basement-0.0.15: Foundation scrap box of array & string
Safe HaskellNone
LanguageHaskell2010

Basement.Compat.Natural

Synopsis

Documentation

data Natural #

Type representing arbitrary-precision non-negative integers.

>>> 2^100 :: Natural
1267650600228229401496703205376

Operations whose result would be negative throw (Underflow :: ArithException),

>>> -1 :: Natural
*** Exception: arithmetic underflow

Since: base-4.8.0.0

Instances

Instances details
Enum Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Enum

Methods

succ :: Natural -> Natural #

pred :: Natural -> Natural #

toEnum :: Int -> Natural #

fromEnum :: Natural -> Int #

enumFrom :: Natural -> [Natural] #

enumFromThen :: Natural -> Natural -> [Natural] #

enumFromTo :: Natural -> Natural -> [Natural] #

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] #

Eq Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Methods

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

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

Integral Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Methods

quot :: Natural -> Natural -> Natural #

rem :: Natural -> Natural -> Natural #

div :: Natural -> Natural -> Natural #

mod :: Natural -> Natural -> Natural #

quotRem :: Natural -> Natural -> (Natural, Natural) #

divMod :: Natural -> Natural -> (Natural, Natural) #

toInteger :: Natural -> Integer #

Data Natural

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: Natural -> Constr #

dataTypeOf :: Natural -> DataType #

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

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

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

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

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

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

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

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

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

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

Num Natural

Note that Natural's Num instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0

Instance details

Defined in GHC.Num

Methods

(+) :: Natural -> Natural -> Natural #

(-) :: Natural -> Natural -> Natural #

(*) :: Natural -> Natural -> Natural #

negate :: Natural -> Natural #

abs :: Natural -> Natural #

signum :: Natural -> Natural #

fromInteger :: Integer -> Natural #

Ord Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Methods

compare :: Natural -> Natural -> Ordering #

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

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

(>) :: Natural -> Natural -> Bool #

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

max :: Natural -> Natural -> Natural #

min :: Natural -> Natural -> Natural #

Read Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Natural #

readList :: ReadS [Natural] #

readPrec :: ReadPrec Natural #

readListPrec :: ReadPrec [Natural] #

Real Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Methods

toRational :: Natural -> Rational #

Show Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS #

show :: Natural -> String #

showList :: [Natural] -> ShowS #

Ix Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Ix

Methods

range :: (Natural, Natural) -> [Natural] #

index :: (Natural, Natural) -> Natural -> Int #

unsafeIndex :: (Natural, Natural) -> Natural -> Int #

inRange :: (Natural, Natural) -> Natural -> Bool #

rangeSize :: (Natural, Natural) -> Int #

unsafeRangeSize :: (Natural, Natural) -> Int #

Bits Natural

Since: base-4.8.0

Instance details

Defined in Data.Bits

Methods

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

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

xor :: Natural -> Natural -> Natural #

complement :: Natural -> Natural #

shift :: Natural -> Int -> Natural #

rotate :: Natural -> Int -> Natural #

zeroBits :: Natural #

bit :: Int -> Natural #

setBit :: Natural -> Int -> Natural #

clearBit :: Natural -> Int -> Natural #

complementBit :: Natural -> Int -> Natural #

testBit :: Natural -> Int -> Bool #

bitSizeMaybe :: Natural -> Maybe Int #

bitSize :: Natural -> Int #

isSigned :: Natural -> Bool #

shiftL :: Natural -> Int -> Natural #

unsafeShiftL :: Natural -> Int -> Natural #

shiftR :: Natural -> Int -> Natural #

unsafeShiftR :: Natural -> Int -> Natural #

rotateL :: Natural -> Int -> Natural #

rotateR :: Natural -> Int -> Natural #

popCount :: Natural -> Int #

Integral Natural Source # 
Instance details

Defined in Basement.Compat.NumLiteral

Methods

fromInteger :: Integer -> Natural Source #

IsNatural Natural Source # 
Instance details

Defined in Basement.Numerical.Number

Methods

toNatural :: Natural -> Natural Source #

IsIntegral Natural Source # 
Instance details

Defined in Basement.Numerical.Number

Methods

toInteger :: Natural -> Integer Source #

Subtractive Natural Source # 
Instance details

Defined in Basement.Numerical.Subtractive

Associated Types

type Difference Natural Source #

Methods

(-) :: Natural -> Natural -> Difference Natural Source #

Additive Natural Source # 
Instance details

Defined in Basement.Numerical.Additive

Methods

azero :: Natural Source #

(+) :: Natural -> Natural -> Natural Source #

scale :: IsNatural n => n -> Natural -> Natural Source #

IDivisible Natural Source # 
Instance details

Defined in Basement.Numerical.Multiplicative

Methods

div :: Natural -> Natural -> Natural Source #

mod :: Natural -> Natural -> Natural Source #

divMod :: Natural -> Natural -> (Natural, Natural) Source #

Multiplicative Natural Source # 
Instance details

Defined in Basement.Numerical.Multiplicative

Methods

midentity :: Natural Source #

(*) :: Natural -> Natural -> Natural Source #

(^) :: (IsNatural n, Enum n, IDivisible n) => Natural -> n -> Natural Source #

NormalForm Natural Source # 
Instance details

Defined in Basement.NormalForm

Methods

toNormalForm :: Natural -> () Source #

IsNatural a => IntegralUpsize a Natural Source # 
Instance details

Defined in Basement.IntegralConv

Methods

integralUpsize :: a -> Natural Source #

IntegralDownsize Integer Natural Source # 
Instance details

Defined in Basement.IntegralConv

Methods

integralDownsize :: Integer -> Natural Source #

integralDownsizeCheck :: Integer -> Maybe Natural Source #

IntegralDownsize Natural Word8 Source # 
Instance details

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word8 Source #

integralDownsizeCheck :: Natural -> Maybe Word8 Source #

IntegralDownsize Natural Word16 Source # 
Instance details

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word16 Source #

integralDownsizeCheck :: Natural -> Maybe Word16 Source #

IntegralDownsize Natural Word32 Source # 
Instance details

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word32 Source #

integralDownsizeCheck :: Natural -> Maybe Word32 Source #

IntegralDownsize Natural Word64 Source # 
Instance details

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word64 Source #

integralDownsizeCheck :: Natural -> Maybe Word64 Source #

IsNatural n => From n Natural Source # 
Instance details

Defined in Basement.From

Methods

from :: n -> Natural Source #

type Difference Natural Source # 
Instance details

Defined in Basement.Numerical.Subtractive

type Difference Natural = Maybe Natural

integerToNatural :: Integer -> Natural Source #

naturalToInteger :: Natural -> Integer Source #