# Numeric.Natural

Copyright (C) 2014 Herbert Valerio Riedel(C) 2011 Edward Kmett see libraries/base/LICENSE [email protected] provisional portable Trustworthy 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

enumFrom :: Natural -> [Natural] Source

Eq Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

#### Methods

Integral Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

#### Methods

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

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

Ord Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

#### Methods

Since: base-4.8.0.0

Instance details

#### Methods

Real Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

#### Methods

Show Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Show

#### Methods

showList :: [Natural] -> ShowS Source

Ix Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Arr

Bits Natural

Since: base-4.8.0

Instance details

Defined in Data.Bits

#### Methods

PrintfArg Natural

Since: base-4.8.0.0

Instance details

Defined in Text.Printf

#### Methods

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