.Lattice.Dropped" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) (C1 ('MetaCons "Drop" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type))

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

Similar to maybe, but for Dropped type.