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/Haskell 9

GHC.Num

Copyright (c) The University of Glasgow 1994-2002
License see libraries/base/LICENSE
Maintainer [email protected]
Stability internal
Portability non-portable (GHC Extensions)
Safe Haskell None
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)
Coherence with toInteger
if the type also implements Integral, then fromInteger is a left inverse for toInteger, i.e. fromInteger (toInteger i) == i

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 Unique Source

Since: base-4.4.0.0
Instance details

Defined in GHC.Internal.Event.Unique

Methods

(+) :: Unique -> Unique -> Unique Source

(-) :: Unique -> Unique -> Unique Source

(*) :: Unique -> Unique -> Unique Source

negate :: Unique -> Unique Source

abs :: Unique -> Unique Source

signum :: Unique -> Unique Source

fromInteger :: Integer -> Unique Source

Num CBool Source
Instance details

Defined in GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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.Internal.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.Internal.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.Internal.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.Internal.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 CBlkCnt Source
Instance details

Defined in GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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 Word16 Source

Since: base-2.1
Instance details

Defined in GHC.Internal.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.Internal.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.Internal.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.Internal.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 Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.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.Internal.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 Int Source

Since: base-2.1
Instance details

Defined in GHC.Internal.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.Internal.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 (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 (Identity a) Source

Since: base-4.9.0.0
Instance details

Defined in GHC.Internal.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 GHC.Internal.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) Source

Since: base-4.7.0.0
Instance details

Defined in GHC.Internal.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 GHC.Internal.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.Internal.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

Multiplication is not associative or distributive:

>>> (0.2 * 0.6 :: Deci) * 0.9 == 0.2 * (0.6 * 0.9)
False

>>> (0.1 + 0.1 :: Deci) * 0.5 == 0.1 * 0.5 + 0.1 * 0.5
False

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 GHC.Internal.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 GHC.Internal.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 GHC.Internal.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

Num (f (g a)) => Num (Compose f g a) Source

Since: base-4.19.0.0
Instance details

Defined in Data.Functor.Compose

Methods

(+) :: Compose f g a -> Compose f g a -> Compose f g a Source

(-) :: Compose f g a -> Compose f g a -> Compose f g a Source

(*) :: Compose f g a -> Compose f g a -> Compose f g a Source

negate :: Compose f g a -> Compose f g a Source

abs :: Compose f g a -> Compose f g a Source

signum :: Compose f g a -> Compose f g a Source

fromInteger :: Integer -> Compose f g a 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

integerAbs :: Integer -> Integer

integerAdd :: Integer -> Integer -> Integer

integerAnd :: Integer -> Integer -> Integer

integerBit :: Word -> Integer

integerBit# :: Word# -> Integer

integerCheck :: Integer -> Bool

integerCheck# :: Integer -> Bool#

integerCompare :: Integer -> Integer -> Ordering

integerComplement :: Integer -> Integer

integerDecodeDouble# :: Double# -> (# Integer, Int# #)

integerDiv :: Integer -> Integer -> Integer

integerDivMod :: Integer -> Integer -> (Integer, Integer)

integerDivMod# :: Integer -> Integer -> (# Integer, Integer #)

integerEncodeDouble :: Integer -> Int -> Double

integerEncodeDouble# :: Integer -> Int# -> Double#

integerEncodeFloat# :: Integer -> Int# -> Float#

integerEq :: Integer -> Integer -> Bool

integerEq# :: Integer -> Integer -> Bool#

integerFromAddr :: Word# -> Addr# -> Bool# -> IO Integer

integerFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Integer #)

integerFromBigNat# :: BigNat# -> Integer

integerFromBigNatNeg# :: BigNat# -> Integer

integerFromBigNatSign# :: Int# -> BigNat# -> Integer

integerFromByteArray :: Word# -> ByteArray# -> Word# -> Bool# -> Integer

integerFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Integer #)

integerFromInt :: Int -> Integer

integerFromInt# :: Int# -> Integer

integerFromInt64# :: Int64# -> Integer

integerFromNatural :: Natural -> Integer

integerFromWord :: Word -> Integer

integerFromWord# :: Word# -> Integer

integerFromWord64# :: Word64# -> Integer

integerFromWordList :: Bool -> [Word] -> Integer

integerFromWordNeg# :: Word# -> Integer

integerFromWordSign# :: Int# -> Word# -> Integer

integerGcd :: Integer -> Integer -> Integer

integerGcde :: Integer -> Integer -> (Integer, Integer, Integer)

