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/Haskell 8

GHC.Num

Copyright (c) The University of Glasgow 1994-2002
License see libraries/base/LICENSE
Maintainer cvs-ghc@haskell.org
Stability internal
Portability non-portable (GHC Extensions)
Safe Haskell Trustworthy
Language Haskell2010

Description

The Num class and the Integer type.

class Num a where Source

Basic numeric class.

The Haskell Report defines no laws for Num. However, (+) and (*) are customarily expected to define a ring and have the following properties:

Associativity of (+)
(x + y) + z = x + (y + z)
Commutativity of (+)
x + y = y + x
fromInteger 0 is the additive identity
x + fromInteger 0 = x
negate gives the additive inverse
x + negate x = fromInteger 0
Associativity of (*)
(x * y) * z = x * (y * z)
fromInteger 1 is the multiplicative identity
x * fromInteger 1 = x and fromInteger 1 * x = x
Distributivity of (*) with respect to (+)
a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6 Source

(-) :: a -> a -> a infixl 6 Source

(*) :: a -> a -> a infixl 7 Source

negate :: a -> a Source

Unary negation.

abs :: a -> a Source

Absolute value.

signum :: a -> a Source

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a Source

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances
Instances details
Num Double

Note that due to the presence of NaN, not all elements of Double have an additive inverse.

>>> 0/0 + (negate 0/0 :: Double)
NaN

Also note that due to the presence of -0, Double's Num instance doesn't have an additive identity

>>> 0 + (-0 :: Double)
0.0

Since: base-2.1
Instance details

Defined in GHC.Float

Methods

(+) :: Double -> Double -> Double Source

(-) :: Double -> Double -> Double Source

(*) :: Double -> Double -> Double Source

negate :: Double -> Double Source

abs :: Double -> Double Source

signum :: Double -> Double Source

fromInteger :: Integer -> Double Source

Num Float

Note that due to the presence of NaN, not all elements of Float have an additive inverse.

>>> 0/0 + (negate 0/0 :: Float)
NaN

Also note that due to the presence of -0, Float's Num instance doesn't have an additive identity

