Copyright	© Oleg Grenrus 2014
License	MIT
Maintainer	Oleg Grenrus <oleg.grenrus@iki.fi>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Algebra.Boolean.Negable

Description

Synopsis

data Neg a
- = Pos a
- | Neg a
class Negable x where
- not :: x -> x

Documentation

data Neg a Source #

Free Negable.

Constructors

Pos a	Positive value
Neg a	Negative value

Instances

Functor Neg Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods fmap :: (a -> b) -> Neg a -> Neg b # (<$) :: a -> Neg b -> Neg a #
CoBoolean1 Neg Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods toBooleanWith :: Boolean c => (a -> c) -> Neg a -> c Source #
Eq a => Eq (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods (==) :: Neg a -> Neg a -> Bool # (/=) :: Neg a -> Neg a -> Bool #
Ord a => Ord (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods compare :: Neg a -> Neg a -> Ordering # (<) :: Neg a -> Neg a -> Bool # (<=) :: Neg a -> Neg a -> Bool # (>) :: Neg a -> Neg a -> Bool # (>=) :: Neg a -> Neg a -> Bool # max :: Neg a -> Neg a -> Neg a # min :: Neg a -> Neg a -> Neg a #
Read a => Read (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods readsPrec :: Int -> ReadS (Neg a) # readList :: ReadS [Neg a] # readPrec :: ReadPrec (Neg a) # readListPrec :: ReadPrec [Neg a] #
Show a => Show (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods showsPrec :: Int -> Neg a -> ShowS # show :: Neg a -> String # showList :: [Neg a] -> ShowS #
NFData a => NFData (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods rnf :: Neg a -> () #
CoBoolean (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods toBoolean :: Boolean b => Neg a -> b Source #
Negable (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods not :: Neg a -> Neg a Source #

class Negable x where Source #

Class to represent invertible values.

Must obey the double negation law: not (not x) = x

The negation appears only in leafs of normal forms, and the underlying proposition class might have built-in negation, thus we use Negable.

Methods

not :: x -> x Source #

Invert the value.

Instances

Negable Bool Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods not :: Bool -> Bool Source #
Monoid m => Negable (Maybe m) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods not :: Maybe m -> Maybe m Source #
Negable (Neg a) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods not :: Neg a -> Neg a Source #
Negable (FreeBoolean a) Source #
Instance details Defined in Data.Algebra.Boolean.FreeBoolean Methods not :: FreeBoolean a -> FreeBoolean a Source #
Negable a => Negable (NNF a) Source #
Instance details Defined in Data.Algebra.Boolean.NNF.Tree Methods not :: NNF a -> NNF a Source #
(Ord a, Negable a) => Negable (NNF a) Source #
Instance details Defined in Data.Algebra.Boolean.NNF.Set Methods not :: NNF a -> NNF a Source #
(Ord a, Negable a) => Negable (DNF a) Source #
Instance details Defined in Data.Algebra.Boolean.DNF.Set Methods not :: DNF a -> DNF a Source #
Negable a => Negable (DNF a) Source #
Instance details Defined in Data.Algebra.Boolean.DNF.List Methods not :: DNF a -> DNF a Source #
(Ord a, Negable a) => Negable (CNF a) Source #
Instance details Defined in Data.Algebra.Boolean.CNF.Set Methods not :: CNF a -> CNF a Source #
Negable a => Negable (CNF a) Source #
Instance details Defined in Data.Algebra.Boolean.CNF.List Methods not :: CNF a -> CNF a Source #
(Negable a, Negable b) => Negable (Either a b) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods not :: Either a b -> Either a b Source #
(Negable a, Negable b) => Negable (a, b) Source #
Instance details Defined in Data.Algebra.Boolean.Negable Methods not :: (a, b) -> (a, b) Source #