Algebra.Lattice.Lifted

Documentation

data Lifted a

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

Constructors

Lift a

Bottom

Instances

Monad Lifted

Methods

(>>=) :: Lifted a -> (a -> Lifted b) -> Lifted b

(>>) :: Lifted a -> Lifted b -> Lifted b

return :: a -> Lifted a

fail :: String -> Lifted a

Functor Lifted

Methods

fmap :: (a -> b) -> Lifted a -> Lifted b

(<$) :: a -> Lifted b -> Lifted a

Applicative Lifted

Methods

pure :: a -> Lifted a

(<*>) :: Lifted (a -> b) -> Lifted a -> Lifted b

liftA2 :: (a -> b -> c) -> Lifted a -> Lifted b -> Lifted c

(*>) :: Lifted a -> Lifted b -> Lifted b

(<*) :: Lifted a -> Lifted b -> Lifted a

Foldable Lifted

Methods

fold :: Monoid m => Lifted m -> m

foldMap :: Monoid m => (a -> m) -> Lifted a -> m

foldr :: (a -> b -> b) -> b -> Lifted a -> b

foldr' :: (a -> b -> b) -> b -> Lifted a -> b

foldl :: (b -> a -> b) -> b -> Lifted a -> b

foldl' :: (b -> a -> b) -> b -> Lifted a -> b

foldr1 :: (a -> a -> a) -> Lifted a -> a

foldl1 :: (a -> a -> a) -> Lifted a -> a

toList :: Lifted a -> [a]

null :: Lifted a -> Bool

length :: Lifted a -> Int

elem :: Eq a => a -> Lifted a -> Bool

maximum :: Ord a => Lifted a -> a

minimum :: Ord a => Lifted a -> a

sum :: Num a => Lifted a -> a

product :: Num a => Lifted a -> a

Traversable Lifted

Methods

traverse :: Applicative f => (a -> f b) -> Lifted a -> f (Lifted b)

sequenceA :: Applicative f => Lifted (f a) -> f (Lifted a)

mapM :: Monad m => (a -> m b) -> Lifted a -> m (Lifted b)

sequence :: Monad m => Lifted (m a) -> m (Lifted a)

Eq a => Eq (Lifted a)

Methods

(==) :: Lifted a -> Lifted a -> Bool

(/=) :: Lifted a -> Lifted a -> Bool

Data a => Data (Lifted a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Lifted a -> c (Lifted a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Lifted a)

toConstr :: Lifted a -> Constr

dataTypeOf :: Lifted a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Lifted a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Lifted a))

gmapT :: (forall b. Data b => b -> b) -> Lifted a -> Lifted a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Lifted a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Lifted a -> r

gmapQ :: (forall d. Data d => d -> u) -> Lifted a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Lifted a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Lifted a -> m (Lifted a)

Ord a => Ord (Lifted a)

Methods

compare :: Lifted a -> Lifted a -> Ordering

(<) :: Lifted a -> Lifted a -> Bool

(<=) :: Lifted a -> Lifted a -> Bool

(>) :: Lifted a -> Lifted a -> Bool

(>=) :: Lifted a -> Lifted a -> Bool

max :: Lifted a -> Lifted a -> Lifted a

min :: Lifted a -> Lifted a -> Lifted a

Read a => Read (Lifted a)

Methods

readsPrec :: Int -> ReadS (Lifted a)

readList :: ReadS [Lifted a]

readPrec :: ReadPrec (Lifted a)

readListPrec :: ReadPrec [Lifted a]

Show a => Show (Lifted a)

Methods

showsPrec :: Int -> Lifted a -> ShowS

show :: Lifted a -> String

showList :: [Lifted a] -> ShowS

Generic (Lifted a)

Associated Types

type Rep (Lifted a) :: * -> *

Methods

from :: Lifted a -> Rep (Lifted a) x

to :: Rep (Lifted a) x -> Lifted a

NFData a => NFData (Lifted a)

Methods

rnf :: Lifted a -> ()

Hashable a => Hashable (Lifted a)

Methods

hashWithSalt :: Int -> Lifted a -> Int

hash :: Lifted a -> Int

BoundedLattice a => BoundedLattice (Lifted a)

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Lifted a)

Methods

top :: Lifted a

JoinSemiLattice a => BoundedJoinSemiLattice (Lifted a)

Methods

bottom :: Lifted a

Lattice a => Lattice (Lifted a)

MeetSemiLattice a => MeetSemiLattice (Lifted a)

Methods

(/\) :: Lifted a -> Lifted a -> Lifted a

meet :: Lifted a -> Lifted a -> Lifted a

JoinSemiLattice a => JoinSemiLattice (Lifted a)

Methods

(\/) :: Lifted a -> Lifted a -> Lifted a

join :: Lifted a -> Lifted a -> Lifted a

Generic1 * Lifted

Associated Types

type Rep1 Lifted (f :: Lifted -> *) :: k -> *

Methods

from1 :: f a -> Rep1 Lifted f a

to1 :: Rep1 Lifted f a -> f a

type Rep (Lifted a)

type Rep (Lifted a) = D1 * (MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" False) ((:+:) * (C1 * (MetaCons "Lift" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a))) (C1 * (MetaCons "Bottom" PrefixI False) (U1 *)))

type Rep1 * Lifted

type Rep1 * Lifted = D1 * (MetaData "Lifted" "Algebra.Lattice.Lifted" "lattices-1.7.1-JS0VzTZGaXfIhOiyIFy1o0" False) ((:+:) * (C1 * (MetaCons "Lift" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) (C1 * (MetaCons "Bottom" PrefixI False) (U1 *)))

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

Interpret Lifted a using the BoundedJoinSemiLattice of a.