Data.Algebra.Boolean.DNF.Set

Documentation

newtype DNF a

Boolean formula in Disjunction Normal Form

Constructors

DNF

Fields

• unDNF :: Set (Set a)

Instances

Foldable DNF

Methods

fold :: Monoid m => DNF m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> DNF a -> a

foldl1 :: (a -> a -> a) -> DNF a -> a

toList :: DNF a -> [a]

null :: DNF a -> Bool

length :: DNF a -> Int

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

maximum :: Ord a => DNF a -> a

minimum :: Ord a => DNF a -> a

sum :: Num a => DNF a -> a

product :: Num a => DNF a -> a

CoBoolean1 DNF

Methods

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

NormalForm DNF

Associated Types

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

Methods

toNormalForm :: a -> DNF a

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

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

Eq a => Eq (DNF a)

Methods

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

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

Ord a => Ord (DNF a)

Methods

compare :: DNF a -> DNF a -> Ordering

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

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

(>) :: DNF a -> DNF a -> Bool

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

max :: DNF a -> DNF a -> DNF a

min :: DNF a -> DNF a -> DNF a

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

Methods

readsPrec :: Int -> ReadS (DNF a)

readList :: ReadS [DNF a]

readPrec :: ReadPrec (DNF a)

readListPrec :: ReadPrec [DNF a]

Show a => Show (DNF a)

Methods

showsPrec :: Int -> DNF a -> ShowS

show :: DNF a -> String

showList :: [DNF a] -> ShowS

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

Methods

true :: DNF a

false :: DNF a

not :: DNF a -> DNF a

(&&) :: DNF a -> DNF a -> DNF a

(||) :: DNF a -> DNF a -> DNF a

xor :: DNF a -> DNF a -> DNF a

(-->) :: DNF a -> DNF a -> DNF a

(<-->) :: DNF a -> DNF a -> DNF a

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

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

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

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

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

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

NFData a => NFData (DNF a)

Methods

rnf :: DNF a -> ()

CoBoolean a => CoBoolean (DNF a)

Methods

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

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

Methods

not :: DNF a -> DNF a

type NFConstraint DNF a

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

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

toDoubleList :: DNF a -> [[a]]

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

module Data.Algebra.Boolean.NormalForm