Data.BoolExpr

Boolean expressions and various representations.

A boolean class

class Boolean f where

A boolean type class.

Methods

(/\) :: f a -> f a -> f a infix 9

(\/) :: f a -> f a -> f a infix 9

bNot :: f a -> f a

bTrue :: f a

bFalse :: f a

bConst :: Signed a -> f a

Instances

Boolean BoolExpr

Defined in Data.BoolExpr

Methods

(/\) :: BoolExpr a -> BoolExpr a -> BoolExpr a

(\/) :: BoolExpr a -> BoolExpr a -> BoolExpr a

bNot :: BoolExpr a -> BoolExpr a

bTrue :: BoolExpr a

bFalse :: BoolExpr a

bConst :: Signed a -> BoolExpr a

Boolean CNF

Defined in Data.BoolExpr

Methods

(/\) :: CNF a -> CNF a -> CNF a

(\/) :: CNF a -> CNF a -> CNF a

bNot :: CNF a -> CNF a

bTrue :: CNF a

bFalse :: CNF a

bConst :: Signed a -> CNF a

Boolean DNF

Defined in Data.BoolExpr

Methods

(/\) :: DNF a -> DNF a -> DNF a

(\/) :: DNF a -> DNF a -> DNF a

bNot :: DNF a -> DNF a

bTrue :: DNF a

bFalse :: DNF a

bConst :: Signed a -> DNF a

b ~ Bool => Boolean (Eval b)

Defined in Data.BoolExpr

Methods

(/\) :: Eval b a -> Eval b a -> Eval b a

(\/) :: Eval b a -> Eval b a -> Eval b a

bNot :: Eval b a -> Eval b a

bTrue :: Eval b a

bFalse :: Eval b a

bConst :: Signed a -> Eval b a

Generic functions derived from Boolean

bAnd :: (Foldable t, Boolean f) => t (f b) -> f b

Generalized and.

bAll :: (Foldable t, Boolean f) => (a -> f b) -> t a -> f b

Generalized all.

bOr :: (Foldable t, Boolean f) => t (f b) -> f b

Generalized or.

bAny :: (Foldable t, Boolean f) => (a -> f b) -> t a -> f b

Generalized any.

Boolean trees

data BoolExpr a

Syntax of boolean expressions parameterized over a set of leaves, named constants.

Constructors

BAnd (BoolExpr a) (BoolExpr a)

BOr (BoolExpr a) (BoolExpr a)

BNot (BoolExpr a)

BTrue

BFalse

BConst (Signed a)

Instances

Foldable BoolExpr

Defined in Data.BoolExpr

Methods

fold :: Monoid m => BoolExpr m -> m

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

foldMap' :: Monoid m => (a -> m) -> BoolExpr a -> m

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

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

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

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

foldr1 :: (a -> a -> a) -> BoolExpr a -> a

foldl1 :: (a -> a -> a) -> BoolExpr a -> a

toList :: BoolExpr a -> [a]

null :: BoolExpr a -> Bool

length :: BoolExpr a -> Int

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

maximum :: Ord a => BoolExpr a -> a

minimum :: Ord a => BoolExpr a -> a

sum :: Num a => BoolExpr a -> a

product :: Num a => BoolExpr a -> a

Traversable BoolExpr

Defined in Data.BoolExpr

Methods

traverse :: Applicative f => (a -> f b) -> BoolExpr a -> f (BoolExpr b)

sequenceA :: Applicative f => BoolExpr (f a) -> f (BoolExpr a)

mapM :: Monad m => (a -> m b) -> BoolExpr a -> m (BoolExpr b)

sequence :: Monad m => BoolExpr (m a) -> m (BoolExpr a)

Functor BoolExpr

Defined in Data.BoolExpr

Methods

fmap :: (a -> b) -> BoolExpr a -> BoolExpr b

(<$) :: a -> BoolExpr b -> BoolExpr a

Boolean BoolExpr

Defined in Data.BoolExpr

Methods

(/\) :: BoolExpr a -> BoolExpr a -> BoolExpr a

(\/) :: BoolExpr a -> BoolExpr a -> BoolExpr a

bNot :: BoolExpr a -> BoolExpr a

bTrue :: BoolExpr a

bFalse :: BoolExpr a

bConst :: Signed a -> BoolExpr a

Show a => Show (BoolExpr a)

Defined in Data.BoolExpr

Methods

showsPrec :: Int -> BoolExpr a -> ShowS

show :: BoolExpr a -> String

showList :: [BoolExpr a] -> ShowS

Eq a => Eq (BoolExpr a)

Defined in Data.BoolExpr

Methods

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

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

Ord a => Ord (BoolExpr a)