>>> 0 + (-0 :: Float)
0.0

Since: base-2.1
Instance details

Defined in GHC.Float

Methods

(+) :: Float -> Float -> Float Source

(-) :: Float -> Float -> Float Source

(*) :: Float -> Float -> Float Source

negate :: Float -> Float Source

abs :: Float -> Float Source

signum :: Float -> Float Source

fromInteger :: Integer -> Float Source

Num Int

Since: base-2.1
Instance details

Defined in GHC.Num

Methods

(+) :: Int -> Int -> Int Source

(-) :: Int -> Int -> Int Source

(*) :: Int -> Int -> Int Source

negate :: Int -> Int Source

abs :: Int -> Int Source

signum :: Int -> Int Source

fromInteger :: Integer -> Int Source

Num Int8

Since: base-2.1
Instance details

Defined in GHC.Int

Methods

(+) :: Int8 -> Int8 -> Int8 Source

(-) :: Int8 -> Int8 -> Int8 Source

(*) :: Int8 -> Int8 -> Int8 Source

negate :: Int8 -> Int8 Source

abs :: Int8 -> Int8 Source

signum :: Int8 -> Int8 Source

fromInteger :: Integer -> Int8 Source

Num Int16

Since: base-2.1
Instance details

Defined in GHC.Int

Methods

(+) :: Int16 -> Int16 -> Int16 Source

(-) :: Int16 -> Int16 -> Int16 Source

(*) :: Int16 -> Int16 -> Int16 Source

negate :: Int16 -> Int16 Source

abs :: Int16 -> Int16 Source

signum :: Int16 -> Int16 Source

fromInteger :: Integer -> Int16 Source

Num Int32

Since: base-2.1
Instance details

Defined in GHC.Int

Methods

(+) :: Int32 -> Int32 -> Int32 Source

(-) :: Int32 -> Int32 -> Int32 Source

(*) :: Int32 -> Int32 -> Int32 Source

negate :: Int32 -> Int32 Source

abs :: Int32 -> Int32 Source

signum :: Int32 -> Int32 Source

fromInteger :: Integer -> Int32 Source

Num Int64

Since: base-2.1
Instance details

Defined in GHC.Int

Methods

(+) :: Int64 -> Int64 -> Int64 Source

(-) :: Int64 -> Int64 -> Int64 Source

(*) :: Int64 -> Int64 -> Int64 Source

negate :: Int64 -> Int64 Source

abs :: Int64 -> Int64 Source

signum :: Int64 -> Int64 Source

fromInteger :: Integer -> Int64 Source

Num Integer

Since: base-2.1
Instance details

Defined in GHC.Num

Methods

(+) :: Integer -> Integer -> Integer Source

(-) :: Integer -> Integer -> Integer Source

(*) :: Integer -> Integer -> Integer Source

negate :: Integer -> Integer Source

abs :: Integer -> Integer Source

signum :: Integer -> Integer Source

fromInteger :: Integer -> Integer 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

Num Word

Since: base-2.1
Instance details

Defined in GHC.Num

Methods

(+) :: Word -> Word -> Word Source

(-) :: Word -> Word -> Word Source

(*) :: Word -> Word -> Word Source

negate :: Word -> Word Source

abs :: Word -> Word Source

signum :: Word -> Word Source

fromInteger :: Integer -> Word Source

Num Word8

Since: base-2.1
Instance details

Defined in GHC.Word

Methods

(+) :: Word8 -> Word8 -> Word8 Source

(-) :: Word8 -> Word8 -> Word8 Source

(*) :: Word8 -> Word8 -> Word8 Source

negate :: Word8 -> Word8 Source

abs :: Word8 -> Word8 Source

signum :: Word8 -> Word8 Source

fromInteger :: Integer -> Word8 Source

Num Word16

Since: base-2.1
Instance details

Defined in GHC.Word

Methods

(+) :: Word16 -> Word16 -> Word16 Source

(-) :: Word16 -> Word16 -> Word16 Source

(*) :: Word16 -> Word16 -> Word16 Source

negate :: Word16 -> Word16 Source

abs :: Word16 -> Word16 Source

signum :: Word16 -> Word16 Source

fromInteger :: Integer -> Word16 Source

Num Word32

Since: base-2.1
Instance details

Defined in GHC.Word

Methods

(+) :: Word32 -> Word32 -> Word32 Source

(-) :: Word32 -> Word32 -> Word32 Source

(*) :: Word32 -> Word32 -> Word32 Source

negate :: Word32 -> Word32 Source

abs :: Word32 -> Word32 Source

signum :: Word32 -> Word32 Source

fromInteger :: Integer -> Word32 Source

Num Word64

Since: base-2.1
Instance details

Defined in GHC.Word

Methods

(+) :: Word64 -> Word64 -> Word64 Source

(-) :: Word64 -> Word64 -> Word64 Source

(*) :: Word64 -> Word64 -> Word64 Source

negate :: Word64 -> Word64 Source

abs :: Word64 -> Word64 Source

signum :: Word64 -> Word64 Source

fromInteger :: Integer -> Word64 Source

Num IntPtr
Instance details

Defined in Foreign.Ptr

Methods

(+) :: IntPtr -> IntPtr -> IntPtr Source

(-) :: IntPtr -> IntPtr -> IntPtr Source

(*) :: IntPtr -> IntPtr -> IntPtr Source

negate :: IntPtr -> IntPtr Source

abs :: IntPtr -> IntPtr Source

signum :: IntPtr -> IntPtr Source

fromInteger :: Integer -> IntPtr Source

Num WordPtr
Instance details

Defined in Foreign.Ptr

Methods

(+) :: WordPtr -> WordPtr -> WordPtr Source

(-) :: WordPtr -> WordPtr -> WordPtr Source

(*) :: WordPtr -> WordPtr -> WordPtr Source

negate :: WordPtr -> WordPtr Source

abs :: WordPtr -> WordPtr Source

signum :: WordPtr -> WordPtr Source

fromInteger :: Integer -> WordPtr Source

Num CUIntMax
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CUIntMax -> CUIntMax -> CUIntMax Source

