Safe Haskell	Trustworthy
Language	Haskell2010

GHC.TypeNats.Internal

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 imported in Ord.

Since: base-4.16.0.0

Synopsis

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

Documentation

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 #
TestCoercion SNat Source #	Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testCoercion :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (Coercion a b) Source #
TestEquality SNat Source #	Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testEquality :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (a :~: b) 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