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GHC.TypeNats.Internal

Safe Haskell Trustworthy
Language Haskell2010

Description

This module exports the Type Nat kind as well as the comparison type family for that kinds. It is needed to prevent module cycles while still allowing these identifiers to be improted in Ord.

Since: base-4.16.0.0

data Natural Source

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Instances
Instances details
Data Natural Source

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
Bits Natural Source

Since: base-4.8.0
Instance details

Defined in GHC.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
Enum Natural Source

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
Ix Natural Source

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
Num Natural Source

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
Read Natural Source

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
Integral Natural Source

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
Real Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Real

Methods

toRational :: Natural -> Rational Source
Show Natural Source

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
PrintfArg Natural Source

Since: base-4.8.0.0
Instance details

Defined in Text.Printf

Methods

formatArg :: Natural -> FieldFormatter Source

parseFormat :: Natural -> ModifierParser Source
Eq Natural
Instance details

Defined in GHC.Num.Natural

Methods

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

(/=) :: Natural -> Natural -> Bool Source
Ord Natural
Instance details

Defined in GHC.Num.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
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
type Compare (a :: Natural) (b :: Natural) Source
Instance details

Defined in Data.Type.Ord

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

type family CmpNat (m :: Natural) (n :: Natural) :: Ordering Source

Comparison of type-level naturals, as a function.

Since: base-4.7.0.0

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/GHC-TypeNats-Internal.html