integerGcde# :: Integer -> Integer -> (# Integer, Integer, Integer #)

integerGe :: Integer -> Integer -> Bool

integerGe# :: Integer -> Integer -> Bool#

integerGt :: Integer -> Integer -> Bool

integerGt# :: Integer -> Integer -> Bool#

integerIsNegative :: Integer -> Bool

integerIsNegative# :: Integer -> Bool#

integerIsOne :: Integer -> Bool

integerIsPowerOf2# :: Integer -> (# (# #) | Word# #)

integerIsZero :: Integer -> Bool

integerLcm :: Integer -> Integer -> Integer

integerLe :: Integer -> Integer -> Bool

integerLe# :: Integer -> Integer -> Bool#

integerLog2 :: Integer -> Word

integerLog2# :: Integer -> Word#

integerLogBase :: Integer -> Integer -> Word

integerLogBase# :: Integer -> Integer -> Word#

integerLogBaseWord :: Word -> Integer -> Word

integerLogBaseWord# :: Word# -> Integer -> Word#

integerLt :: Integer -> Integer -> Bool

integerLt# :: Integer -> Integer -> Bool#

integerMod :: Integer -> Integer -> Integer

integerMul :: Integer -> Integer -> Integer

integerNe :: Integer -> Integer -> Bool

integerNe# :: Integer -> Integer -> Bool#

integerNegate :: Integer -> Integer

integerOne :: Integer

integerOr :: Integer -> Integer -> Integer

integerPopCount# :: Integer -> Int#

integerPowMod# :: Integer -> Integer -> Natural -> (# Natural | () #)

integerQuot :: Integer -> Integer -> Integer

integerQuotRem :: Integer -> Integer -> (Integer, Integer)

integerQuotRem# :: Integer -> Integer -> (# Integer, Integer #)

integerRecipMod# :: Integer -> Natural -> (# Natural | () #)

integerRem :: Integer -> Integer -> Integer

integerShiftL :: Integer -> Word -> Integer

integerShiftL# :: Integer -> Word# -> Integer

integerShiftR :: Integer -> Word -> Integer

integerShiftR# :: Integer -> Word# -> Integer

integerSignum :: Integer -> Integer

integerSignum# :: Integer -> Int#

integerSizeInBase# :: Word# -> Integer -> Word#

integerSqr :: Integer -> Integer

integerSub :: Integer -> Integer -> Integer

integerTestBit :: Integer -> Word -> Bool

integerTestBit# :: Integer -> Word# -> Bool#

integerToAddr :: Integer -> Addr# -> Bool# -> IO Word

integerToAddr# :: Integer -> Addr# -> Bool# -> State# s -> (# State# s, Word# #)

integerToBigNatClamp# :: Integer -> BigNat#

integerToBigNatSign# :: Integer -> (# Int#, BigNat# #)

integerToInt :: Integer -> Int

integerToInt# :: Integer -> Int#

integerToInt64# :: Integer -> Int64#

integerToMutableByteArray :: Integer -> MutableByteArray# RealWorld -> Word# -> Bool# -> IO Word

integerToMutableByteArray# :: Integer -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #)

integerToNatural :: Integer -> Natural

integerToNaturalClamp :: Integer -> Natural

integerToNaturalThrow :: Integer -> Natural

integerToWord :: Integer -> Word

integerToWord# :: Integer -> Word#

integerToWord64# :: Integer -> Word64#

integerXor :: Integer -> Integer -> Integer

integerZero :: Integer

data Integer

Constructors

IS Int#
IP ByteArray#
IN ByteArray#
Instances
Instances details
PrintfArg Integer Source

