Data.Algebra.Boolean.NormalForm

Documentation

class CoBoolean1 nf => NormalForm nf where

Class unifying different boolean normal forms.

Minimal complete definition

toNormalForm, simplify, fromFreeBoolean

Associated Types

type NFConstraint nf a :: Constraint

NormalForm could be constrained, so the Set based implementations could be included.

Methods

toNormalForm :: a -> nf a

Lift a value into normal form.

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

Simplify the formula, if some terms are ⊥ or ⊤.

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

transform from free boolean form

Instances

NormalForm FreeBoolean

Associated Types

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

Methods

toNormalForm :: a -> FreeBoolean a

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

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

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

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

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

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

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

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

module Data.Algebra.Boolean.CoBoolean