Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Data.Boolean.Definition

Contents

Boolean
Bool
Structure

Description

boolean structure for multivalent logic.

Synopsis

class Boolean b where
- false :: b
- true :: b
- not :: b -> b
- (||) :: b -> b -> b
- or :: [b] -> b
- (&&) :: b -> b -> b
- and :: [b] -> b
- (~>) :: b -> b -> b
- (<~>) :: b -> b -> b
- eqvl :: [b] -> b
data Bool
- = False
- | True
otherwise :: Bool
data Bol

Boolean

class Boolean b where Source #

types with a Boolean structure, allowing multivalent logic.

Note Every Enum type which is also Bounded has a natural implementation as false = minBound, true = maxBound, (||) = max, (&&) = min (as there are min and max bounds the operator (||) and (&&) should be implemented with a lazy variant of min and max) and not b = toEnum (fromEnum maxBound - fromEnum t).

Minimal complete definition

true, false, not, ((||), (&&) | or, and)

Methods

false :: b Source #

true :: b Source #

not :: b -> b Source #

(||) :: b -> b -> b infixr 2 Source #

or :: [b] -> b Source #

(&&) :: b -> b -> b infixr 3 Source #

and :: [b] -> b Source #

(~>) :: b -> b -> b infixr 1 Source #

(<~>) :: b -> b -> b infixr 1 Source #

eqvl :: [b] -> b Source #

Instances

Instances details

Boolean Statement Source #
Instance details Defined in OAlg.Data.Statement.Definition Methods false :: Statement Source # true :: Statement Source # not :: Statement -> Statement Source # (\|\|) :: Statement -> Statement -> Statement Source # or :: [Statement] -> Statement Source # (&&) :: Statement -> Statement -> Statement Source # and :: [Statement] -> Statement Source # (~>) :: Statement -> Statement -> Statement Source # (<~>) :: Statement -> Statement -> Statement Source # eqvl :: [Statement] -> Statement Source #
Boolean Valid Source #
Instance details Defined in OAlg.Data.Statement.Definition Methods false :: Valid Source # true :: Valid Source # not :: Valid -> Valid Source # (\|\|) :: Valid -> Valid -> Valid Source # or :: [Valid] -> Valid Source # (&&) :: Valid -> Valid -> Valid Source # and :: [Valid] -> Valid Source # (~>) :: Valid -> Valid -> Valid Source # (<~>) :: Valid -> Valid -> Valid Source # eqvl :: [Valid] -> Valid Source #
Boolean Bool Source #
Instance details Defined in OAlg.Data.Boolean.Definition Methods false :: Bool Source # true :: Bool Source # not :: Bool -> Bool Source # (\|\|) :: Bool -> Bool -> Bool Source # or :: [Bool] -> Bool Source # (&&) :: Bool -> Bool -> Bool Source # and :: [Bool] -> Bool Source # (~>) :: Bool -> Bool -> Bool Source # (<~>) :: Bool -> Bool -> Bool Source # eqvl :: [Bool] -> Bool Source #

Bool

data Bool #

Constructors

False
True

Instances

Instances details

Bounded Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool # maxBound :: Bool #
Enum Bool	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool # pred :: Bool -> Bool # toEnum :: Int -> Bool # fromEnum :: Bool -> Int # enumFrom :: Bool -> [Bool] # enumFromThen :: Bool -> Bool -> [Bool] # enumFromTo :: Bool -> Bool -> [Bool] # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #
Generic Bool
Instance details Defined in GHC.Generics Associated Types type Rep Bool :: Type -> Type # Methods from :: Bool -> Rep Bool x # to :: Rep Bool x -> Bool #
SingKind Bool	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Associated Types type DemoteRep Bool Methods fromSing :: forall (a :: Bool). Sing a -> DemoteRep Bool
Ix Bool	Since: base-2.1
Instance details Defined in GHC.Ix Methods range :: (Bool, Bool) -> [Bool] # index :: (Bool, Bool) -> Bool -> Int # unsafeIndex :: (Bool, Bool) -> Bool -> Int # inRange :: (Bool, Bool) -> Bool -> Bool # rangeSize :: (Bool, Bool) -> Int # unsafeRangeSize :: (Bool, Bool) -> Int #
Read Bool	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool # readList :: ReadS [Bool] # readPrec :: ReadPrec Bool # readListPrec :: ReadPrec [Bool] #
Show Bool	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Bool -> ShowS # show :: Bool -> String # showList :: [Bool] -> ShowS #
NFData Bool
Instance details Defined in Control.DeepSeq Methods rnf :: Bool -> () #
Eq Bool
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool # (/=) :: Bool -> Bool -> Bool #
Ord Bool
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering # (<) :: Bool -> Bool -> Bool # (<=) :: Bool -> Bool -> Bool # (>) :: Bool -> Bool -> Bool # (>=) :: Bool -> Bool -> Bool # max :: Bool -> Bool -> Bool # min :: Bool -> Bool -> Bool #
HNFData Bool Source #
Instance details Defined in OAlg.Control.HNFData Methods rhnf :: Bool -> () Source #
Boolean Bool Source #
Instance details Defined in OAlg.Data.Boolean.Definition Methods false :: Bool Source # true :: Bool Source # not :: Bool -> Bool Source # (\|\|) :: Bool -> Bool -> Bool Source # or :: [Bool] -> Bool Source # (&&) :: Bool -> Bool -> Bool Source # and :: [Bool] -> Bool Source # (~>) :: Bool -> Bool -> Bool Source # (<~>) :: Bool -> Bool -> Bool Source # eqvl :: [Bool] -> Bool Source #
Validable Bool Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Bool -> Statement Source #
Random Bool
Instance details Defined in System.Random Methods randomR :: RandomGen g => (Bool, Bool) -> g -> (Bool, g) # random :: RandomGen g => g -> (Bool, g) # randomRs :: RandomGen g => (Bool, Bool) -> g -> [Bool] # randoms :: RandomGen g => g -> [Bool] #
Uniform Bool
Instance details Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Bool #
UniformRange Bool
Instance details Defined in System.Random.Internal Methods uniformRM :: StatefulGen g m => (Bool, Bool) -> g -> m Bool #
SingI 'False	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'False
SingI 'True	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods sing :: Sing 'True
Boolean b => Embeddable Bool b Source #
Instance details Defined in OAlg.Data.Canonical Methods inj :: Bool -> b Source #
Projectible Bool Valid Source #
Instance details Defined in OAlg.Data.Statement.Definition Methods prj :: Valid -> Bool Source #
Lift Bool
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Quote m => Bool -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Bool -> Code m Bool #
type DemoteRep Bool
Instance details Defined in GHC.Generics type DemoteRep Bool = Bool
type Rep Bool	Since: base-4.6.0.0
Instance details Defined in GHC.Generics type Rep Bool = D1 ('MetaData "Bool" "GHC.Types" "ghc-prim" 'False) (C1 ('MetaCons "False" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "True" 'PrefixI 'False) (U1 :: Type -> Type))
data Sing (a :: Bool)
Instance details Defined in GHC.Generics data Sing (a :: Bool) where STrue :: Sing 'True SFalse :: Sing 'False

otherwise :: Bool #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

Structure

data Bol Source #

type representing Boolean structures.

Instances

Instances details

type Structure Bol x Source #
Instance details Defined in OAlg.Data.Boolean.Definition type Structure Bol x = Boolean x