Numeric.Natural

Copyright (C) 2014 Herbert Valerio Riedel
(C) 2011 Edward Kmett
License see libraries/base/LICENSE
Maintainer [email protected]
Stability provisional
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

The arbitrary-precision Natural number type.

Since: base-4.8.0.0

data Natural Source

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 Source

pred :: Natural -> Natural Source

toEnum :: Int -> Natural Source

fromEnum :: Natural -> Int Source

enumFrom :: Natural -> [Natural] Source

enumFromThen :: Natural -> Natural -> [Natural] Source

enumFromTo :: Natural -> Natural -> [Natural] Source

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source

Eq Natural

Since: base-4.8.0.0
Instance details

Defined in GHC.Natural

Methods

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

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

Integral Natural

Since: base-4.8.0.0
Instance details

Defined in GHC.Real

Methods

quot :: Natural -> Natural -> Natural Source

rem :: Natural -> Natural -> Natural Source

div :: Natural -> Natural -> Natural Source

mod :: Natural -> Natural -> Natural Source

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

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

toInteger :: Natural -> Integer Source

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 Source

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

toConstr :: Natural -> Constr Source

dataTypeOf :: Natural -> DataType Source

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

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

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

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

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

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

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

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

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

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

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 Source

(-) :: Natural -> Natural -> Natural Source

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

negate :: Natural -> Natural Source

abs :: Natural -> Natural Source

signum :: Natural -> Natural Source

fromInteger :: Integer -> Natural Source

Ord Natural

Since: base-4.8.0.0
Instance details

Defined in GHC.Natural

Methods

compare :: Natural -> Natural -> Ordering Source

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

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

(>) :: Natural -> Natural -> Bool Source

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

max :: Natural -> Natural -> Natural Source

min :: Natural -> Natural -> Natural Source

Read Natural

Since: base-4.8.0.0
Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Natural Source

readList :: ReadS [Natural] Source

readPrec :: ReadPrec Natural Source

readListPrec :: ReadPrec [Natural] Source

Real Natural

Since: base-4.8.0.0
Instance details

Defined in GHC.Real

Methods

toRational :: Natural -> Rational Source

Show Natural

Since: base-4.8.0.0
Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS Source

show :: Natural -> String Source

showList :: [Natural] -> ShowS Source

Ix Natural

Since: base-4.8.0.0
Instance details

Defined in GHC.Ix

Methods

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

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

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

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

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

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

Bits Natural

Since: base-4.8.0
Instance details

Defined in Data.Bits

Methods

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

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

xor :: Natural -> Natural -> Natural Source

complement :: Natural -> Natural Source

shift :: Natural -> Int -> Natural Source

rotate :: Natural -> Int -> Natural Source

zeroBits :: Natural Source

bit :: Int -> Natural Source

setBit :: Natural -> Int -> Natural Source

clearBit :: Natural -> Int -> Natural Source

complementBit :: Natural -> Int -> Natural Source

testBit :: Natural -> Int -> Bool Source

bitSizeMaybe :: Natural -> Maybe Int Source

bitSize :: Natural -> Int Source

isSigned :: Natural -> Bool Source

shiftL :: Natural -> Int -> Natural Source

unsafeShiftL :: Natural -> Int -> Natural Source

shiftR :: Natural -> Int -> Natural Source

unsafeShiftR :: Natural -> Int -> Natural Source

rotateL :: Natural -> Int -> Natural Source

rotateR :: Natural -> Int -> Natural Source

popCount :: Natural -> Int Source

PrintfArg Natural

Since: base-4.8.0.0
Instance details

Defined in Text.Printf

Methods

formatArg :: Natural -> FieldFormatter Source

parseFormat :: Natural -> ModifierParser Source

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.10.2/docs/html/libraries/base-4.14.1.0/Numeric-Natural.html