(-) :: CUIntMax -> CUIntMax -> CUIntMax Source

(*) :: CUIntMax -> CUIntMax -> CUIntMax Source

negate :: CUIntMax -> CUIntMax Source

abs :: CUIntMax -> CUIntMax Source

signum :: CUIntMax -> CUIntMax Source

fromInteger :: Integer -> CUIntMax Source

Num CIntMax
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CIntMax -> CIntMax -> CIntMax Source

(-) :: CIntMax -> CIntMax -> CIntMax Source

(*) :: CIntMax -> CIntMax -> CIntMax Source

negate :: CIntMax -> CIntMax Source

abs :: CIntMax -> CIntMax Source

signum :: CIntMax -> CIntMax Source

fromInteger :: Integer -> CIntMax Source

Num CUIntPtr
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source

(-) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source

(*) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source

negate :: CUIntPtr -> CUIntPtr Source

abs :: CUIntPtr -> CUIntPtr Source

signum :: CUIntPtr -> CUIntPtr Source

fromInteger :: Integer -> CUIntPtr Source

Num CIntPtr
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CIntPtr -> CIntPtr -> CIntPtr Source

(-) :: CIntPtr -> CIntPtr -> CIntPtr Source

(*) :: CIntPtr -> CIntPtr -> CIntPtr Source

negate :: CIntPtr -> CIntPtr Source

abs :: CIntPtr -> CIntPtr Source

signum :: CIntPtr -> CIntPtr Source

fromInteger :: Integer -> CIntPtr Source

Num CSUSeconds
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source

(-) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source

(*) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source

negate :: CSUSeconds -> CSUSeconds Source

abs :: CSUSeconds -> CSUSeconds Source

signum :: CSUSeconds -> CSUSeconds Source

fromInteger :: Integer -> CSUSeconds Source

Num CUSeconds
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CUSeconds -> CUSeconds -> CUSeconds Source

(-) :: CUSeconds -> CUSeconds -> CUSeconds Source

(*) :: CUSeconds -> CUSeconds -> CUSeconds Source

negate :: CUSeconds -> CUSeconds Source

abs :: CUSeconds -> CUSeconds Source

signum :: CUSeconds -> CUSeconds Source

fromInteger :: Integer -> CUSeconds Source

Num CTime
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CTime -> CTime -> CTime Source

(-) :: CTime -> CTime -> CTime Source

(*) :: CTime -> CTime -> CTime Source

negate :: CTime -> CTime Source

abs :: CTime -> CTime Source

signum :: CTime -> CTime Source

fromInteger :: Integer -> CTime Source

Num CClock
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CClock -> CClock -> CClock Source

(-) :: CClock -> CClock -> CClock Source

(*) :: CClock -> CClock -> CClock Source

negate :: CClock -> CClock Source

abs :: CClock -> CClock Source

signum :: CClock -> CClock Source

fromInteger :: Integer -> CClock Source

Num CSigAtomic
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source

(-) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source

(*) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source

negate :: CSigAtomic -> CSigAtomic Source

abs :: CSigAtomic -> CSigAtomic Source

signum :: CSigAtomic -> CSigAtomic Source

fromInteger :: Integer -> CSigAtomic Source

Num CWchar
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CWchar -> CWchar -> CWchar Source

(-) :: CWchar -> CWchar -> CWchar Source

(*) :: CWchar -> CWchar -> CWchar Source

negate :: CWchar -> CWchar Source

abs :: CWchar -> CWchar Source

signum :: CWchar -> CWchar Source

fromInteger :: Integer -> CWchar Source

Num CSize
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CSize -> CSize -> CSize Source