Defined in Data.BoolExpr

Methods

compare :: BoolExpr a -> BoolExpr a -> Ordering

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

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

(>) :: BoolExpr a -> BoolExpr a -> Bool

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

max :: BoolExpr a -> BoolExpr a -> BoolExpr a

min :: BoolExpr a -> BoolExpr a -> BoolExpr a

reduceBoolExpr :: BoolExpr Bool -> Bool

Reduce a boolean tree annotated by booleans to a single boolean.

evalBoolExpr :: (a -> Bool) -> BoolExpr a -> Bool

Boolean evaluation semantic

newtype Eval b a

Constructors

Eval

Fields

• runEval :: (a -> b) -> b

Instances

b ~ Bool => Boolean (Eval b)

Defined in Data.BoolExpr

Methods

(/\) :: Eval b a -> Eval b a -> Eval b a

(\/) :: Eval b a -> Eval b a -> Eval b a

bNot :: Eval b a -> Eval b a

bTrue :: Eval b a

bFalse :: Eval b a

bConst :: Signed a -> Eval b a

runEvalId :: Eval a a -> a

Signed constants

data Signed a

Signed values are either positive or negative.

Constructors

Positive a

Negative a

Instances

Foldable Signed

Defined in Data.BoolExpr

Methods

fold :: Monoid m => Signed m -> m

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

foldMap' :: Monoid m => (a -> m) -> Signed a -> m

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

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

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

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

foldr1 :: (a -> a -> a) -> Signed a -> a

foldl1 :: (a -> a -> a) -> Signed a -> a

toList :: Signed a -> [a]

null :: Signed a -> Bool

length :: Signed a -> Int

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

maximum :: Ord a => Signed a -> a

minimum :: Ord a => Signed a -> a

sum :: Num a => Signed a -> a

product :: Num a => Signed a -> a

Traversable Signed

Defined in Data.BoolExpr

Methods

traverse :: Applicative f => (a -> f b) -> Signed a -> f (Signed b)

sequenceA :: Applicative f => Signed (f a) -> f (Signed a)

mapM :: Monad m => (a -> m b) -> Signed a -> m (Signed b)

sequence :: Monad m => Signed (m a) -> m (Signed a)

Applicative Signed

Defined in Data.BoolExpr

Methods

pure :: a -> Signed a

(<*>) :: Signed (a -> b) -> Signed a -> Signed b

liftA2 :: (a -> b -> c) -> Signed a -> Signed b -> Signed c

(*>) :: Signed a -> Signed b -> Signed b

(<*) :: Signed a -> Signed b -> Signed a

Functor Signed

Defined in Data.BoolExpr

Methods

fmap :: (a -> b) -> Signed a -> Signed b

(<$) :: a -> Signed b -> Signed a

Monad Signed

Defined in Data.BoolExpr

Methods

(>>=) :: Signed a -> (a -> Signed b) -> Signed b

(>>) :: Signed a -> Signed b -> Signed b

return :: a -> Signed a

Read a => Read (Signed a)

Defined in Data.BoolExpr

Methods

readsPrec :: Int -> ReadS (Signed a)

readList :: ReadS [Signed a]

readPrec :: ReadPrec (Signed a)

readListPrec :: ReadPrec [Signed a]

Show a => Show (Signed a)

Defined in Data.BoolExpr

Methods

showsPrec :: Int -> Signed a -> ShowS

show :: Signed a -> String

showList :: [Signed a] -> ShowS

Eq a => Eq (Signed a)

Defined in Data.BoolExpr

Methods

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

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

Ord a => Ord (Signed a)

Defined in Data.BoolExpr

Methods

compare :: Signed a -> Signed a -> Ordering

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

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

(>) :: Signed a -> Signed a -> Bool

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

max :: Signed a -> Signed a -> Signed a

min :: Signed a -> Signed a -> Signed a

negateSigned :: Signed a -> Signed a

evalSigned :: (a -> Bool) -> Signed a -> Bool

reduceSigned :: Signed Bool -> Bool

constants :: BoolExpr a -> [Signed a]

Returns constants used in a given boolean tree, these constants are returned signed depending one how many negations stands over a given constant.

negateConstant :: Boolean f => Signed a -> f a

Conjunctive Normal Form

newtype CNF a

Constructors

CNF

Fields

• unCNF :: Conj (Disj (Signed a))

Instances

Functor CNF

Defined in Data.BoolExpr

Methods

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

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

Boolean CNF

Defined in Data.BoolExpr

Methods

(/\) :: CNF a -> CNF a -> CNF a

(\/) :: CNF a -> CNF a -> CNF a

bNot :: CNF a -> CNF a

bTrue :: CNF a

bFalse :: CNF a

bConst :: Signed a -> CNF a

Monoid (CNF a)

