Data.Algebra.Boolean.NNF.Set

Documentation

data NNF a

Boolean formula in Negation Normal Form

Boolean operations will perform transformations as below:

Constructors

NNFTrue

NNFFalse

NNFValue a

NNFOr (Set (NNF a))

NNFAnd (Set (NNF a))

Instances

Foldable NNF

Methods

fold :: Monoid m => NNF m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> NNF a -> a

foldl1 :: (a -> a -> a) -> NNF a -> a

toList :: NNF a -> [a]

null :: NNF a -> Bool

length :: NNF a -> Int

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

maximum :: Ord a => NNF a -> a

minimum :: Ord a => NNF a -> a

sum :: Num a => NNF a -> a

product :: Num a => NNF a -> a

CoBoolean1 NNF

Methods

toBooleanWith :: Boolean c => (a -> c) -> NNF a -> c

NormalForm NNF

Associated Types

type NFConstraint (NNF :: * -> *) a :: Constraint

Methods

toNormalForm :: a -> NNF a

simplify :: NFConstraint NNF a => (a -> Maybe Bool) -> NNF a -> NNF a

fromFreeBoolean :: NFConstraint NNF a => FreeBoolean a -> NNF a

Eq a => Eq (NNF a)

Methods

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

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

Ord a => Ord (NNF a)

Methods

compare :: NNF a -> NNF a -> Ordering

(<) :: NNF a -> NNF a -> Bool

(<=) :: NNF a -> NNF a -> Bool

(>) :: NNF a -> NNF a -> Bool

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

max :: NNF a -> NNF a -> NNF a

min :: NNF a -> NNF a -> NNF a

(Ord a, Read a) => Read (NNF a)

Methods

readsPrec :: Int -> ReadS (NNF a)

readList :: ReadS [NNF a]

readPrec :: ReadPrec (NNF a)

readListPrec :: ReadPrec [NNF a]

Show a => Show (NNF a)

Methods

showsPrec :: Int -> NNF a -> ShowS

show :: NNF a -> String

showList :: [NNF a] -> ShowS

(Ord a, Negable a) => Boolean (NNF a)

Methods

true :: NNF a

false :: NNF a

not :: NNF a -> NNF a

(&&) :: NNF a -> NNF a -> NNF a

(||) :: NNF a -> NNF a -> NNF a

xor :: NNF a -> NNF a -> NNF a

(-->) :: NNF a -> NNF a -> NNF a

(<-->) :: NNF a -> NNF a -> NNF a

and :: Foldable t => t (NNF a) -> NNF a

or :: Foldable t => t (NNF a) -> NNF a

nand :: Foldable t => t (NNF a) -> NNF a

all :: Foldable t => (a -> NNF a) -> t a -> NNF a

any :: Foldable t => (a -> NNF a) -> t a -> NNF a

nor :: Foldable t => t (NNF a) -> NNF a

NFData a => NFData (NNF a)

Methods

rnf :: NNF a -> ()

CoBoolean a => CoBoolean (NNF a)

Methods

toBoolean :: Boolean b => NNF a -> b

(Ord a, Negable a) => Negable (NNF a)

Methods

not :: NNF a -> NNF a

type NFConstraint NNF a

type NFConstraint NNF a = (Ord a, Negable a)

module Data.Algebra.Boolean.NormalForm