Data.Semilattice.Tumble

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

Documentation

newtype Tumble a

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

Methods

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

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

Foldable Tumble

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

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)

Methods

minBound :: Tumble a

maxBound :: Tumble a

Enum a => Enum (Tumble a)

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)

Methods

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

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

Num a => Num (Tumble a)

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)

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)

Methods

readsPrec :: Int -> ReadS (Tumble a)

readList :: ReadS [Tumble a]

readPrec :: ReadPrec (Tumble a)

readListPrec :: ReadPrec [Tumble a]

Show a => Show (Tumble a)

Methods

showsPrec :: Int -> Tumble a -> ShowS

show :: Tumble a -> String

showList :: [Tumble a] -> ShowS

Upper a => Lower (Tumble a)

Methods

lowerBound :: Tumble a

Meet a => Join (Tumble a)

Methods

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

Lower a => Upper (Tumble a)

Methods

upperBound :: Tumble a

Join a => Meet (Tumble a)

Methods

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

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