Algebra.Lattice.Levitated

Documentation

data Levitated a

Graft a distinct top and bottom onto an otherwise unbounded lattice. The top is the absorbing element for the join, and the bottom is the absorbing element for the meet.

Constructors

Top

Levitate a

Bottom

Instances

Monad Levitated

Methods

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

(>>) :: Levitated a -> Levitated b -> Levitated b

return :: a -> Levitated a

fail :: String -> Levitated a

Functor Levitated

Methods

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

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

Applicative Levitated

Methods

pure :: a -> Levitated a

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

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

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

Foldable Levitated

Methods

fold :: Monoid m => Levitated m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Levitated a -> a

foldl1 :: (a -> a -> a) -> Levitated a -> a

toList :: Levitated a -> [a]

null :: Levitated a -> Bool

length :: Levitated a -> Int

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

maximum :: Ord a => Levitated a -> a

minimum :: Ord a => Levitated a -> a

sum :: Num a => Levitated a -> a

product :: Num a => Levitated a -> a

Traversable Levitated

Methods

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

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

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

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

Generic1 Levitated

Associated Types

type Rep1 (Levitated :: * -> *) :: * -> *

Methods

from1 :: Levitated a -> Rep1 Levitated a

to1 :: Rep1 Levitated a -> Levitated a

Eq a => Eq (Levitated a)

Methods

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

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

Data a => Data (Levitated a)

Methods

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

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

toConstr :: Levitated a -> Constr

dataTypeOf :: Levitated a -> DataType

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Levitated a)

Methods

compare :: Levitated a -> Levitated a -> Ordering

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

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

(>) :: Levitated a -> Levitated a -> Bool

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

max :: Levitated a -> Levitated a -> Levitated a

min :: Levitated a -> Levitated a -> Levitated a

Read a => Read (Levitated a)

Methods

readsPrec :: Int -> ReadS (Levitated a)

readList :: ReadS [Levitated a]

readPrec :: ReadPrec (Levitated a)

readListPrec :: ReadPrec [Levitated a]

Show a => Show (Levitated a)

Methods

showsPrec :: Int -> Levitated a -> ShowS

show :: Levitated a -> String

showList :: [Levitated a] -> ShowS

Generic (Levitated a)

Associated Types

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

Methods

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

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

NFData a => NFData (Levitated a)

Methods

rnf :: Levitated a -> ()

Hashable a => Hashable (Levitated a)

Methods

hashWithSalt :: Int -> Levitated a -> Int

hash :: Levitated a -> Int

Lattice a => BoundedLattice (Levitated a)

MeetSemiLattice a => BoundedMeetSemiLattice (Levitated a)

Methods

top :: Levitated a

JoinSemiLattice a => BoundedJoinSemiLattice (Levitated a)

Methods

bottom :: Levitated a

Lattice a => Lattice (Levitated a)

MeetSemiLattice a => MeetSemiLattice (Levitated a)

Methods

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

meet :: Levitated a -> Levitated a -> Levitated a

JoinSemiLattice a => JoinSemiLattice (Levitated a)

Methods

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

join :: Levitated a -> Levitated a -> Levitated a

type Rep1 Levitated

type Rep1 Levitated = D1 (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-1.7-LVxdjRPvAj7FxWDUYmNHEJ" False) ((:+:) (C1 (MetaCons "Top" PrefixI False) U1) ((:+:) (C1 (MetaCons "Levitate" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) (C1 (MetaCons "Bottom" PrefixI False) U1)))

type Rep (Levitated a)

type Rep (Levitated a) = D1 (MetaData "Levitated" "Algebra.Lattice.Levitated" "lattices-1.7-LVxdjRPvAj7FxWDUYmNHEJ" False) ((:+:) (C1 (MetaCons "Top" PrefixI False) U1) ((:+:) (C1 (MetaCons "Levitate" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) (C1 (MetaCons "Bottom" PrefixI False) U1)))

retractLevitated :: BoundedLattice a => Levitated a -> a

Interpret Levitated a using the BoundedLattice of a.