Safe Haskell	None
Language	Haskell2010

Basement.Compat.Natural

Synopsis

Documentation

data Natural #

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 # pred :: Natural -> Natural # toEnum :: Int -> Natural # fromEnum :: Natural -> Int # enumFrom :: Natural -> [Natural] # enumFromThen :: Natural -> Natural -> [Natural] # enumFromTo :: Natural -> Natural -> [Natural] # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] #
Eq Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural # rem :: Natural -> Natural -> Natural # div :: Natural -> Natural -> Natural # mod :: Natural -> Natural -> Natural # quotRem :: Natural -> Natural -> (Natural, Natural) # divMod :: Natural -> Natural -> (Natural, Natural) # toInteger :: Natural -> Integer #
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 # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Natural # toConstr :: Natural -> Constr # dataTypeOf :: Natural -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Natural) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Natural) # gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r # gmapQ :: (forall d. Data d => d -> u) -> Natural -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Natural -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Natural -> m Natural # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural #
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 # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Ord Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods compare :: Natural -> Natural -> Ordering # (<) :: Natural -> Natural -> Bool # (<=) :: Natural -> Natural -> Bool # (>) :: Natural -> Natural -> Bool # (>=) :: Natural -> Natural -> Bool # max :: Natural -> Natural -> Natural # min :: Natural -> Natural -> Natural #
Read Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Ix Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Ix Methods range :: (Natural, Natural) -> [Natural] # index :: (Natural, Natural) -> Natural -> Int # unsafeIndex :: (Natural, Natural) -> Natural -> Int # inRange :: (Natural, Natural) -> Natural -> Bool # rangeSize :: (Natural, Natural) -> Int # unsafeRangeSize :: (Natural, Natural) -> Int #
Bits Natural	Since: base-4.8.0
Instance details Defined in Data.Bits Methods (.&.) :: Natural -> Natural -> Natural # (.\|.) :: Natural -> Natural -> Natural # xor :: Natural -> Natural -> Natural # complement :: Natural -> Natural # shift :: Natural -> Int -> Natural # rotate :: Natural -> Int -> Natural # zeroBits :: Natural # bit :: Int -> Natural # setBit :: Natural -> Int -> Natural # clearBit :: Natural -> Int -> Natural # complementBit :: Natural -> Int -> Natural # testBit :: Natural -> Int -> Bool # bitSizeMaybe :: Natural -> Maybe Int # bitSize :: Natural -> Int # isSigned :: Natural -> Bool # shiftL :: Natural -> Int -> Natural # unsafeShiftL :: Natural -> Int -> Natural # shiftR :: Natural -> Int -> Natural # unsafeShiftR :: Natural -> Int -> Natural # rotateL :: Natural -> Int -> Natural # rotateR :: Natural -> Int -> Natural # popCount :: Natural -> Int #
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 #