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.Wide

Description

Synopsis

data Wide a
- = Top
- | Middle a
- | Bottom

Documentation

data Wide a Source #

Graft a distinct top and bottom onto any type. The Top is identity for /\ and the absorbing element for \/ . The Bottom is the identity for \/ and and the absorbing element for /\ . Two Middle values join to top, unless they are equal.

Constructors

Top
Middle a
Bottom

Instances

Instances details

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