(-) :: CSize -> CSize -> CSize Source

(*) :: CSize -> CSize -> CSize Source

negate :: CSize -> CSize Source

abs :: CSize -> CSize Source

signum :: CSize -> CSize Source

fromInteger :: Integer -> CSize Source

Num CPtrdiff
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source

(-) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source

(*) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source

negate :: CPtrdiff -> CPtrdiff Source

abs :: CPtrdiff -> CPtrdiff Source

signum :: CPtrdiff -> CPtrdiff Source

fromInteger :: Integer -> CPtrdiff Source

Num CDouble
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CDouble -> CDouble -> CDouble Source

(-) :: CDouble -> CDouble -> CDouble Source

(*) :: CDouble -> CDouble -> CDouble Source

negate :: CDouble -> CDouble Source

abs :: CDouble -> CDouble Source

signum :: CDouble -> CDouble Source

fromInteger :: Integer -> CDouble Source

Num CFloat
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CFloat -> CFloat -> CFloat Source

(-) :: CFloat -> CFloat -> CFloat Source

(*) :: CFloat -> CFloat -> CFloat Source

negate :: CFloat -> CFloat Source

abs :: CFloat -> CFloat Source

signum :: CFloat -> CFloat Source

fromInteger :: Integer -> CFloat Source

Num CBool
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CBool -> CBool -> CBool Source

(-) :: CBool -> CBool -> CBool Source

(*) :: CBool -> CBool -> CBool Source

negate :: CBool -> CBool Source

abs :: CBool -> CBool Source

signum :: CBool -> CBool Source

fromInteger :: Integer -> CBool Source

Num CULLong
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CULLong -> CULLong -> CULLong Source

(-) :: CULLong -> CULLong -> CULLong Source

(*) :: CULLong -> CULLong -> CULLong Source

negate :: CULLong -> CULLong Source

abs :: CULLong -> CULLong Source

signum :: CULLong -> CULLong Source

fromInteger :: Integer -> CULLong Source

Num CLLong
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CLLong -> CLLong -> CLLong Source

(-) :: CLLong -> CLLong -> CLLong Source

(*) :: CLLong -> CLLong -> CLLong Source

negate :: CLLong -> CLLong Source

abs :: CLLong -> CLLong Source

signum :: CLLong -> CLLong Source

fromInteger :: Integer -> CLLong Source

Num CULong
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CULong -> CULong -> CULong Source

(-) :: CULong -> CULong -> CULong Source

(*) :: CULong -> CULong -> CULong Source

negate :: CULong -> CULong Source

abs :: CULong -> CULong Source

signum :: CULong -> CULong Source

fromInteger :: Integer -> CULong Source

Num CLong
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CLong -> CLong -> CLong Source

(-) :: CLong -> CLong -> CLong Source

(*) :: CLong -> CLong -> CLong Source

negate :: CLong -> CLong Source

abs :: CLong -> CLong Source

signum :: CLong -> CLong Source

fromInteger :: Integer -> CLong Source

Num CUInt
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CUInt -> CUInt -> CUInt Source

(-) :: CUInt -> CUInt -> CUInt Source

(*) :: CUInt -> CUInt -> CUInt Source

negate :: CUInt -> CUInt Source

abs :: CUInt -> CUInt Source

signum :: CUInt -> CUInt Source

fromInteger :: Integer -> CUInt Source

Num CInt
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CInt -> CInt -> CInt Source

(-) :: CInt -> CInt -> CInt Source

(*) :: CInt -> CInt -> CInt Source

negate :: CInt -> CInt Source

abs :: CInt -> CInt Source

signum :: CInt -> CInt Source

fromInteger :: Integer -> CInt Source

Num CUShort
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CUShort -> CUShort -> CUShort Source

(-) :: CUShort -> CUShort -> CUShort Source

(*) :: CUShort -> CUShort -> CUShort Source

negate :: CUShort -> CUShort Source

abs :: CUShort -> CUShort Source

signum :: CUShort -> CUShort Source

fromInteger :: Integer -> CUShort Source

Num CShort
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CShort -> CShort -> CShort Source

