{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -Wall #-}
module NumHask.Algebra.Abstract.Lattice where
import Data.Int (Int16, Int32, Int64, Int8)
import Data.Word (Word16, Word32, Word64, Word8)
import GHC.Natural (Natural (..))
import NumHask.Algebra.Abstract.Field
import Data.Bool
import Data.Eq
import GHC.Float (Float, Double)
import GHC.Int (Int)
import GHC.Num (Integer)
import GHC.Word (Word)
import Data.Ord (Ord(..))
import GHC.Enum (Bounded(..))
import Data.Function (const)
class (Eq a) => JoinSemiLattice a where
infixr 5 \/
(\/) :: a -> a -> a
joinLeq :: (JoinSemiLattice a) => a -> a -> Bool
joinLeq x y = (x \/ y) == y
class (Eq a) => MeetSemiLattice a where
infixr 6 /\
(/\) :: a -> a -> a
meetLeq :: (MeetSemiLattice a) => a -> a -> Bool
meetLeq x y = (x /\ y) == x
class (JoinSemiLattice a, MeetSemiLattice a) => Lattice a
instance (JoinSemiLattice a, MeetSemiLattice a) => Lattice a
class JoinSemiLattice a => BoundedJoinSemiLattice a where
bottom :: a
class MeetSemiLattice a => BoundedMeetSemiLattice a where
top :: a
class (JoinSemiLattice a, MeetSemiLattice a, BoundedJoinSemiLattice a, BoundedMeetSemiLattice a) => BoundedLattice a
instance (JoinSemiLattice a, MeetSemiLattice a, BoundedJoinSemiLattice a, BoundedMeetSemiLattice a) => BoundedLattice a
instance JoinSemiLattice Float where
(\/) = min
instance MeetSemiLattice Float where
(/\) = max
instance JoinSemiLattice Double where
(\/) = min
instance MeetSemiLattice Double where
(/\) = max
instance JoinSemiLattice Int where
(\/) = min
instance MeetSemiLattice Int where
(/\) = max
instance JoinSemiLattice Integer where
(\/) = min
instance MeetSemiLattice Integer where
(/\) = max
instance JoinSemiLattice Bool where
(\/) = (||)
instance MeetSemiLattice Bool where
(/\) = (&&)
instance JoinSemiLattice Natural where
(\/) = min
instance MeetSemiLattice Natural where
(/\) = max
instance JoinSemiLattice Int8 where
(\/) = min
instance MeetSemiLattice Int8 where
(/\) = max
instance JoinSemiLattice Int16 where
(\/) = min
instance MeetSemiLattice Int16 where
(/\) = max
instance JoinSemiLattice Int32 where
(\/) = min
instance MeetSemiLattice Int32 where
(/\) = max
instance JoinSemiLattice Int64 where
(\/) = min
instance MeetSemiLattice Int64 where
(/\) = max
instance JoinSemiLattice Word where
(\/) = min
instance MeetSemiLattice Word where
(/\) = max
instance JoinSemiLattice Word8 where
(\/) = min
instance MeetSemiLattice Word8 where
(/\) = max
instance JoinSemiLattice Word16 where
(\/) = min
instance MeetSemiLattice Word16 where
(/\) = max
instance JoinSemiLattice Word32 where
(\/) = min
instance MeetSemiLattice Word32 where
(/\) = max
instance JoinSemiLattice Word64 where
(\/) = min
instance MeetSemiLattice Word64 where
(/\) = max
instance (Eq (a -> b), JoinSemiLattice b) => JoinSemiLattice (a -> b) where
f \/ f' = \a -> f a \/ f' a
instance (Eq (a -> b), MeetSemiLattice b) => MeetSemiLattice (a -> b) where
f /\ f' = \a -> f a /\ f' a
instance BoundedJoinSemiLattice Float where
bottom = negInfinity
instance BoundedMeetSemiLattice Float where
top = infinity
instance BoundedJoinSemiLattice Double where
bottom = negInfinity
instance BoundedMeetSemiLattice Double where
top = infinity
instance BoundedJoinSemiLattice Int where
bottom = minBound
instance BoundedMeetSemiLattice Int where
top = maxBound
instance BoundedJoinSemiLattice Bool where
bottom = False
instance BoundedMeetSemiLattice Bool where
top = True
instance BoundedJoinSemiLattice Natural where
bottom = 0
instance BoundedJoinSemiLattice Int8 where
bottom = minBound
instance BoundedMeetSemiLattice Int8 where
top = maxBound
instance BoundedJoinSemiLattice Int16 where
bottom = minBound
instance BoundedMeetSemiLattice Int16 where
top = maxBound
instance BoundedJoinSemiLattice Int32 where
bottom = minBound
instance BoundedMeetSemiLattice Int32 where
top = maxBound
instance BoundedJoinSemiLattice Int64 where
bottom = minBound
instance BoundedMeetSemiLattice Int64 where
top = maxBound
instance BoundedJoinSemiLattice Word where
bottom = minBound
instance BoundedMeetSemiLattice Word where
top = maxBound
instance BoundedJoinSemiLattice Word8 where
bottom = minBound
instance BoundedMeetSemiLattice Word8 where
top = maxBound
instance BoundedJoinSemiLattice Word16 where
bottom = minBound
instance BoundedMeetSemiLattice Word16 where
top = maxBound
instance BoundedJoinSemiLattice Word32 where
bottom = minBound
instance BoundedMeetSemiLattice Word32 where
top = maxBound
instance BoundedJoinSemiLattice Word64 where
bottom = minBound
instance BoundedMeetSemiLattice Word64 where
top = maxBound
instance (Eq (a -> b), BoundedJoinSemiLattice b) => BoundedJoinSemiLattice (a -> b) where
bottom = const bottom
instance (Eq (a -> b), BoundedMeetSemiLattice b) => BoundedMeetSemiLattice (a -> b) where
top = const top