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.Lifted

Description

Synopsis

data Lifted a
- = Bottom
- | Lift a
retractLifted :: BoundedJoinSemiLattice a => Lifted a -> a
foldLifted :: b -> (a -> b) -> Lifted a -> b

Documentation

data Lifted a Source #

Graft a distinct bottom onto an otherwise unbounded lattice. As a bonus, the bottom will be an absorbing element for the meet.

Constructors

Bottom
Lift a

Instances

Instances details

Monad Lifted Source #
Instance details Defined in Algebra.Lattice.Lifted Methods (>>=) :: Lifted a -> (a -> Lifted b) -> Lifted b Source # (>>) :: Lifted a -> Lifted b -> Lifted b Source # return :: a -> Lifted a Source #
Functor Lifted Source #
Instance details Defined in Algebra.Lattice.Lifted Methods fmap :: (a -> b) -> Lifted a -> Lifted b Source # (<$) :: a -> Lifted b -> Lifted a Source #
Applicative Lifted Source #
Instance details Defined in Algebra.Lattice.Lifted Methods pure :: a -> Lifted a Source # (<>) :: Lifted (a -> b) -> Lifted a -> Lifted b Source # liftA2 :: (a -> b -> c) -> Lifted a -> Lifted b -> Lifted c Source # (>) :: Lifted a -> Lifted b -> Lifted b Source # (<*) :: Lifted a -> Lifted b -> Lifted a Source #
Foldable Lifted Source #
Instance details Defined in Algebra.Lattice.Lifted Methods fold :: Monoid m => Lifted m -> m Source # foldMap :: Monoid m => (a -> m) -> Lifted a -> m Source # foldMap' :: Monoid m => (a -> m) -> Lifted a -> m Source # foldr :: (a -> b -> b) -> b -> Lifted a -> b Source # foldr' :: (a -> b -> b) -> b -> Lifted a -> b Source # foldl :: (b -> a -> b) -> b -> Lifted a -> b Source # foldl' :: (b -> a -> b) -> b -> Lifted a -> b Source # foldr1 :: (a -> a -> a) -> Lifted a -> a Source # foldl1 :: (a -> a -> a) -> Lifted a -> a Source # toList :: Lifted a -> [a] Source # null :: Lifted a -> Bool Source # length :: Lifted a -> Int Source # elem :: Eq a => a -> Lifted a -> Bool Source # maximum :: Ord a => Lifted a -> a Source # minimum :: Ord a => Lifted a -> a Source # sum :: Num a => Lifted a -> a Source # product :: Num a => Lifted a -> a Source #
Traversable Lifted Source #
Instance details Defined in Algebra.Lattice.Lifted Methods traverse :: Applicative f => (a -> f b) -> Lifted a -> f ( Lifted b) Source # sequenceA :: Applicative f => Lifted (f a) -> f ( Lifted a) Source # mapM :: Monad m => (a -> m b) -> Lifted a -> m ( Lifted b) Source # sequence :: Monad m => Lifted (m a) -> m ( Lifted a) Source #
Eq a => Eq ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods (==) :: Lifted a -> Lifted a -> Bool Source # (/=) :: Lifted a -> Lifted a -> Bool Source #
Data a => Data ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> Lifted a -> c ( Lifted a) Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c ( Lifted a) Source # toConstr :: Lifted a -> Constr Source # dataTypeOf :: Lifted a -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c ( Lifted a)) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c ( Lifted a)) Source # gmapT :: ( forall b. Data b => b -> b) -> Lifted a -> Lifted a Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Lifted a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Lifted a -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Lifted a -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Lifted a -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Lifted a -> m ( Lifted a) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Lifted a -> m ( Lifted a) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Lifted a -> m ( Lifted a) Source #
Ord a => Ord ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods compare :: Lifted a -> Lifted a -> Ordering Source # (<) :: Lifted a -> Lifted a -> Bool Source # (<=) :: Lifted a -> Lifted a -> Bool Source # (>) :: Lifted a -> Lifted a -> Bool Source # (>=) :: Lifted a -> Lifted a -> Bool Source # max :: Lifted a -> Lifted a -> Lifted a Source # min :: Lifted a -> Lifted a -> Lifted a Source #
Read a => Read ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods readsPrec :: Int -> ReadS ( Lifted a) Source # readList :: ReadS [ Lifted a] Source # readPrec :: ReadPrec ( Lifted a) Source # readListPrec :: ReadPrec [ Lifted a] Source #
Show a => Show ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods showsPrec :: Int -> Lifted a -> ShowS Source # show :: Lifted a -> String Source # showList :: [ Lifted a] -> ShowS Source #
Generic ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Associated Types type Rep ( Lifted a) :: Type -> Type Source # Methods from :: Lifted a -> Rep ( Lifted a) x Source # to :: Rep ( Lifted a) x -> Lifted a Source #
Function a => Function ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods function :: ( Lifted a -> b) -> Lifted a :-> b Source #
Arbitrary a => Arbitrary ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods arbitrary :: Gen ( Lifted a) Source # shrink :: Lifted a -> [ Lifted a] Source #
CoArbitrary a => CoArbitrary ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods coarbitrary :: Lifted a -> Gen b -> Gen b Source #
NFData a => NFData ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods rnf :: Lifted a -> () Source #
Hashable a => Hashable ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods hashWithSalt :: Int -> Lifted a -> Int Source # hash :: Lifted a -> Int Source #
Universe a => Universe ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods universe :: [ Lifted a] Source #
Finite a => Finite ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods universeF :: [ Lifted a] Source # cardinality :: Tagged ( Lifted a) Natural Source #
PartialOrd a => PartialOrd ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods leq :: Lifted a -> Lifted a -> Bool Source # comparable :: Lifted a -> Lifted a -> Bool Source #
BoundedMeetSemiLattice a => BoundedMeetSemiLattice ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods top :: Lifted a Source #
Lattice a => BoundedJoinSemiLattice ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods bottom :: Lifted a Source #
Lattice a => Lattice ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted Methods (\/) :: Lifted a -> Lifted a -> Lifted a Source # (/\) :: Lifted a -> Lifted a -> Lifted a Source #
Generic1 Lifted Source #
Instance details Defined in Algebra.Lattice.Lifted Associated Types type Rep1 Lifted :: k -> Type Source # Methods from1 :: forall (a :: k). Lifted a -> Rep1 Lifted a Source # to1 :: forall (a :: k). Rep1 Lifted a -> Lifted a Source #
type Rep ( Lifted a) Source #
Instance details Defined in Algebra.Lattice.Lifted type Rep ( Lifted a) = D1 (' MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' False ) ( C1 (' MetaCons "Bottom" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: C1 (' MetaCons "Lift" ' PrefixI ' False ) ( S1 (' MetaSel (' Nothing :: Maybe Symbol ) ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 a)))
type Rep1 Lifted Source #
Instance details Defined in Algebra.Lattice.Lifted type Rep1 Lifted = D1 (' MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-2.1-Aj77JapAM1ZIiO74F5gL5i" ' False ) ( C1 (' MetaCons "Bottom" ' PrefixI ' False ) ( U1 :: Type -> Type ) :+: C1 (' MetaCons "Lift" ' PrefixI ' False ) ( S1 (' MetaSel (' Nothing :: Maybe Symbol ) ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) Par1 ))

retractLifted :: BoundedJoinSemiLattice a => Lifted a -> a Source #

Interpret Lifted a using the BoundedJoinSemiLattice of a .

foldLifted :: b -> (a -> b) -> Lifted a -> b Source #

Similar to maybe , but for Lifted type.