Safe Haskell	None
Language	Haskell2010

Data.Semilattice.Tumble

Description

Inverting a Join semilattice gives rise to a Meet semilattice, and vice versa.

Synopsis

Documentation

newtype Tumble a Source #

Tumble gives a Join semilattice for any Meet semilattice and vice versa, Lower bounds for Upper bounds and vice versa, and swaps the bounds of Bounded instances.

Constructors

Tumble
Fields getTumble :: a

Instances

Functor Tumble Source #
Methods fmap :: (a -> b) -> Tumble a -> Tumble b # (<$) :: a -> Tumble b -> Tumble a #
Foldable Tumble Source #
Methods fold :: Monoid m => Tumble m -> m # foldMap :: Monoid m => (a -> m) -> Tumble a -> m # foldr :: (a -> b -> b) -> b -> Tumble a -> b # foldr' :: (a -> b -> b) -> b -> Tumble a -> b # foldl :: (b -> a -> b) -> b -> Tumble a -> b # foldl' :: (b -> a -> b) -> b -> Tumble a -> b # foldr1 :: (a -> a -> a) -> Tumble a -> a # foldl1 :: (a -> a -> a) -> Tumble a -> a # toList :: Tumble a -> [a] # null :: Tumble a -> Bool # length :: Tumble a -> Int # elem :: Eq a => a -> Tumble a -> Bool # maximum :: Ord a => Tumble a -> a # minimum :: Ord a => Tumble a -> a # sum :: Num a => Tumble a -> a # product :: Num a => Tumble a -> a #
Traversable Tumble Source #
Methods traverse :: Applicative f => (a -> f b) -> Tumble a -> f (Tumble b) # sequenceA :: Applicative f => Tumble (f a) -> f (Tumble a) # mapM :: Monad m => (a -> m b) -> Tumble a -> m (Tumble b) # sequence :: Monad m => Tumble (m a) -> m (Tumble a) #
Bounded a => Bounded (Tumble a) Source #
Methods minBound :: Tumble a # maxBound :: Tumble a #
Enum a => Enum (Tumble a) Source #
Methods succ :: Tumble a -> Tumble a # pred :: Tumble a -> Tumble a # toEnum :: Int -> Tumble a # fromEnum :: Tumble a -> Int # enumFrom :: Tumble a -> [Tumble a] # enumFromThen :: Tumble a -> Tumble a -> [Tumble a] # enumFromTo :: Tumble a -> Tumble a -> [Tumble a] # enumFromThenTo :: Tumble a -> Tumble a -> Tumble a -> [Tumble a] #
Eq a => Eq (Tumble a) Source #
Methods (==) :: Tumble a -> Tumble a -> Bool # (/=) :: Tumble a -> Tumble a -> Bool #
Num a => Num (Tumble a) Source #
Methods (+) :: Tumble a -> Tumble a -> Tumble a # (-) :: Tumble a -> Tumble a -> Tumble a # (*) :: Tumble a -> Tumble a -> Tumble a # negate :: Tumble a -> Tumble a # abs :: Tumble a -> Tumble a # signum :: Tumble a -> Tumble a # fromInteger :: Integer -> Tumble a #
Ord a => Ord (Tumble a) Source #
Methods compare :: Tumble a -> Tumble a -> Ordering # (<) :: Tumble a -> Tumble a -> Bool # (<=) :: Tumble a -> Tumble a -> Bool # (>) :: Tumble a -> Tumble a -> Bool # (>=) :: Tumble a -> Tumble a -> Bool # max :: Tumble a -> Tumble a -> Tumble a # min :: Tumble a -> Tumble a -> Tumble a #
Read a => Read (Tumble a) Source #
Methods readsPrec :: Int -> ReadS (Tumble a) # readList :: ReadS [Tumble a] # readPrec :: ReadPrec (Tumble a) # readListPrec :: ReadPrec [Tumble a] #
Show a => Show (Tumble a) Source #
Methods showsPrec :: Int -> Tumble a -> ShowS # show :: Tumble a -> String # showList :: [Tumble a] -> ShowS #
Upper a => Lower (Tumble a) Source #
Methods lowerBound :: Tumble a Source #
Meet a => Join (Tumble a) Source #
Methods (\/) :: Tumble a -> Tumble a -> Tumble a Source #
Lower a => Upper (Tumble a) Source #
Methods upperBound :: Tumble a Source #
Join a => Meet (Tumble a) Source #
Methods (/\) :: Tumble a -> Tumble a -> Tumble a Source #

Idempotence:

x /\ x == (x :: Tumble Bool)

Associativity:

a /\ (b /\ c) == (a /\ b) /\ (c :: Tumble Bool)

Commutativity:

a /\ b == b /\ (a :: Tumble Bool)

Identity:

upperBound /\ a == (a :: Tumble Bool)

Absorption:

lowerBound /\ a == (lowerBound :: Tumble Bool)

Idempotence:

x \/ x == (x :: Tumble Bool)

Associativity:

a \/ (b \/ c) == (a \/ b) \/ (c :: Tumble Bool)

Commutativity:

a \/ b == b \/ (a :: Tumble Bool)

Identity:

lowerBound \/ a == (a :: Tumble Bool)

Absorption:

upperBound \/ a == (upperBound :: Tumble Bool)

Bounded:

upperBound == (maxBound :: Tumble Bool)

Identity of /\:

upperBound /\ a == (a :: Tumble Bool)

Absorbing element of \/:

upperBound \/ a == (upperBound :: Tumble Bool)

Ord:

compare upperBound (a :: Tumble Bool) /= LT

Bounded:

lowerBound == (minBound :: Tumble Bool)

Identity of \/:

lowerBound \/ a == (a :: Tumble Bool)

Absorbing element of /\:

lowerBound /\ a == (lowerBound :: Tumble Bool)

Ord:

compare lowerBound (a :: Tumble Bool) /= GT

>>> import Test.QuickCheck
>>> instance Arbitrary a => Arbitrary (Tumble a) where arbitrary = Tumble <$> arbitrary ; shrink (Tumble a) = Tumble <$> shrink a