Safe Haskell	Safe-Inferred
Language	GHC2021

Integer.Natural

Contents

Type
Subtraction
Conversion
One (1)

Synopsis

data Natural
subtract :: Natural -> Natural -> Signed
toPositive :: Natural -> Maybe Positive
fromPositive :: Positive -> Natural
toInteger :: Natural -> Integer
fromInteger :: Integer -> Maybe Natural
toSigned :: Natural -> Signed
fromSigned :: Signed -> Maybe Natural
toInt :: Natural -> Maybe Int
fromInt :: Int -> Maybe Natural
toWord :: Natural -> Maybe Word
fromWord :: Word -> Natural
one :: Natural
addOne :: Integer -> Integer
subtractOne :: Natural -> Maybe Signed

Type

data Natural #

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Instances

Instances details

Bits Natural	Since: base-4.8.0
Instance details Defined in GHC.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 #
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] #
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 #
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 #
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 #
NFData Natural	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Natural -> () #
Eq Natural
Instance details Defined in GHC.Num.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Ord Natural
Instance details Defined in GHC.Num.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 #
BoundedBelow Natural Source #
Instance details Defined in Integer.BoundedBelow Methods minBound :: Natural Source #
ConvertWithFinite Natural Source #
Instance details Defined in Integer.Finite Methods toWord :: Natural -> Maybe Word Source # fromWord :: Word -> Maybe Natural Source # toInt :: Natural -> Maybe Int Source # fromInt :: Int -> Maybe Natural Source #
Subtraction Natural Source #
Instance details Defined in Integer.Subtraction Methods subtractInteger :: Natural -> Natural -> Integer Source # subtractSigned :: Natural -> Natural -> Signed Source #
IntegerConvert Positive Natural Source #
Instance details Defined in Integer.Conversion Methods convert :: Positive -> Natural Source #
IntegerConvert Natural Signed Source #
Instance details Defined in Integer.Conversion Methods convert :: Natural -> Signed Source #
IntegerConvert Natural Integer Source #
Instance details Defined in Integer.Conversion Methods convert :: Natural -> Integer Source #
IntegerConvert Natural Natural Source #
Instance details Defined in Integer.Conversion Methods convert :: Natural -> Natural Source #
IntegerEquiv Natural Natural Source #
Instance details Defined in Integer.Conversion
IntegerNarrow Positive Natural Source #
Instance details Defined in Integer.Conversion Methods narrow :: Positive -> Maybe Natural Source #
IntegerNarrow Signed Natural Source #
Instance details Defined in Integer.Conversion Methods narrow :: Signed -> Maybe Natural Source #
IntegerNarrow Integer Natural Source #
Instance details Defined in Integer.Conversion Methods narrow :: Integer -> Maybe Natural Source #
IntegerNarrow Natural Positive Source #
Instance details Defined in Integer.Conversion Methods narrow :: Natural -> Maybe Positive Source #
IntegerNarrow Natural Signed Source #
Instance details Defined in Integer.Conversion Methods narrow :: Natural -> Maybe Signed Source #
IntegerNarrow Natural Integer Source #
Instance details Defined in Integer.Conversion Methods narrow :: Natural -> Maybe Integer Source #
IntegerNarrow Natural Natural Source #
Instance details Defined in Integer.Conversion Methods narrow :: Natural -> Maybe Natural Source #