Since: base-2.1
Instance details

Defined in Text.Printf

Methods

formatArg :: Integer -> FieldFormatter Source

parseFormat :: Integer -> ModifierParser Source

Bits Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Bits

Methods

(.&.) :: Integer -> Integer -> Integer Source

(.|.) :: Integer -> Integer -> Integer Source

xor :: Integer -> Integer -> Integer Source

complement :: Integer -> Integer Source

shift :: Integer -> Int -> Integer Source

rotate :: Integer -> Int -> Integer Source

zeroBits :: Integer Source

bit :: Int -> Integer Source

setBit :: Integer -> Int -> Integer Source

clearBit :: Integer -> Int -> Integer Source

complementBit :: Integer -> Int -> Integer Source

testBit :: Integer -> Int -> Bool Source

bitSizeMaybe :: Integer -> Maybe Int Source

bitSize :: Integer -> Int Source

isSigned :: Integer -> Bool Source

shiftL :: Integer -> Int -> Integer Source

unsafeShiftL :: Integer -> Int -> Integer Source

shiftR :: Integer -> Int -> Integer Source

unsafeShiftR :: Integer -> Int -> Integer Source

rotateL :: Integer -> Int -> Integer Source

rotateR :: Integer -> Int -> Integer Source

popCount :: Integer -> Int Source

Data Integer Source

Since: base-4.0.0.0
Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer Source

toConstr :: Integer -> Constr Source

dataTypeOf :: Integer -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) Source

gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

Enum Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Enum

Methods

succ :: Integer -> Integer Source

pred :: Integer -> Integer Source

toEnum :: Int -> Integer Source

fromEnum :: Integer -> Int Source

enumFrom :: Integer -> [Integer] Source

enumFromThen :: Integer -> Integer -> [Integer] Source

enumFromTo :: Integer -> Integer -> [Integer] Source

enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source

Ix Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Ix

Methods

range :: (Integer, Integer) -> [Integer] Source

index :: (Integer, Integer) -> Integer -> Int Source

unsafeIndex :: (Integer, Integer) -> Integer -> Int Source

inRange :: (Integer, Integer) -> Integer -> Bool Source

rangeSize :: (Integer, Integer) -> Int Source

unsafeRangeSize :: (Integer, Integer) -> Int Source

Num Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.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

Read Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS Integer Source

readList :: ReadS [Integer] Source

readPrec :: ReadPrec Integer Source

readListPrec :: ReadPrec [Integer] Source

Integral Integer Source

Since: base-2.0.1
Instance details

Defined in GHC.Internal.Real

Methods

quot :: Integer -> Integer -> Integer Source

rem :: Integer -> Integer -> Integer Source

div :: Integer -> Integer -> Integer Source

mod :: Integer -> Integer -> Integer Source

quotRem :: Integer -> Integer -> (Integer, Integer) Source

divMod :: Integer -> Integer -> (Integer, Integer) Source

toInteger :: Integer -> Integer Source

Real Integer Source

Since: base-2.0.1
Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Integer -> Rational Source

Show Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Integer -> ShowS Source

show :: Integer -> String Source

showList :: [Integer] -> ShowS Source

Eq Integer
Instance details

Defined in GHC.Num.Integer

Methods

(==) :: Integer -> Integer -> Bool Source

(/=) :: Integer -> Integer -> Bool Source

Ord Integer
Instance details

Defined in GHC.Num.Integer

Methods

compare :: Integer -> Integer -> Ordering Source

(<) :: Integer -> Integer -> Bool Source

(<=) :: Integer -> Integer -> Bool Source

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

(>=) :: Integer -> Integer -> Bool Source

max :: Integer -> Integer -> Integer Source

min :: Integer -> Integer -> Integer Source

Lift Integer Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Integer -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Integer -> Code m Integer Source

naturalAdd :: Natural -> Natural -> Natural

naturalAnd :: Natural -> Natural -> Natural

naturalAndNot :: Natural -> Natural -> Natural

naturalBit :: Word -> Natural

naturalBit# :: Word# -> Natural

naturalCheck :: Natural -> Bool

naturalCheck# :: Natural -> Bool#

naturalClearBit :: Natural -> Word -> Natural

naturalClearBit# :: Natural -> Word# -> Natural

naturalCompare :: Natural -> Natural -> Ordering

naturalComplementBit :: Natural -> Word -> Natural

naturalComplementBit# :: Natural -> Word# -> Natural

naturalEncodeDouble# :: Natural -> Int# -> Double#

naturalEncodeFloat# :: Natural -> Int# -> Float#

naturalEq :: Natural -> Natural -> Bool

naturalEq# :: Natural -> Natural -> Bool#

naturalFromAddr :: Word# -> Addr# -> Bool# -> IO Natural

naturalFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Natural #)

