Safe Haskell	Safe
Language	Haskell2010

Algebra.Lattice.Stacked

Synopsis

data Stacked a b
- = Lower a
- | Upper b
foldStacked :: (l -> r) -> (u -> r) -> Stacked l u -> r

Documentation

data Stacked a b Source #

Stacked two lattices, one on top of another. All minimal elements of upper lattice cover all maximal elements of lower lattice.

Constructors

Lower a
Upper b

Instances

Monad (Stacked a) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods (>>=) :: Stacked a a0 -> (a0 -> Stacked a b) -> Stacked a b # (>>) :: Stacked a a0 -> Stacked a b -> Stacked a b # return :: a0 -> Stacked a a0 # fail :: String -> Stacked a a0 #
Functor (Stacked a) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods fmap :: (a0 -> b) -> Stacked a a0 -> Stacked a b # (<$) :: a0 -> Stacked a b -> Stacked a a0 #
Applicative (Stacked a) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods pure :: a0 -> Stacked a a0 # (<>) :: Stacked a (a0 -> b) -> Stacked a a0 -> Stacked a b # liftA2 :: (a0 -> b -> c) -> Stacked a a0 -> Stacked a b -> Stacked a c # (>) :: Stacked a a0 -> Stacked a b -> Stacked a b # (<*) :: Stacked a a0 -> Stacked a b -> Stacked a a0 #
Foldable (Stacked a) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods fold :: Monoid m => Stacked a m -> m # foldMap :: Monoid m => (a0 -> m) -> Stacked a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Stacked a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Stacked a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Stacked a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Stacked a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Stacked a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Stacked a a0 -> a0 # toList :: Stacked a a0 -> [a0] # null :: Stacked a a0 -> Bool # length :: Stacked a a0 -> Int # elem :: Eq a0 => a0 -> Stacked a a0 -> Bool # maximum :: Ord a0 => Stacked a a0 -> a0 # minimum :: Ord a0 => Stacked a a0 -> a0 # sum :: Num a0 => Stacked a a0 -> a0 # product :: Num a0 => Stacked a a0 -> a0 #
Traversable (Stacked a) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods traverse :: Applicative f => (a0 -> f b) -> Stacked a a0 -> f (Stacked a b) # sequenceA :: Applicative f => Stacked a (f a0) -> f (Stacked a a0) # mapM :: Monad m => (a0 -> m b) -> Stacked a a0 -> m (Stacked a b) # sequence :: Monad m => Stacked a (m a0) -> m (Stacked a a0) #
Generic1 (Stacked a :: Type -> Type) Source #
Instance details Defined in Algebra.Lattice.Stacked Associated Types type Rep1 (Stacked a) :: k -> Type # Methods from1 :: Stacked a a0 -> Rep1 (Stacked a) a0 # to1 :: Rep1 (Stacked a) a0 -> Stacked a a0 #
(Eq a, Eq b) => Eq (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods (==) :: Stacked a b -> Stacked a b -> Bool # (/=) :: Stacked a b -> Stacked a b -> Bool #
(Data a, Data b) => Data (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Stacked a b -> c (Stacked a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Stacked a b) # toConstr :: Stacked a b -> Constr # dataTypeOf :: Stacked a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Stacked a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Stacked a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Stacked a b -> Stacked a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Stacked a b -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Stacked a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Stacked a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Stacked a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Stacked a b -> m (Stacked a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Stacked a b -> m (Stacked a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Stacked a b -> m (Stacked a b) #
(Ord a, Ord b) => Ord (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods compare :: Stacked a b -> Stacked a b -> Ordering # (<) :: Stacked a b -> Stacked a b -> Bool # (<=) :: Stacked a b -> Stacked a b -> Bool # (>) :: Stacked a b -> Stacked a b -> Bool # (>=) :: Stacked a b -> Stacked a b -> Bool # max :: Stacked a b -> Stacked a b -> Stacked a b # min :: Stacked a b -> Stacked a b -> Stacked a b #
(Read a, Read b) => Read (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods readsPrec :: Int -> ReadS (Stacked a b) # readList :: ReadS [Stacked a b] # readPrec :: ReadPrec (Stacked a b) # readListPrec :: ReadPrec [Stacked a b] #
(Show a, Show b) => Show (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods showsPrec :: Int -> Stacked a b -> ShowS # show :: Stacked a b -> String # showList :: [Stacked a b] -> ShowS #
Generic (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Associated Types type Rep (Stacked a b) :: Type -> Type # Methods from :: Stacked a b -> Rep (Stacked a b) x # to :: Rep (Stacked a b) x -> Stacked a b #
(Arbitrary a, Arbitrary b) => Arbitrary (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods arbitrary :: Gen (Stacked a b) # shrink :: Stacked a b -> [Stacked a b] #
(NFData a, NFData b) => NFData (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods rnf :: Stacked a b -> () #
(Hashable a, Hashable b) => Hashable (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods hashWithSalt :: Int -> Stacked a b -> Int # hash :: Stacked a b -> Int #
(Universe a, Universe b) => Universe (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods universe :: [Stacked a b] #
(Finite a, Finite b) => Finite (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods universeF :: [Stacked a b] # cardinality :: Tagged (Stacked a b) Natural #
(PartialOrd a, PartialOrd b) => PartialOrd (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods leq :: Stacked a b -> Stacked a b -> Bool Source # comparable :: Stacked a b -> Stacked a b -> Bool Source #
(Lattice a, BoundedMeetSemiLattice b) => BoundedMeetSemiLattice (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods top :: Stacked a b Source #
(BoundedJoinSemiLattice a, Lattice b) => BoundedJoinSemiLattice (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods bottom :: Stacked a b Source #
(Lattice a, Lattice b) => Lattice (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked Methods (\/) :: Stacked a b -> Stacked a b -> Stacked a b Source # (/\) :: Stacked a b -> Stacked a b -> Stacked a b Source #
type Rep1 (Stacked a :: Type -> Type) Source #
Instance details Defined in Algebra.Lattice.Stacked type Rep1 (Stacked a :: Type -> Type) = D1 (MetaData "Stacked" "Algebra.Lattice.Stacked" "lattices-2.0.2-HdMTcqWeXqlAAQvdNaFFrQ" False) (C1 (MetaCons "Lower" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Upper" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Stacked a b) Source #
Instance details Defined in Algebra.Lattice.Stacked type Rep (Stacked a b) = D1 (MetaData "Stacked" "Algebra.Lattice.Stacked" "lattices-2.0.2-HdMTcqWeXqlAAQvdNaFFrQ" False) (C1 (MetaCons "Lower" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Upper" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b)))

foldStacked :: (l -> r) -> (u -> r) -> Stacked l u -> r Source #