ghc-8.2.2: The GHC API

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 #

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 (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (BooleanFormula a)) Source #

dataCast2 :: Typeable (* -> * -> *) 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 #

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 #