naturalFromBigNat# :: BigNat# -> Natural

naturalFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Natural #)

naturalFromWord :: Word -> Natural

naturalFromWord# :: Word# -> Natural

naturalFromWord2# :: Word# -> Word# -> Natural

naturalFromWordList :: [Word] -> Natural

naturalGcd :: Natural -> Natural -> Natural

naturalGe :: Natural -> Natural -> Bool

naturalGe# :: Natural -> Natural -> Bool#

naturalGt :: Natural -> Natural -> Bool

naturalGt# :: Natural -> Natural -> Bool#

naturalIsOne :: Natural -> Bool

naturalIsPowerOf2# :: Natural -> (# (# #) | Word# #)

naturalIsZero :: Natural -> Bool

naturalLcm :: Natural -> Natural -> Natural

naturalLe :: Natural -> Natural -> Bool

naturalLe# :: Natural -> Natural -> Bool#

naturalLog2 :: Natural -> Word

naturalLog2# :: Natural -> Word#

naturalLogBase :: Natural -> Natural -> Word

naturalLogBase# :: Natural -> Natural -> Word#

naturalLogBaseWord :: Word -> Natural -> Word

naturalLogBaseWord# :: Word# -> Natural -> Word#

naturalLt :: Natural -> Natural -> Bool

naturalLt# :: Natural -> Natural -> Bool#

naturalMul :: Natural -> Natural -> Natural

naturalNe :: Natural -> Natural -> Bool

naturalNe# :: Natural -> Natural -> Bool#

naturalNegate :: Natural -> Natural

naturalOne :: Natural

naturalOr :: Natural -> Natural -> Natural

naturalPopCount :: Natural -> Word

naturalPopCount# :: Natural -> Word#

naturalPowMod :: Natural -> Natural -> Natural -> Natural

naturalQuot :: Natural -> Natural -> Natural

naturalQuotRem :: Natural -> Natural -> (Natural, Natural)

naturalQuotRem# :: Natural -> Natural -> (# Natural, Natural #)

naturalRem :: Natural -> Natural -> Natural

naturalSetBit :: Natural -> Word -> Natural

naturalSetBit# :: Natural -> Word# -> Natural

naturalShiftL :: Natural -> Word -> Natural

naturalShiftL# :: Natural -> Word# -> Natural

naturalShiftR :: Natural -> Word -> Natural

naturalShiftR# :: Natural -> Word# -> Natural

naturalSignum :: Natural -> Natural

naturalSizeInBase# :: Word# -> Natural -> Word#

naturalSqr :: Natural -> Natural

naturalSub :: Natural -> Natural -> (# (# #) | Natural #)

naturalSubThrow :: Natural -> Natural -> Natural

naturalSubUnsafe :: Natural -> Natural -> Natural

naturalTestBit :: Natural -> Word -> Bool

naturalTestBit# :: Natural -> Word# -> Bool#

naturalToAddr :: Natural -> Addr# -> Bool# -> IO Word

naturalToAddr# :: Natural -> Addr# -> Bool# -> State# s -> (# State# s, Word# #)

naturalToBigNat# :: Natural -> BigNat#

naturalToMutableByteArray# :: Natural -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #)

naturalToWord :: Natural -> Word

naturalToWord# :: Natural -> Word#

naturalToWordClamp :: Natural -> Word

naturalToWordClamp# :: Natural -> Word#

naturalToWordMaybe# :: Natural -> (# (# #) | Word# #)