Defined in Data.BoolExpr

Methods

mempty :: CNF a

mappend :: CNF a -> CNF a -> CNF a

mconcat :: [CNF a] -> CNF a

Semigroup (CNF a)

Defined in Data.BoolExpr

Methods

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

sconcat :: NonEmpty (CNF a) -> CNF a

stimes :: Integral b => b -> CNF a -> CNF a

Show a => Show (CNF a)

Defined in Data.BoolExpr

Methods

showsPrec :: Int -> CNF a -> ShowS

show :: CNF a -> String

showList :: [CNF a] -> ShowS

newtype Conj a

Constructors

Conj

Fields

• unConj :: [a]

Instances

Functor Conj

Defined in Data.BoolExpr

Methods

fmap :: (a -> b) -> Conj a -> Conj b

(<$) :: a -> Conj b -> Conj a

Monoid (Conj a)

Defined in Data.BoolExpr

Methods

mempty :: Conj a

mappend :: Conj a -> Conj a -> Conj a

mconcat :: [Conj a] -> Conj a

Semigroup (Conj a)

Defined in Data.BoolExpr

Methods

(<>) :: Conj a -> Conj a -> Conj a

sconcat :: NonEmpty (Conj a) -> Conj a

stimes :: Integral b => b -> Conj a -> Conj a

Show a => Show (Conj a)

Defined in Data.BoolExpr

Methods

showsPrec :: Int -> Conj a -> ShowS

show :: Conj a -> String

showList :: [Conj a] -> ShowS

fromCNF :: Boolean f => CNF a -> f a

Convert a CNF (a boolean expression in conjunctive normal form) to any other form supported by Boolean.

boolTreeToCNF :: BoolExpr a -> CNF a

Convert a boolean tree to a conjunctive normal form.

reduceCNF :: CNF Bool -> Bool

Reduce a boolean expression in conjunctive normal form to a single boolean.

Disjunctive Normal Form

newtype Disj a

Constructors

Disj

Fields

• unDisj :: [a]

Instances

Functor Disj

Defined in Data.BoolExpr

Methods

fmap :: (a -> b) -> Disj a -> Disj b

(<$) :: a -> Disj b -> Disj a

Monoid (Disj a)

Defined in Data.BoolExpr

Methods

mempty :: Disj a

mappend :: Disj a -> Disj a -> Disj a

mconcat :: [Disj a] -> Disj a

Semigroup (Disj a)

Defined in Data.BoolExpr

Methods

(<>) :: Disj a -> Disj a -> Disj a

sconcat :: NonEmpty (Disj a) -> Disj a

stimes :: Integral b => b -> Disj a -> Disj a

Show a => Show (Disj a)

Defined in Data.BoolExpr

Methods

showsPrec :: Int -> Disj a -> ShowS

show :: Disj a -> String

showList :: [Disj a] -> ShowS

newtype DNF a

Constructors

DNF

Fields

• unDNF :: Disj (Conj (Signed a))

Instances

Functor DNF

Defined in Data.BoolExpr

Methods

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

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

Boolean DNF

Defined in Data.BoolExpr

Methods

(/\) :: DNF a -> DNF a -> DNF a

(\/) :: DNF a -> DNF a -> DNF a

bNot :: DNF a -> DNF a

bTrue :: DNF a

bFalse :: DNF a

bConst :: Signed a -> DNF a

Monoid (DNF a)

Defined in Data.BoolExpr

Methods

mempty :: DNF a

mappend :: DNF a -> DNF a -> DNF a

mconcat :: [DNF a] -> DNF a

Semigroup (DNF a)

Defined in Data.BoolExpr

Methods

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

sconcat :: NonEmpty (DNF a) -> DNF a

stimes :: Integral b => b -> DNF a -> DNF a

Show a => Show (DNF a)

Defined in Data.BoolExpr

Methods

showsPrec :: Int -> DNF a -> ShowS

show :: DNF a -> String

showList :: [DNF a] -> ShowS

fromDNF :: Boolean f => DNF a -> f a

Convert a DNF (a boolean expression in disjunctive normal form) to any other form supported by Boolean.

boolTreeToDNF :: BoolExpr a -> DNF a

Convert a boolean tree to a disjunctive normal form.

reduceDNF :: DNF Bool -> Bool

Reduce a boolean expression in disjunctive normal form to a single boolean.

Other transformations

dualize :: Boolean f => BoolExpr a -> f a

fromBoolExpr :: Boolean f => BoolExpr a -> f a

Turns a boolean tree into any boolean type.

pushNotInwards :: Boolean f => BoolExpr a -> f a

Push the negations inwards as much as possible. The resulting boolean tree no longer use negations.