module Algebra.Lattice.Lifted (
Lifted(..)
) where
#ifndef MIN_VERSION_base
#define MIN_VERSION_base(x,y,z) 1
#endif
import Algebra.Lattice
#if MIN_VERSION_base(4,8,0)
#else
import Data.Monoid (Monoid(..))
import Data.Foldable
import Data.Traversable
#endif
import Control.Applicative
import Control.DeepSeq
import Data.Data
import Data.Hashable
import GHC.Generics
data Lifted a = Lift a
| Bottom
deriving ( Eq, Ord, Show, Read, Data, Typeable, Generic
#if __GLASGOW_HASKELL__ >= 706
, Generic1
#endif
)
instance Functor Lifted where
fmap _ Bottom = Bottom
fmap f (Lift a) = Lift (f a)
instance Foldable Lifted where
foldMap _ Bottom = mempty
foldMap f (Lift a) = f a
instance Traversable Lifted where
traverse _ Bottom = pure Bottom
traverse f (Lift a) = Lift <$> f a
instance NFData a => NFData (Lifted a) where
rnf Bottom = ()
rnf (Lift a) = rnf a
instance Hashable a => Hashable (Lifted a)
instance JoinSemiLattice a => JoinSemiLattice (Lifted a) where
Lift x `join` Lift y = Lift (x `join` y)
Bottom `join` lift_y = lift_y
lift_x `join` Bottom = lift_x
instance MeetSemiLattice a => MeetSemiLattice (Lifted a) where
Lift x `meet` Lift y = Lift (x `meet` y)
Bottom `meet` _ = Bottom
_ `meet` Bottom = Bottom
instance Lattice a => Lattice (Lifted a) where
instance JoinSemiLattice a => BoundedJoinSemiLattice (Lifted a) where
bottom = Bottom
instance BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Lifted a) where
top = Lift top
instance BoundedLattice a => BoundedLattice (Lifted a) where