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

data Dropped a
- = Drop a
- | Top
retractDropped :: BoundedMeetSemiLattice a => Dropped a -> a
foldDropped :: b -> (a -> b) -> Dropped a -> b

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

Monad Dropped Source #
Instance details Defined in Algebra.Lattice.Dropped Methods (>>=) :: Dropped a -> (a -> Dropped b) -> Dropped b Source # (>>) :: Dropped a -> Dropped b -> Dropped b Source # return :: a -> Dropped a Source #
Functor Dropped Source #
Instance details Defined in Algebra.Lattice.Dropped Methods fmap :: (a -> b) -> Dropped a -> Dropped b Source # (<$) :: a -> Dropped b -> Dropped a Source #
Applicative Dropped Source #
Instance details Defined in Algebra.Lattice.Dropped Methods pure :: a -> Dropped a Source # (<>) :: Dropped (a -> b) -> Dropped a -> Dropped b Source # liftA2 :: (a -> b -> c) -> Dropped a -> Dropped b -> Dropped c Source # (>) :: Dropped a -> Dropped b -> Dropped b Source # (<*) :: Dropped a -> Dropped b -> Dropped a Source #
Foldable Dropped Source #
Instance details Defined in Algebra.Lattice.Dropped Methods fold :: Monoid m => Dropped m -> m Source # foldMap :: Monoid m => (a -> m) -> Dropped a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dropped a -> m Source # foldr :: (a -> b -> b) -> b -> Dropped a -> b Source # foldr' :: (a -> b -> b) -> b -> Dropped a -> b Source # foldl :: (b -> a -> b) -> b -> Dropped a -> b Source # foldl' :: (b -> a -> b) -> b -> Dropped a -> b Source # foldr1 :: (a -> a -> a) -> Dropped a -> a Source # foldl1 :: (a -> a -> a) -> Dropped a -> a Source # toList :: Dropped a -> [a] Source # null :: Dropped a -> Bool Source # length :: Dropped a -> Int Source # elem :: Eq a => a -> Dropped a -> Bool Source # maximum :: Ord a => Dropped a -> a Source # minimum :: Ord a => Dropped a -> a Source # sum :: Num a => Dropped a -> a Source # product :: Num a => Dropped a -> a Source #
Traversable Dropped Source #
Instance details Defined in Algebra.Lattice.Dropped Methods traverse :: Applicative f => (a -> f b) -> Dropped a -> f ( Dropped b) Source # sequenceA :: Applicative f => Dropped (f a) -> f ( Dropped a) Source # mapM :: Monad m => (a -> m b) -> Dropped a -> m ( Dropped b) Source # sequence :: Monad m => Dropped (m a) -> m ( Dropped a) Source #
Eq a => Eq ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods (==) :: Dropped a -> Dropped a -> Bool Source # (/=) :: Dropped a -> Dropped a -> Bool Source #
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) Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c ( Dropped a) Source # toConstr :: Dropped a -> Constr Source # dataTypeOf :: Dropped a -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c ( Dropped a)) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c ( Dropped a)) Source # gmapT :: ( forall b. Data b => b -> b) -> Dropped a -> Dropped a Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Dropped a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Dropped a -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Dropped a -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Dropped a -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Dropped a -> m ( Dropped a) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Dropped a -> m ( Dropped a) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Dropped a -> m ( Dropped a) Source #
Ord a => Ord ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods compare :: Dropped a -> Dropped a -> Ordering Source # (<) :: Dropped a -> Dropped a -> Bool Source # (<=) :: Dropped a -> Dropped a -> Bool Source # (>) :: Dropped a -> Dropped a -> Bool Source # (>=) :: Dropped a -> Dropped a -> Bool Source # max :: Dropped a -> Dropped a -> Dropped a Source # min :: Dropped a -> Dropped a -> Dropped a Source #
Read a => Read ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods readsPrec :: Int -> ReadS ( Dropped a) Source # readList :: ReadS [ Dropped a] Source # readPrec :: ReadPrec ( Dropped a) Source # readListPrec :: ReadPrec [ Dropped a] Source #
Show a => Show ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods showsPrec :: Int -> Dropped a -> ShowS Source # show :: Dropped a -> String Source # showList :: [ Dropped a] -> ShowS Source #
Generic ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Associated Types type Rep ( Dropped a) :: Type -> Type Source # Methods from :: Dropped a -> Rep ( Dropped a) x Source # to :: Rep ( Dropped a) x -> Dropped a Source #
Function a => Function ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods function :: ( Dropped a -> b) -> Dropped a :-> b Source #
Arbitrary a => Arbitrary ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods arbitrary :: Gen ( Dropped a) Source # shrink :: Dropped a -> [ Dropped a] Source #
CoArbitrary a => CoArbitrary ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods coarbitrary :: Dropped a -> Gen b -> Gen b Source #
NFData a => NFData ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods rnf :: Dropped a -> () Source #
Hashable a => Hashable ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods hashWithSalt :: Int -> Dropped a -> Int Source # hash :: Dropped a -> Int Source #
Universe a => Universe ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods universe :: [ Dropped a] Source #
Finite a => Finite ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped Methods universeF :: [ Dropped a] Source # cardinality :: Tagged ( Dropped a) Natural 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 #
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 Source # Methods from1 :: forall (a :: k). Dropped a -> Rep1 Dropped a Source # to1 :: forall (a :: k). Rep1 Dropped a -> Dropped a Source #
type Rep ( Dropped a) Source #
Instance details Defined in Algebra.Lattice.Dropped type Rep ( Dropped a) = D1 (' MetaData "Dropped" "Algebra.Lattice.Dropped" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' 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-2.1-Aj77JapAM1ZIiO74F5gL5i" ' False ) ( C1 (' MetaCons "Drop" ' PrefixI ' False ) ( S1 (' MetaSel (' Nothing :: Maybe Symbol ) ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) Par1 ) :+: C1 (' MetaCons "Top" ' PrefixI ' False ) ( U1 :: Type -> Type ))

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

Interpret Dropped a using the BoundedMeetSemiLattice of a .

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

Similar to maybe , but for Dropped type.