Safe Haskell	None
Language	Haskell2010

Basement.Compat.Natural

Synopsis

Documentation

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 #
Integral Natural Source #
Instance details Defined in Basement.Compat.NumLiteral Methods fromInteger :: Integer -> Natural Source #
IsNatural Natural Source #
Instance details Defined in Basement.Numerical.Number Methods toNatural :: Natural -> Natural Source #
IsIntegral Natural Source #
Instance details Defined in Basement.Numerical.Number Methods toInteger :: Natural -> Integer Source #
Subtractive Natural Source #
Instance details Defined in Basement.Numerical.Subtractive Associated Types type Difference Natural Source # Methods (-) :: Natural -> Natural -> Difference Natural Source #
Additive Natural Source #
Instance details Defined in Basement.Numerical.Additive Methods azero :: Natural Source # (+) :: Natural -> Natural -> Natural Source # scale :: IsNatural n => n -> Natural -> Natural Source #
IDivisible Natural Source #
Instance details Defined in Basement.Numerical.Multiplicative Methods div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # divMod :: Natural -> Natural -> ( Natural , Natural ) Source #
Multiplicative Natural Source #
Instance details Defined in Basement.Numerical.Multiplicative Methods midentity :: Natural Source # (*) :: Natural -> Natural -> Natural Source # (^) :: ( IsNatural n, Enum n, IDivisible n) => Natural -> n -> Natural Source #
NormalForm Natural Source #
Instance details Defined in Basement.NormalForm Methods toNormalForm :: Natural -> () Source #
IsNatural a => IntegralUpsize a Natural Source #
Instance details Defined in Basement.IntegralConv Methods integralUpsize :: a -> Natural Source #
IntegralDownsize Integer Natural Source #
Instance details Defined in Basement.IntegralConv Methods integralDownsize :: Integer -> Natural Source # integralDownsizeCheck :: Integer -> Maybe Natural Source #
IntegralDownsize Natural Word8 Source #
Instance details Defined in Basement.IntegralConv Methods integralDownsize :: Natural -> Word8 Source # integralDownsizeCheck :: Natural -> Maybe Word8 Source #
IntegralDownsize Natural Word16 Source #
Instance details Defined in Basement.IntegralConv Methods integralDownsize :: Natural -> Word16 Source # integralDownsizeCheck :: Natural -> Maybe Word16 Source #
IntegralDownsize Natural Word32 Source #
Instance details Defined in Basement.IntegralConv Methods integralDownsize :: Natural -> Word32 Source # integralDownsizeCheck :: Natural -> Maybe Word32 Source #
IntegralDownsize Natural Word64 Source #
Instance details Defined in Basement.IntegralConv Methods integralDownsize :: Natural -> Word64 Source # integralDownsizeCheck :: Natural -> Maybe Word64 Source #
IsNatural n => From n Natural Source #
Instance details Defined in Basement.From Methods from :: n -> Natural Source #
type Difference Natural Source #
Instance details Defined in Basement.Numerical.Subtractive type Difference Natural = Maybe Natural

integerToNatural :: Integer -> Natural Source #

naturalToInteger :: Natural -> Integer Source #