naturalXor :: Natural -> Natural -> Natural

naturalZero :: Natural

data Natural

Constructors

NS Word#
NB ByteArray#
Instances
Instances details
PrintfArg Natural Source

Since: base-4.8.0.0
Instance details

Defined in Text.Printf

Methods

formatArg :: Natural -> FieldFormatter Source

parseFormat :: Natural -> ModifierParser Source

Bits Natural Source

Since: base-4.8.0
Instance details

Defined in GHC.Internal.Bits

Methods

(.&.) :: Natural -> Natural -> Natural Source

(.|.) :: Natural -> Natural -> Natural Source

xor :: Natural -> Natural -> Natural Source

complement :: Natural -> Natural Source

shift :: Natural -> Int -> Natural Source

rotate :: Natural -> Int -> Natural Source

zeroBits :: Natural Source

bit :: Int -> Natural Source

setBit :: Natural -> Int -> Natural Source

clearBit :: Natural -> Int -> Natural Source

complementBit :: Natural -> Int -> Natural Source

testBit :: Natural -> Int -> Bool Source

bitSizeMaybe :: Natural -> Maybe Int Source

bitSize :: Natural -> Int Source

isSigned :: Natural -> Bool Source

shiftL :: Natural -> Int -> Natural Source

unsafeShiftL :: Natural -> Int -> Natural Source

shiftR :: Natural -> Int -> Natural Source

unsafeShiftR :: Natural -> Int -> Natural Source

rotateL :: Natural -> Int -> Natural Source

rotateR :: Natural -> Int -> Natural Source

popCount :: Natural -> Int Source

Data Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Natural -> c Natural Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Natural Source

toConstr :: Natural -> Constr Source

dataTypeOf :: Natural -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Natural) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Natural) Source

gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Natural -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Natural -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source

Enum Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Internal.Enum

Methods

succ :: Natural -> Natural Source

pred :: Natural -> Natural Source

toEnum :: Int -> Natural Source

fromEnum :: Natural -> Int Source

enumFrom :: Natural -> [Natural] Source

enumFromThen :: Natural -> Natural -> [Natural] Source

enumFromTo :: Natural -> Natural -> [Natural] Source

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source

Ix Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Internal.Ix

Methods

range :: (Natural, Natural) -> [Natural] Source

index :: (Natural, Natural) -> Natural -> Int Source

unsafeIndex :: (Natural, Natural) -> Natural -> Int Source

inRange :: (Natural, Natural) -> Natural -> Bool Source

rangeSize :: (Natural, Natural) -> Int Source

unsafeRangeSize :: (Natural, Natural) -> Int 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.Internal.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

Read Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS Natural Source

readList :: ReadS [Natural] Source

readPrec :: ReadPrec Natural Source

readListPrec :: ReadPrec [Natural] Source

Integral Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Internal.Real

Methods

quot :: Natural -> Natural -> Natural Source

rem :: Natural -> Natural -> Natural Source

div :: Natural -> Natural -> Natural Source

mod :: Natural -> Natural -> Natural Source

quotRem :: Natural -> Natural -> (Natural, Natural) Source

divMod :: Natural -> Natural -> (Natural, Natural) Source

toInteger :: Natural -> Integer Source

Real Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Natural -> Rational Source

Show Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Natural -> ShowS Source

show :: Natural -> String Source

showList :: [Natural] -> ShowS Source

Eq Natural
Instance details

Defined in GHC.Num.Natural

Methods

(==) :: Natural -> Natural -> Bool Source

(/=) :: Natural -> Natural -> Bool Source

Ord Natural
Instance details

Defined in GHC.Num.Natural

Methods

compare :: Natural -> Natural -> Ordering Source

(<) :: Natural -> Natural -> Bool Source

(<=) :: Natural -> Natural -> Bool Source

(>) :: Natural -> Natural -> Bool Source

(>=) :: Natural -> Natural -> Bool Source

max :: Natural -> Natural -> Natural Source

min :: Natural -> Natural -> Natural Source

KnownNat n => HasResolution (n :: Nat) Source

For example, Fixed 1000 will give you a Fixed with a resolution of 1000.
Instance details

Defined in Data.Fixed

Methods

resolution :: p n -> Integer Source

TestCoercion SNat Source

Since: base-4.18.0.0
Instance details

Defined in GHC.Internal.TypeNats

Methods

testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b) Source

TestEquality SNat Source

Since: base-4.18.0.0
Instance details

Defined in GHC.Internal.TypeNats

Methods

testEquality :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (a :~: b) Source

Lift Natural Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Natural -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Natural -> Code m Natural Source

type Compare (a :: Natural) (b :: Natural) Source
Instance details

Defined in GHC.Internal.Data.Type.Ord

type Compare (a :: Natural) (b :: Natural) = CmpNat a b

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https://downloads.haskell.org/~ghc/9.12.1/docs/libraries/base-4.21.0.0-8e62/GHC-Num.html