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

Boolean

class Logical b => 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

Methods

false :: b Source #

true :: b Source #

not :: b -> b Source #

or :: [b] -> b 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 # or :: [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 # or :: [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 # or :: [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

Data Bool

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool #

toConstr :: Bool -> Constr #

dataTypeOf :: Bool -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Bool) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) #

gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r #

gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool #

Storable Bool

Since: base-2.1

Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Bool -> Int #

alignment :: Bool -> Int #

peekElemOff :: Ptr Bool -> Int -> IO Bool #

pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () #

peekByteOff :: Ptr b -> Int -> IO Bool #

pokeByteOff :: Ptr b -> Int -> Bool -> IO () #

peek :: Ptr Bool -> IO Bool #

poke :: Ptr Bool -> Bool -> IO () #

Bits Bool

Interpret Bool as 1-bit bit-field

Since: base-4.7.0.0

Instance details

Defined in GHC.Bits

Methods

(.&.) :: Bool -> Bool -> Bool #

(.|.) :: Bool -> Bool -> Bool #

xor :: Bool -> Bool -> Bool #

complement :: Bool -> Bool #

shift :: Bool -> Int -> Bool #

rotate :: Bool -> Int -> Bool #

zeroBits :: Bool #

bit :: Int -> Bool #

setBit :: Bool -> Int -> Bool #

clearBit :: Bool -> Int -> Bool #

complementBit :: Bool -> Int -> Bool #

testBit :: Bool -> Int -> Bool #

bitSizeMaybe :: Bool -> Maybe Int #

bitSize :: Bool -> Int #

isSigned :: Bool -> Bool #

shiftL :: Bool -> Int -> Bool #

unsafeShiftL :: Bool -> Int -> Bool #

shiftR :: Bool -> Int -> Bool #

unsafeShiftR :: Bool -> Int -> Bool #

rotateL :: Bool -> Int -> Bool #

rotateR :: Bool -> Int -> Bool #

popCount :: Bool -> Int #

FiniteBits Bool

Since: base-4.7.0.0

Instance details

Defined in GHC.Bits

Methods

finiteBitSize :: Bool -> Int #

countLeadingZeros :: Bool -> Int #

countTrailingZeros :: Bool -> Int #

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	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))

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
Instance details Defined in GHC.Generics type DemoteRep Bool = 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 #

or :: [Bool] -> Bool Source #

and :: [Bool] -> Bool Source #

(~>) :: Bool -> Bool -> Bool Source #

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

eqvl :: [Bool] -> Bool Source #

Erasable Bool Source #

Instance details

Defined in OAlg.Data.Logical

Methods

(//) :: Bool -> Bool -> Bool Source #

Logical Bool Source #

Instance details

Defined in OAlg.Data.Logical

Methods

(||) :: Bool -> Bool -> Bool Source #

(&&) :: Bool -> Bool -> Bool Source #

Validable Bool Source #

Instance details

Defined in OAlg.Data.Validable

Methods

valid :: Bool -> Statement Source #

Lattice Bool Source #

Instance details

Defined in OAlg.Structure.Lattice.Definition

Empty Bool Source #

Instance details

Defined in OAlg.Structure.PartiallyOrdered.Definition

Methods

empty :: Bool Source #

isEmpty :: Bool -> Bool Source #

Full Bool Source #

Instance details

Defined in OAlg.Structure.PartiallyOrdered.Definition

Methods

full :: Bool Source #

isFull :: Bool -> Bool Source #

PartiallyOrdered Bool Source #

Instance details

Defined in OAlg.Structure.PartiallyOrdered.Definition

Methods

(<<=) :: Bool -> Bool -> Bool 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 #

isInRange :: (Bool, Bool) -> Bool -> Bool #

IArray UArray Bool

Instance details

Defined in Data.Array.Base

Methods

bounds :: Ix i => UArray i Bool -> (i, i) #

numElements :: Ix i => UArray i Bool -> Int #

unsafeArray :: Ix i => (i, i) -> [(Int, Bool)] -> UArray i Bool #

unsafeAt :: Ix i => UArray i Bool -> Int -> Bool #

unsafeReplace :: Ix i => UArray i Bool -> [(Int, Bool)] -> UArray i Bool #

unsafeAccum :: Ix i => (Bool -> e' -> Bool) -> UArray i Bool -> [(Int, e')] -> UArray i Bool #

unsafeAccumArray :: Ix i => (Bool -> e' -> Bool) -> Bool -> (i, i) -> [(Int, e')] -> UArray i 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 #

MArray IOUArray Bool IO

Instance details

Defined in Data.Array.IO.Internals

Methods

getBounds :: Ix i => IOUArray i Bool -> IO (i, i) #

getNumElements :: Ix i => IOUArray i Bool -> IO Int #

newArray :: Ix i => (i, i) -> Bool -> IO (IOUArray i Bool) #

newArray_ :: Ix i => (i, i) -> IO (IOUArray i Bool) #

unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Bool) #

unsafeRead :: Ix i => IOUArray i Bool -> Int -> IO Bool #

unsafeWrite :: Ix i => IOUArray i Bool -> Int -> Bool -> IO () #

MArray (STUArray s) Bool (ST s)

Instance details

Defined in Data.Array.Base

Methods

getBounds :: Ix i => STUArray s i Bool -> ST s (i, i) #

getNumElements :: Ix i => STUArray s i Bool -> ST s Int #

newArray :: Ix i => (i, i) -> Bool -> ST s (STUArray s i Bool) #

newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Bool) #

unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Bool) #

unsafeRead :: Ix i => STUArray s i Bool -> Int -> ST s Bool #

unsafeWrite :: Ix i => STUArray s i Bool -> Int -> Bool -> ST s () #

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 = ...