(-) :: CShort -> CShort -> CShort Source

(*) :: CShort -> CShort -> CShort Source

negate :: CShort -> CShort Source

abs :: CShort -> CShort Source

signum :: CShort -> CShort Source

fromInteger :: Integer -> CShort Source

Num CUChar
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CUChar -> CUChar -> CUChar Source

(-) :: CUChar -> CUChar -> CUChar Source

(*) :: CUChar -> CUChar -> CUChar Source

negate :: CUChar -> CUChar Source

abs :: CUChar -> CUChar Source

signum :: CUChar -> CUChar Source

fromInteger :: Integer -> CUChar Source

Num CSChar
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CSChar -> CSChar -> CSChar Source

(-) :: CSChar -> CSChar -> CSChar Source

(*) :: CSChar -> CSChar -> CSChar Source

negate :: CSChar -> CSChar Source

abs :: CSChar -> CSChar Source

signum :: CSChar -> CSChar Source

fromInteger :: Integer -> CSChar Source

Num CChar
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CChar -> CChar -> CChar Source

(-) :: CChar -> CChar -> CChar Source

(*) :: CChar -> CChar -> CChar Source

negate :: CChar -> CChar Source

abs :: CChar -> CChar Source

signum :: CChar -> CChar Source

fromInteger :: Integer -> CChar Source

Num Fd
Instance details

Defined in System.Posix.Types

Methods

(+) :: Fd -> Fd -> Fd Source

(-) :: Fd -> Fd -> Fd Source

(*) :: Fd -> Fd -> Fd Source

negate :: Fd -> Fd Source

abs :: Fd -> Fd Source

signum :: Fd -> Fd Source

fromInteger :: Integer -> Fd Source

Num CKey
Instance details

Defined in System.Posix.Types

Methods

(+) :: CKey -> CKey -> CKey Source

(-) :: CKey -> CKey -> CKey Source

(*) :: CKey -> CKey -> CKey Source

negate :: CKey -> CKey Source

abs :: CKey -> CKey Source

signum :: CKey -> CKey Source

fromInteger :: Integer -> CKey Source

Num CId
Instance details

Defined in System.Posix.Types

Methods

(+) :: CId -> CId -> CId Source

(-) :: CId -> CId -> CId Source

(*) :: CId -> CId -> CId Source

negate :: CId -> CId Source

abs :: CId -> CId Source

signum :: CId -> CId Source

fromInteger :: Integer -> CId Source

Num CFsFilCnt
Instance details

Defined in System.Posix.Types

Methods

(+) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source

(-) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source

(*) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source

negate :: CFsFilCnt -> CFsFilCnt Source

abs :: CFsFilCnt -> CFsFilCnt Source

signum :: CFsFilCnt -> CFsFilCnt Source

fromInteger :: Integer -> CFsFilCnt Source

Num CFsBlkCnt
Instance details

Defined in System.Posix.Types

Methods

(+) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source

(-) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source

(*) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source

negate :: CFsBlkCnt -> CFsBlkCnt Source

abs :: CFsBlkCnt -> CFsBlkCnt Source

signum :: CFsBlkCnt -> CFsBlkCnt Source

fromInteger :: Integer -> CFsBlkCnt Source

Num CClockId
Instance details

Defined in System.Posix.Types

Methods

(+) :: CClockId -> CClockId -> CClockId Source

(-) :: CClockId -> CClockId -> CClockId Source

(*) :: CClockId -> CClockId -> CClockId Source

negate :: CClockId -> CClockId Source

abs :: CClockId -> CClockId Source

signum :: CClockId -> CClockId Source

