Safe Haskell	None
Language	Haskell2010

BooleanFormula

Description

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 Source

Constructors

Var a
And [LBooleanFormula a]
Or [LBooleanFormula a]
Parens (LBooleanFormula a)

Instances

Functor BooleanFormula
Methods fmap :: (a -> b) -> BooleanFormula a -> BooleanFormula b Source (<$) :: a -> BooleanFormula b -> BooleanFormula a Source
Foldable BooleanFormula
Methods fold :: Monoid m => BooleanFormula m -> m Source foldMap :: Monoid m => (a -> m) -> BooleanFormula a -> m Source foldr :: (a -> b -> b) -> b -> BooleanFormula a -> b Source foldr' :: (a -> b -> b) -> b -> BooleanFormula a -> b Source foldl :: (b -> a -> b) -> b -> BooleanFormula a -> b Source foldl' :: (b -> a -> b) -> b -> BooleanFormula a -> b Source foldr1 :: (a -> a -> a) -> BooleanFormula a -> a Source foldl1 :: (a -> a -> a) -> BooleanFormula a -> a Source toList :: BooleanFormula a -> [a] Source null :: BooleanFormula a -> Bool Source length :: BooleanFormula a -> Int Source elem :: Eq a => a -> BooleanFormula a -> Bool Source maximum :: Ord a => BooleanFormula a -> a Source minimum :: Ord a => BooleanFormula a -> a Source sum :: Num a => BooleanFormula a -> a Source product :: Num a => BooleanFormula a -> a Source
Traversable BooleanFormula
Methods traverse :: Applicative f => (a -> f b) -> BooleanFormula a -> f (BooleanFormula b) Source sequenceA :: Applicative f => BooleanFormula (f a) -> f (BooleanFormula a) Source mapM :: Monad m => (a -> m b) -> BooleanFormula a -> m (BooleanFormula b) Source sequence :: Monad m => BooleanFormula (m a) -> m (BooleanFormula a) Source
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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (BooleanFormula a) Source toConstr :: BooleanFormula a -> Constr Source dataTypeOf :: BooleanFormula a -> DataType Source dataCast1 :: Typeable (TYPE Lifted -> TYPE Lifted) t => (forall d. Data d => c (t d)) -> Maybe (c (BooleanFormula a)) Source dataCast2 :: Typeable (TYPE Lifted -> TYPE Lifted -> TYPE Lifted) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (BooleanFormula a)) Source gmapT :: (forall b. Data b => b -> b) -> BooleanFormula a -> BooleanFormula a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> BooleanFormula a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> BooleanFormula a -> r Source gmapQ :: (forall d. Data d => d -> u) -> BooleanFormula a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> BooleanFormula a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> BooleanFormula a -> m (BooleanFormula a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> BooleanFormula a -> m (BooleanFormula a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> BooleanFormula a -> m (BooleanFormula a) Source
Outputable a => Outputable (BooleanFormula a)
Methods ppr :: BooleanFormula a -> SDoc Source pprPrec :: Rational -> BooleanFormula a -> SDoc Source
Binary a => Binary (BooleanFormula a)
Methods put_ :: BinHandle -> BooleanFormula a -> IO () Source put :: BinHandle -> BooleanFormula a -> IO (Bin (BooleanFormula a)) Source get :: BinHandle -> IO (BooleanFormula a) Source

type LBooleanFormula a = Located (BooleanFormula a) Source

mkFalse :: BooleanFormula a Source

mkTrue :: BooleanFormula a Source

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

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

mkVar :: a -> BooleanFormula a Source

isFalse :: BooleanFormula a -> Bool Source

isTrue :: BooleanFormula a -> Bool Source

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

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

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

implies :: Eq a => BooleanFormula a -> BooleanFormula a -> Bool Source

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

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

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