base-4.20.0.0: Core data structures and operations
Copyright(C) 2014 Herbert Valerio Riedel
(C) 2011 Edward Kmett
Licensesee libraries/base/LICENSE
Maintainerlibraries@haskell.org
Stabilityprovisional
Portabilityportable
Safe HaskellSafe
LanguageHaskell2010

Numeric.Natural

Description

The arbitrary-precision Natural number type.

Since: base-4.8.0.0

Synopsis

Documentation

data Natural #

Instances

Instances details
PrintfArg Natural Source #

Since: base-4.8.0.0

Instance details

Defined in Text.Printf

Bits Natural

@since base-4.8.0

Instance details

Defined in GHC.Internal.Bits

Data Natural

@since base-4.8.0.0

Instance details

Defined in GHC.Internal.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 #

Enum Natural

@since base-4.8.0.0

Instance details

Defined in GHC.Internal.Enum

Ix Natural

@since base-4.8.0.0

Instance details

Defined in GHC.Internal.Ix

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.Internal.Num

Read Natural

@since base-4.8.0.0

Instance details

Defined in GHC.Internal.Read

Integral Natural

@since base-4.8.0.0

Instance details

Defined in GHC.Internal.Real

Real Natural

@since base-4.8.0.0

Instance details

Defined in GHC.Internal.Real

Show Natural

@since base-4.8.0.0

Instance details

Defined in GHC.Internal.Show

Eq Natural 
Instance details

Defined in GHC.Num.Natural

Ord Natural 
Instance details

Defined in GHC.Num.Natural

KnownNat n => HasResolution (n :: Nat) Source #

For example, Fixed 1000 will give you a Fixed with a resolution of 1000.

Instance details

Defined in Data.Fixed

Methods

resolution :: p n -> Integer Source #

TestCoercion SNat

@since base-4.18.0.0

Instance details

Defined in GHC.Internal.TypeNats

Methods

testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b) Source #

TestEquality SNat

@since base-4.18.0.0

Instance details

Defined in GHC.Internal.TypeNats

Methods

testEquality :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (a :~: b) Source #

type Compare (a :: Natural) (b :: Natural) 
Instance details

Defined in GHC.Internal.Data.Type.Ord

type Compare (a :: Natural) (b :: Natural) = CmpNat a b

minusNaturalMaybe :: Natural -> Natural -> Maybe Natural Source #

Natural subtraction. Returns Nothings for non-positive results.

@since base-4.8.0.0