fromInteger :: Integer -> CClockId Source

Num CBlkCnt
Instance details

Defined in System.Posix.Types

Methods

(+) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source

(-) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source

(*) :: CBlkCnt -> CBlkCnt -> CBlkCnt Source

negate :: CBlkCnt -> CBlkCnt Source

abs :: CBlkCnt -> CBlkCnt Source

signum :: CBlkCnt -> CBlkCnt Source

fromInteger :: Integer -> CBlkCnt Source

Num CBlkSize
Instance details

Defined in System.Posix.Types

Methods

(+) :: CBlkSize -> CBlkSize -> CBlkSize Source

(-) :: CBlkSize -> CBlkSize -> CBlkSize Source

(*) :: CBlkSize -> CBlkSize -> CBlkSize Source

negate :: CBlkSize -> CBlkSize Source

abs :: CBlkSize -> CBlkSize Source

signum :: CBlkSize -> CBlkSize Source

fromInteger :: Integer -> CBlkSize Source

Num CRLim
Instance details

Defined in System.Posix.Types

Methods

(+) :: CRLim -> CRLim -> CRLim Source

(-) :: CRLim -> CRLim -> CRLim Source

(*) :: CRLim -> CRLim -> CRLim Source

negate :: CRLim -> CRLim Source

abs :: CRLim -> CRLim Source

signum :: CRLim -> CRLim Source

fromInteger :: Integer -> CRLim Source

Num CTcflag
Instance details

Defined in System.Posix.Types

Methods

(+) :: CTcflag -> CTcflag -> CTcflag Source

(-) :: CTcflag -> CTcflag -> CTcflag Source

(*) :: CTcflag -> CTcflag -> CTcflag Source

negate :: CTcflag -> CTcflag Source

abs :: CTcflag -> CTcflag Source

signum :: CTcflag -> CTcflag Source

fromInteger :: Integer -> CTcflag Source

Num CSpeed
Instance details

Defined in System.Posix.Types

Methods

(+) :: CSpeed -> CSpeed -> CSpeed Source

(-) :: CSpeed -> CSpeed -> CSpeed Source

(*) :: CSpeed -> CSpeed -> CSpeed Source

negate :: CSpeed -> CSpeed Source

abs :: CSpeed -> CSpeed Source

signum :: CSpeed -> CSpeed Source

fromInteger :: Integer -> CSpeed Source

Num CCc
Instance details

Defined in System.Posix.Types

Methods

(+) :: CCc -> CCc -> CCc Source

(-) :: CCc -> CCc -> CCc Source

(*) :: CCc -> CCc -> CCc Source

negate :: CCc -> CCc Source

abs :: CCc -> CCc Source

signum :: CCc -> CCc Source

fromInteger :: Integer -> CCc Source

Num CUid
Instance details

Defined in System.Posix.Types

Methods

(+) :: CUid -> CUid -> CUid Source

(-) :: CUid -> CUid -> CUid Source

(*) :: CUid -> CUid -> CUid Source

negate :: CUid -> CUid Source

abs :: CUid -> CUid Source

signum :: CUid -> CUid Source

fromInteger :: Integer -> CUid Source

Num CNlink
Instance details

Defined in System.Posix.Types

Methods

(+) :: CNlink -> CNlink -> CNlink Source

(-) :: CNlink -> CNlink -> CNlink Source

(*) :: CNlink -> CNlink -> CNlink Source

negate :: CNlink -> CNlink Source

abs :: CNlink -> CNlink Source

signum :: CNlink -> CNlink Source

fromInteger :: Integer -> CNlink Source

Num CGid
Instance details

Defined in System.Posix.Types

Methods

(+) :: CGid -> CGid -> CGid Source

(-) :: CGid -> CGid -> CGid Source

(*) :: CGid -> CGid -> CGid Source

negate :: CGid -> CGid Source

abs :: CGid -> CGid Source

signum :: CGid -> CGid Source

fromInteger :: Integer -> CGid Source

Num CSsize
Instance details

Defined in System.Posix.Types

Methods

(+) :: CSsize -> CSsize -> CSsize Source

(-) :: CSsize -> CSsize -> CSsize Source

(*) :: CSsize -> CSsize -> CSsize Source

