Data.BoolExpr

A boolean class

class Boolean f where

A boolean type class.

Methods

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

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

bNot :: f a -> f a

bTrue :: f a

bFalse :: f a

bConst :: a -> f a

Instances

Boolean DNF

Boolean CNF

Boolean BoolExpr

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 a

Instances

Functor BoolExpr

Foldable BoolExpr

Traversable BoolExpr

Boolean BoolExpr

Eq a => Eq (BoolExpr a)

Ord a => Ord (BoolExpr a)

Show a => Show (BoolExpr a)

reduceBoolExpr :: BoolExpr Bool -> Bool

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

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

Signed constants

data Signed a

Signed values are either positive of negative.

Constructors

Positive a

Negative a

Instances

Eq a => Eq (Signed a)

Ord a => Ord (Signed a)

Read a => Read (Signed a)

Show a => Show (Signed a)

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.

Conjunctive Normal Form

newtype CNF a

Constructors

CNF

Fields

unCNF :: Conj (Disj a)

Instances

Functor CNF

Boolean CNF

Show a => Show (CNF a)

Monoid (CNF a)

newtype Conj a

Constructors

Conj

Fields

unConj :: [a]

Instances

Functor Conj

Show a => Show (Conj a)

Monoid (Conj a)

boolTreeToCNF :: NegateConstant a -> 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

Show a => Show (Disj a)

Monoid (Disj a)

newtype DNF a

Constructors

DNF

Fields

unDNF :: Disj (Conj a)

Instances

Functor DNF

Boolean DNF

Show a => Show (DNF a)

Monoid (DNF a)

boolTreeToDNF :: (a -> BoolExpr a) -> 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 :: NegateConstant a -> BoolExpr a -> BoolExpr a

pushNotInwards :: NegateConstant a -> BoolExpr a -> BoolExpr a

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