BooleanFormula

Boolean formulas without quantifiers and without negation. Such a formula consists of variables, conjunctions (and), and disjunctions (or).

This module is used to represent minimal complete definitions for classes.

Documentation

data BooleanFormula a

Constructors

Var a

And [LBooleanFormula a]

Or [LBooleanFormula a]

Parens (LBooleanFormula a)

Instances

Functor BooleanFormula

Methods

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

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

Foldable BooleanFormula

Methods

fold :: Monoid m => BooleanFormula m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> BooleanFormula a -> a

foldl1 :: (a -> a -> a) -> BooleanFormula a -> a

toList :: BooleanFormula a -> [a]

null :: BooleanFormula a -> Bool

length :: BooleanFormula a -> Int

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

maximum :: Ord a => BooleanFormula a -> a

minimum :: Ord a => BooleanFormula a -> a

sum :: Num a => BooleanFormula a -> a

product :: Num a => BooleanFormula a -> a

Traversable BooleanFormula

Methods

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

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

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

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

Eq a => Eq (BooleanFormula a)

Methods

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

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

Data a => Data (BooleanFormula a)

Methods

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

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

toConstr :: BooleanFormula a -> Constr

dataTypeOf :: BooleanFormula a -> DataType

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

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

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

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

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

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

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

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

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

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

OutputableBndr a => Outputable (BooleanFormula a)

Methods

ppr :: BooleanFormula a -> SDoc

pprPrec :: Rational -> BooleanFormula a -> SDoc

Binary a => Binary (BooleanFormula a)

Methods

put_ :: BinHandle -> BooleanFormula a -> IO ()

put :: BinHandle -> BooleanFormula a -> IO (Bin * (BooleanFormula a))

get :: BinHandle -> IO (BooleanFormula a)

type LBooleanFormula a = Located (BooleanFormula a)

mkFalse :: BooleanFormula a

mkTrue :: BooleanFormula a

mkAnd :: Eq a => [LBooleanFormula a] -> BooleanFormula a

mkOr :: Eq a => [LBooleanFormula a] -> BooleanFormula a

mkVar :: a -> BooleanFormula a

isFalse :: BooleanFormula a -> Bool

isTrue :: BooleanFormula a -> Bool

eval :: (a -> Bool) -> BooleanFormula a -> Bool

simplify :: Eq a => (a -> Maybe Bool) -> BooleanFormula a -> BooleanFormula a

isUnsatisfied :: Eq a => (a -> Bool) -> BooleanFormula a -> Maybe (BooleanFormula a)

implies :: Uniquable a => BooleanFormula a -> BooleanFormula a -> Bool

impliesAtom :: Eq a => BooleanFormula a -> a -> Bool

pprBooleanFormula :: (Rational -> a -> SDoc) -> Rational -> BooleanFormula a -> SDoc

pprBooleanFormulaNice :: Outputable a => BooleanFormula a -> SDoc