negate :: CSsize -> CSsize Source

abs :: CSsize -> CSsize Source

signum :: CSsize -> CSsize Source

fromInteger :: Integer -> CSsize Source

Num CPid
Instance details

Defined in System.Posix.Types

Methods

(+) :: CPid -> CPid -> CPid Source

(-) :: CPid -> CPid -> CPid Source

(*) :: CPid -> CPid -> CPid Source

negate :: CPid -> CPid Source

abs :: CPid -> CPid Source

signum :: CPid -> CPid Source

fromInteger :: Integer -> CPid Source

Num COff
Instance details

Defined in System.Posix.Types

Methods

(+) :: COff -> COff -> COff Source

(-) :: COff -> COff -> COff Source

(*) :: COff -> COff -> COff Source

negate :: COff -> COff Source

abs :: COff -> COff Source

signum :: COff -> COff Source

fromInteger :: Integer -> COff Source

Num CMode
Instance details

Defined in System.Posix.Types

Methods

(+) :: CMode -> CMode -> CMode Source

(-) :: CMode -> CMode -> CMode Source

(*) :: CMode -> CMode -> CMode Source

negate :: CMode -> CMode Source

abs :: CMode -> CMode Source

signum :: CMode -> CMode Source

fromInteger :: Integer -> CMode Source

Num CIno
Instance details

Defined in System.Posix.Types

Methods

(+) :: CIno -> CIno -> CIno Source

(-) :: CIno -> CIno -> CIno Source

(*) :: CIno -> CIno -> CIno Source

negate :: CIno -> CIno Source

abs :: CIno -> CIno Source

signum :: CIno -> CIno Source

fromInteger :: Integer -> CIno Source

Num CDev
Instance details

Defined in System.Posix.Types

Methods

(+) :: CDev -> CDev -> CDev Source

(-) :: CDev -> CDev -> CDev Source

(*) :: CDev -> CDev -> CDev Source

negate :: CDev -> CDev Source

abs :: CDev -> CDev Source

signum :: CDev -> CDev Source

fromInteger :: Integer -> CDev Source

Integral a => Num (Ratio a)

Since: base-2.0.1
Instance details

Defined in GHC.Real

Methods

(+) :: Ratio a -> Ratio a -> Ratio a Source

(-) :: Ratio a -> Ratio a -> Ratio a Source

(*) :: Ratio a -> Ratio a -> Ratio a Source

negate :: Ratio a -> Ratio a Source

abs :: Ratio a -> Ratio a Source

signum :: Ratio a -> Ratio a Source

fromInteger :: Integer -> Ratio a Source

Num a => Num (Down a)

Since: base-4.11.0.0
Instance details

Defined in Data.Ord

Methods

(+) :: Down a -> Down a -> Down a Source

(-) :: Down a -> Down a -> Down a Source

(*) :: Down a -> Down a -> Down a Source

negate :: Down a -> Down a Source

abs :: Down a -> Down a Source

signum :: Down a -> Down a Source

fromInteger :: Integer -> Down a Source

Num a => Num (Product a)

Since: base-4.7.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Product a -> Product a -> Product a Source

(-) :: Product a -> Product a -> Product a Source

(*) :: Product a -> Product a -> Product a Source

negate :: Product a -> Product a Source

abs :: Product a -> Product a Source

signum :: Product a -> Product a Source

fromInteger :: Integer -> Product a Source

Num a => Num (Sum a)

Since: base-4.7.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Sum a -> Sum a -> Sum a Source

(-) :: Sum a -> Sum a -> Sum a Source

(*) :: Sum a -> Sum a -> Sum a Source

negate :: Sum a -> Sum a Source

abs :: Sum a -> Sum a Source

signum :: Sum a -> Sum a Source

fromInteger :: Integer -> Sum a Source

Num a => Num (Identity a)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Identity

