Algebra.Lattice.Dropped

Documentation

data Dropped a

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

Constructors

Top

Drop a

Instances

Monad Dropped

Methods

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

(>>) :: Dropped a -> Dropped b -> Dropped b

return :: a -> Dropped a

fail :: String -> Dropped a

Functor Dropped

Methods

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

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

Applicative Dropped

Methods

pure :: a -> Dropped a

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

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

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

Foldable Dropped

Methods

fold :: Monoid m => Dropped m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Dropped a -> a

foldl1 :: (a -> a -> a) -> Dropped a -> a

toList :: Dropped a -> [a]

null :: Dropped a -> Bool

length :: Dropped a -> Int

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

maximum :: Ord a => Dropped a -> a

minimum :: Ord a => Dropped a -> a

sum :: Num a => Dropped a -> a

product :: Num a => Dropped a -> a

Traversable Dropped

Methods

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

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

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

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

Generic1 Dropped

Associated Types

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

Methods

from1 :: Dropped a -> Rep1 Dropped a

to1 :: Rep1 Dropped a -> Dropped a

Eq a => Eq (Dropped a)

Methods

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

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

Data a => Data (Dropped a)

Methods

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

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

toConstr :: Dropped a -> Constr

dataTypeOf :: Dropped a -> DataType

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Dropped a)

Methods

compare :: Dropped a -> Dropped a -> Ordering

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

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

(>) :: Dropped a -> Dropped a -> Bool

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

max :: Dropped a -> Dropped a -> Dropped a

min :: Dropped a -> Dropped a -> Dropped a

Read a => Read (Dropped a)

Methods

readsPrec :: Int -> ReadS (Dropped a)

readList :: ReadS [Dropped a]

readPrec :: ReadPrec (Dropped a)

readListPrec :: ReadPrec [Dropped a]

Show a => Show (Dropped a)

Methods

showsPrec :: Int -> Dropped a -> ShowS

show :: Dropped a -> String

showList :: [Dropped a] -> ShowS

Generic (Dropped a)

Associated Types

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

Methods

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

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

NFData a => NFData (Dropped a)

Methods

rnf :: Dropped a -> ()

Hashable a => Hashable (Dropped a)

Methods

hashWithSalt :: Int -> Dropped a -> Int

hash :: Dropped a -> Int

BoundedLattice a => BoundedLattice (Dropped a)

MeetSemiLattice a => BoundedMeetSemiLattice (Dropped a)

Methods

top :: Dropped a

BoundedJoinSemiLattice a => BoundedJoinSemiLattice (Dropped a)

Methods

bottom :: Dropped a

Lattice a => Lattice (Dropped a)

MeetSemiLattice a => MeetSemiLattice (Dropped a)

Methods

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

meet :: Dropped a -> Dropped a -> Dropped a

JoinSemiLattice a => JoinSemiLattice (Dropped a)

Methods

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

join :: Dropped a -> Dropped a -> Dropped a

type Rep1 Dropped

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

type Rep (Dropped a)

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

retractDropped :: BoundedMeetSemiLattice a => Dropped a -> a

Interpret Dropped a using the BoundedMeetSemiLattice of a.