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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 CBool Source
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 CChar Source
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 CClock Source
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 CDouble Source
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 Source
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 CInt Source
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 CIntMax Source
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 CIntPtr Source
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 CLLong Source
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 CLong Source
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 CPtrdiff Source
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 CSChar Source
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 CSUSeconds Source
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 CShort Source
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 CSigAtomic Source
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 CSize Source
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 CTime Source
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 CUChar Source
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 CUInt Source
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 CUIntMax Source
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 CUIntPtr Source
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 CULLong Source
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 CULong Source
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 CUSeconds Source
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 CUShort Source
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 CWchar Source
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 IntPtr Source
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 Source
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 Int16 Source

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 Source

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 Source

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 Int8 Source

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 Word16 Source

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 Source

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 Source

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 Word8 Source

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 CBlkCnt Source
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 Source
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 CCc Source
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 CClockId Source
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 CDev Source
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
Num CFsBlkCnt Source
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 CFsFilCnt Source
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 CGid Source
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 CId Source
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 CIno Source
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 CKey Source
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 CMode Source
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 CNfds Source
Instance details

Defined in System.Posix.Types

Methods

(+) :: CNfds -> CNfds -> CNfds Source

(-) :: CNfds -> CNfds -> CNfds Source

(*) :: CNfds -> CNfds -> CNfds Source

negate :: CNfds -> CNfds Source

abs :: CNfds -> CNfds Source

signum :: CNfds -> CNfds Source

fromInteger :: Integer -> CNfds Source
Num CNlink Source
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 COff Source
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 CPid Source
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 CRLim Source
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 CSocklen Source
Instance details

Defined in System.Posix.Types

Methods

(+) :: CSocklen -> CSocklen -> CSocklen Source

(-) :: CSocklen -> CSocklen -> CSocklen Source

(*) :: CSocklen -> CSocklen -> CSocklen Source

negate :: CSocklen -> CSocklen Source

abs :: CSocklen -> CSocklen Source

signum :: CSocklen -> CSocklen Source

fromInteger :: Integer -> CSocklen Source
Num CSpeed Source
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 CSsize Source
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 CTcflag Source
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 CUid Source
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 Fd Source
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 Integer Source

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 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
Num Double Source

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 Source

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 Source

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 Word Source

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
RealFloat a => Num (Complex a) Source

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 (Identity a) Source

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 (Down a) Source

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 (Max a) Source

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) Source

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
Num a => Num (Product a) Source

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) Source

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
Integral a => Num (Ratio a) Source

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
HasResolution a => Num (Fixed a) Source

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
Num a => Num (Op a b) Source
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 a => Num (Const a b) Source

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

Note that even if the underlying Num and Applicative instances are lawful, for most Applicatives, this instance will not be lawful. If you use this instance with the list Applicative, the following customary laws will not hold:

Commutativity:

>>> Ap [10,20] + Ap [1,2]
Ap {getAp = [11,12,21,22]}
>>> Ap [1,2] + Ap [10,20]
Ap {getAp = [11,21,12,22]}

Additive inverse:

>>> Ap [] + negate (Ap [])
Ap {getAp = []}
>>> fromInteger 0 :: Ap [] Int
Ap {getAp = [0]}

Distributivity:

>>> Ap [1,2] * (3 + 4)
Ap {getAp = [7,14]}
>>> (Ap [1,2] * 3) + (Ap [1,2] * 4)
Ap {getAp = [7,11,10,14]}

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

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

quotRemInteger :: Integer -> Integer -> (# Integer, Integer #) Source

Deprecated: Use integerQuotRem# instead

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.Num.Integer

module GHC.Num.Natural

module GHC.Natural

module GHC.Integer

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/GHC-Num.html