Data.Algebra.Boolean.CNF.Set

Documentation

newtype CNF a

Boolean formula in Conjunction Normal Form

Constructors

CNF

Fields

• unCNF :: Set (Set a)

Instances

Foldable CNF

Methods

fold :: Monoid m => CNF m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> CNF a -> a

foldl1 :: (a -> a -> a) -> CNF a -> a

toList :: CNF a -> [a]

null :: CNF a -> Bool

length :: CNF a -> Int

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

maximum :: Ord a => CNF a -> a

minimum :: Ord a => CNF a -> a

sum :: Num a => CNF a -> a

product :: Num a => CNF a -> a

CoBoolean1 CNF

Methods

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

NormalForm CNF

Associated Types

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

Methods

toNormalForm :: a -> CNF a

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

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

Eq a => Eq (CNF a)

Methods

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

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

Ord a => Ord (CNF a)

Methods

compare :: CNF a -> CNF a -> Ordering

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

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

(>) :: CNF a -> CNF a -> Bool

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

max :: CNF a -> CNF a -> CNF a

min :: CNF a -> CNF a -> CNF a

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

Methods

readsPrec :: Int -> ReadS (CNF a)

readList :: ReadS [CNF a]

readPrec :: ReadPrec (CNF a)

readListPrec :: ReadPrec [CNF a]

Show a => Show (CNF a)

Methods

showsPrec :: Int -> CNF a -> ShowS

show :: CNF a -> String

showList :: [CNF a] -> ShowS

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

Methods

true :: CNF a

false :: CNF a

not :: CNF a -> CNF a

(&&) :: CNF a -> CNF a -> CNF a

(||) :: CNF a -> CNF a -> CNF a

xor :: CNF a -> CNF a -> CNF a

(-->) :: CNF a -> CNF a -> CNF a

(<-->) :: CNF a -> CNF a -> CNF a

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

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

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

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

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

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

NFData a => NFData (CNF a)

Methods

rnf :: CNF a -> ()

CoBoolean a => CoBoolean (CNF a)

Methods

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

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

Methods

not :: CNF a -> CNF a

type NFConstraint CNF a

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

fromDoubleList :: Ord a => [[a]] -> CNF a

toDoubleList :: CNF a -> [[a]]

fromNNF :: (Ord a, Negable a) => NNF a -> CNF a

module Data.Algebra.Boolean.NormalForm