Methods

(+) :: Identity a -> Identity a -> Identity a Source

(-) :: Identity a -> Identity a -> Identity a Source

(*) :: Identity a -> Identity a -> Identity a Source

negate :: Identity a -> Identity a Source

abs :: Identity a -> Identity a Source

signum :: Identity a -> Identity a Source

fromInteger :: Integer -> Identity a Source

Num a => Num (Max a)

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

(+) :: Max a -> Max a -> Max a Source

(-) :: Max a -> Max a -> Max a Source

(*) :: Max a -> Max a -> Max a Source

negate :: Max a -> Max a Source

abs :: Max a -> Max a Source

signum :: Max a -> Max a Source

fromInteger :: Integer -> Max a Source

Num a => Num (Min a)

Since: base-4.9.0.0
Instance details

Defined in Data.Semigroup

Methods

(+) :: Min a -> Min a -> Min a Source

(-) :: Min a -> Min a -> Min a Source

(*) :: Min a -> Min a -> Min a Source

negate :: Min a -> Min a Source

abs :: Min a -> Min a Source

signum :: Min a -> Min a Source

fromInteger :: Integer -> Min a Source

HasResolution a => Num (Fixed a)

Since: base-2.1
Instance details

Defined in Data.Fixed

Methods

(+) :: Fixed a -> Fixed a -> Fixed a Source

(-) :: Fixed a -> Fixed a -> Fixed a Source

(*) :: Fixed a -> Fixed a -> Fixed a Source

negate :: Fixed a -> Fixed a Source

abs :: Fixed a -> Fixed a Source

signum :: Fixed a -> Fixed a Source

fromInteger :: Integer -> Fixed a Source

RealFloat a => Num (Complex a)

Since: base-2.1
Instance details

Defined in Data.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a Source

(-) :: Complex a -> Complex a -> Complex a Source

(*) :: Complex a -> Complex a -> Complex a Source

negate :: Complex a -> Complex a Source

abs :: Complex a -> Complex a Source

signum :: Complex a -> Complex a Source

fromInteger :: Integer -> Complex a Source

Num a => Num (Op a b)
Instance details

Defined in Data.Functor.Contravariant

Methods

(+) :: Op a b -> Op a b -> Op a b Source

(-) :: Op a b -> Op a b -> Op a b Source

(*) :: Op a b -> Op a b -> Op a b Source

negate :: Op a b -> Op a b Source

abs :: Op a b -> Op a b Source

signum :: Op a b -> Op a b Source

fromInteger :: Integer -> Op a b Source

Num (f a) => Num (Alt f a)

Since: base-4.8.0.0
Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Alt f a -> Alt f a -> Alt f a Source

(-) :: Alt f a -> Alt f a -> Alt f a Source

(*) :: Alt f a -> Alt f a -> Alt f a Source

negate :: Alt f a -> Alt f a Source

abs :: Alt f a -> Alt f a Source

signum :: Alt f a -> Alt f a Source

fromInteger :: Integer -> Alt f a Source

(Applicative f, Num a) => Num (Ap f a)

Since: base-4.12.0.0
Instance details

Defined in Data.Monoid

Methods

(+) :: Ap f a -> Ap f a -> Ap f a Source

(-) :: Ap f a -> Ap f a -> Ap f a Source

(*) :: Ap f a -> Ap f a -> Ap f a Source

negate :: Ap f a -> Ap f a Source

abs :: Ap f a -> Ap f a Source

signum :: Ap f a -> Ap f a Source

fromInteger :: Integer -> Ap f a Source

Num a => Num (Const a b)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Const

Methods

(+) :: Const a b -> Const a b -> Const a b Source

(-) :: Const a b -> Const a b -> Const a b Source

(*) :: Const a b -> Const a b -> Const a b Source

negate :: Const a b -> Const a b Source

abs :: Const a b -> Const a b Source

signum :: Const a b -> Const a b Source

fromInteger :: Integer -> Const a b Source

subtract :: Num a => a -> a -> a Source

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

module GHC.Integer

module GHC.Natural

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/base-4.13.0.0/GHC-Num.html