Algebra.Lattice.Stacked

Documentation

data Stacked a b

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)

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

Functor (Stacked a)

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)

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)

Defined in Algebra.Lattice.Stacked

Methods

fold :: Monoid m => Stacked a m -> m

foldMap :: Monoid m => (a0 -> m) -> Stacked a a0 -> 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)

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)

Defined in Algebra.Lattice.Stacked

Associated Types

type Rep1 (Stacked a) :: k -> Type

Methods

from1 :: forall (a0 :: k). Stacked a a0 -> Rep1 (Stacked a) a0

to1 :: forall (a0 :: k). Rep1 (Stacked a) a0 -> Stacked a a0

(Eq a, Eq b) => Eq (Stacked a b)

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)

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 :: forall r r'. (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)

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)

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)

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)

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)

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)

Defined in Algebra.Lattice.Stacked

Methods

rnf :: Stacked a b -> ()

(Hashable a, Hashable b) => Hashable (Stacked a b)

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)

Defined in Algebra.Lattice.Stacked

Methods

universe :: [Stacked a b]

(Finite a, Finite b) => Finite (Stacked a b)

Defined in Algebra.Lattice.Stacked

Methods

universeF :: [Stacked a b]

cardinality :: Tagged (Stacked a b) Natural

(PartialOrd a, PartialOrd b) => PartialOrd (Stacked a b)

Defined in Algebra.Lattice.Stacked

Methods

leq :: Stacked a b -> Stacked a b -> Bool

comparable :: Stacked a b -> Stacked a b -> Bool

(Lattice a, BoundedMeetSemiLattice b) => BoundedMeetSemiLattice (Stacked a b)

Defined in Algebra.Lattice.Stacked

Methods

top :: Stacked a b

(BoundedJoinSemiLattice a, Lattice b) => BoundedJoinSemiLattice (Stacked a b)

Defined in Algebra.Lattice.Stacked

Methods

bottom :: Stacked a b

(Lattice a, Lattice b) => Lattice (Stacked a b)

Defined in Algebra.Lattice.Stacked

Methods

(\/) :: Stacked a b -> Stacked a b -> Stacked a b

(/\) :: Stacked a b -> Stacked a b -> Stacked a b

type Rep1 (Stacked a :: Type -> Type)

Defined in Algebra.Lattice.Stacked

type Rep1 (Stacked a :: Type -> Type) = D1 ('MetaData "Stacked" "Algebra.Lattice.Stacked" "lattices-2.0.3-JaQkD7oObsZDbblLH9Uars" '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)

Defined in Algebra.Lattice.Stacked

type Rep (Stacked a b) = D1 ('MetaData "Stacked" "Algebra.Lattice.Stacked" "lattices-2.0.3-JaQkD7oObsZDbblLH9Uars" '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