OAlg.Data.Boolean.Definition

boolean structure for multivalent logic.

Boolean

class Boolean b where

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

true :: b

not :: b -> b

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

or :: [b] -> b

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

and :: [b] -> b

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

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

eqvl :: [b] -> b

Instances

Boolean Statement

Defined in OAlg.Data.Statement.Definition

Methods

false :: Statement

true :: Statement

not :: Statement -> Statement

(||) :: Statement -> Statement -> Statement

or :: [Statement] -> Statement

(&&) :: Statement -> Statement -> Statement

and :: [Statement] -> Statement

(~>) :: Statement -> Statement -> Statement

(<~>) :: Statement -> Statement -> Statement

eqvl :: [Statement] -> Statement

Boolean Valid

Defined in OAlg.Data.Statement.Definition

Methods

false :: Valid

true :: Valid

not :: Valid -> Valid

(||) :: Valid -> Valid -> Valid

or :: [Valid] -> Valid

(&&) :: Valid -> Valid -> Valid

and :: [Valid] -> Valid

(~>) :: Valid -> Valid -> Valid

(<~>) :: Valid -> Valid -> Valid

eqvl :: [Valid] -> Valid

Boolean Bool

Defined in OAlg.Data.Boolean.Definition

Methods

false :: Bool

true :: Bool

not :: Bool -> Bool

(||) :: Bool -> Bool -> Bool

or :: [Bool] -> Bool

(&&) :: Bool -> Bool -> Bool

and :: [Bool] -> Bool

(~>) :: Bool -> Bool -> Bool

(<~>) :: Bool -> Bool -> Bool

eqvl :: [Bool] -> Bool

Bool

data Bool

Constructors

False

True

Instances

Bounded Bool

Since: base-2.1

Defined in GHC.Enum

Methods

minBound :: Bool

maxBound :: Bool

Enum Bool

Since: base-2.1

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

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

Defined in GHC.Generics

Associated Types

type DemoteRep Bool

Methods

fromSing :: forall (a :: Bool). Sing a -> DemoteRep Bool

Ix Bool

Since: base-2.1

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

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Bool

readList :: ReadS [Bool]

readPrec :: ReadPrec Bool

readListPrec :: ReadPrec [Bool]

Show Bool

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Bool -> ShowS

show :: Bool -> String

showList :: [Bool] -> ShowS

NFData Bool

Defined in Control.DeepSeq

Methods

rnf :: Bool -> ()

Eq Bool

Defined in GHC.Classes

Methods

(==) :: Bool -> Bool -> Bool

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

Ord Bool

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

Defined in OAlg.Control.HNFData

Methods

rhnf :: Bool -> ()

Boolean Bool

Defined in OAlg.Data.Boolean.Definition

Methods

false :: Bool

true :: Bool

not :: Bool -> Bool

(||) :: Bool -> Bool -> Bool

or :: [Bool] -> Bool

(&&) :: Bool -> Bool -> Bool

and :: [Bool] -> Bool

(~>) :: Bool -> Bool -> Bool

(<~>) :: Bool -> Bool -> Bool

eqvl :: [Bool] -> Bool

Validable Bool

Defined in OAlg.Data.Validable

Methods

valid :: Bool -> Statement

Random Bool

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

Defined in System.Random.Internal

Methods

uniformM :: StatefulGen g m => g -> m Bool

UniformRange Bool

Defined in System.Random.Internal

Methods

uniformRM :: StatefulGen g m => (Bool, Bool) -> g -> m Bool

SingI 'False

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

sing :: Sing 'False

SingI 'True

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

sing :: Sing 'True

Boolean b => Embeddable Bool b

Defined in OAlg.Data.Canonical

Methods

inj :: Bool -> b

Projectible Bool Valid

Defined in OAlg.Data.Statement.Definition

Methods

prj :: Valid -> Bool

Lift Bool

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

Defined in GHC.Generics

type DemoteRep Bool = Bool

type Rep Bool

Since: base-4.6.0.0

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)

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

type representing Boolean structures.

Instances

type Structure Bol x

Defined in OAlg.Data.Boolean.Definition

type Structure Bol x = Boolean x