base-4.15.0.0: Basic libraries
Copyright(c) The University of Glasgow 1994-2002
Licensesee libraries/base/LICENSE
Maintainercvs-ghc@haskell.org
Stabilityinternal
Portabilitynon-portable (GHC Extensions)
Safe HaskellTrustworthy
LanguageHaskell2010

GHC.Num

Description

The Num class and the Integer type.

Synopsis

Documentation

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 CNfds # 
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 CSocklen # 
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 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 #

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 #

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 #

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) #

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 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.

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

Deprecated: Use integerQuotRem# instead

module GHC.Num.Integer

module GHC.Num.Natural

module GHC.Natural

module GHC.Integer