Basement.Numerical.Additive

Documentation

class Additive a where

Represent class of things that can be added together, contains a neutral element and is commutative.

x + azero = x
azero + x = x
x + y = y + x

Minimal complete definition

azero, (+)

Methods

azero :: a

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

scale :: IsNatural n => n -> a -> a

Instances

Additive Double

Methods

azero :: Double

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

scale :: IsNatural n => n -> Double -> Double

Additive Float

Methods

azero :: Float

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

scale :: IsNatural n => n -> Float -> Float

Additive Int

Methods

azero :: Int

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

scale :: IsNatural n => n -> Int -> Int

Additive Int8

Methods

azero :: Int8

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

scale :: IsNatural n => n -> Int8 -> Int8

Additive Int16

Methods

azero :: Int16

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

scale :: IsNatural n => n -> Int16 -> Int16

Additive Int32

Methods

azero :: Int32

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

scale :: IsNatural n => n -> Int32 -> Int32

Additive Int64

Methods

azero :: Int64

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

scale :: IsNatural n => n -> Int64 -> Int64

Additive Integer

Methods

azero :: Integer

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

scale :: IsNatural n => n -> Integer -> Integer

Additive Natural

Methods

azero :: Natural

(+) :: Natural -> Natural -> Natural

scale :: IsNatural n => n -> Natural -> Natural

Additive Word

Methods

azero :: Word

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

scale :: IsNatural n => n -> Word -> Word

Additive Word8

Methods

azero :: Word8

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

scale :: IsNatural n => n -> Word8 -> Word8

Additive Word16

Methods

azero :: Word16

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

scale :: IsNatural n => n -> Word16 -> Word16

Additive Word32

Methods

azero :: Word32

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

scale :: IsNatural n => n -> Word32 -> Word32

Additive Word64

Methods

azero :: Word64

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

scale :: IsNatural n => n -> Word64 -> Word64

Additive COff

Methods

azero :: COff

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

scale :: IsNatural n => n -> COff -> COff

Additive CChar

Methods

azero :: CChar

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

scale :: IsNatural n => n -> CChar -> CChar

Additive CSChar

Methods

azero :: CSChar

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

scale :: IsNatural n => n -> CSChar -> CSChar

Additive CUChar

Methods

azero :: CUChar

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

scale :: IsNatural n => n -> CUChar -> CUChar

Additive CShort

Methods

azero :: CShort

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

scale :: IsNatural n => n -> CShort -> CShort

Additive CUShort

Methods

azero :: CUShort

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

scale :: IsNatural n => n -> CUShort -> CUShort

Additive CInt

Methods

azero :: CInt

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

scale :: IsNatural n => n -> CInt -> CInt

Additive CUInt

Methods

azero :: CUInt

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

scale :: IsNatural n => n -> CUInt -> CUInt

Additive CLong

Methods

azero :: CLong

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

scale :: IsNatural n => n -> CLong -> CLong

Additive CULong

Methods

azero :: CULong

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

scale :: IsNatural n => n -> CULong -> CULong

Additive CLLong

Methods

azero :: CLLong

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

scale :: IsNatural n => n -> CLLong -> CLLong

Additive CULLong

Methods

azero :: CULLong

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

scale :: IsNatural n => n -> CULLong -> CULLong

Additive CFloat

Methods

azero :: CFloat

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

scale :: IsNatural n => n -> CFloat -> CFloat

Additive CDouble

Methods

azero :: CDouble

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

scale :: IsNatural n => n -> CDouble -> CDouble

Additive CPtrdiff

Methods

azero :: CPtrdiff

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

scale :: IsNatural n => n -> CPtrdiff -> CPtrdiff

Additive CSize

Methods

azero :: CSize

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

scale :: IsNatural n => n -> CSize -> CSize

Additive CWchar

Methods

azero :: CWchar

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

scale :: IsNatural n => n -> CWchar -> CWchar

Additive CSigAtomic

Methods

azero :: CSigAtomic

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

scale :: IsNatural n => n -> CSigAtomic -> CSigAtomic

Additive CClock

Methods

azero :: CClock

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

scale :: IsNatural n => n -> CClock -> CClock

Additive CTime

Methods

azero :: CTime

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

scale :: IsNatural n => n -> CTime -> CTime

Additive CUSeconds

Methods

azero :: CUSeconds

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

scale :: IsNatural n => n -> CUSeconds -> CUSeconds

Additive CSUSeconds

Methods

azero :: CSUSeconds

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

scale :: IsNatural n => n -> CSUSeconds -> CSUSeconds

Additive CIntPtr

Methods

azero :: CIntPtr

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

scale :: IsNatural n => n -> CIntPtr -> CIntPtr

Additive CUIntPtr

Methods

azero :: CUIntPtr

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

scale :: IsNatural n => n -> CUIntPtr -> CUIntPtr

Additive CIntMax

Methods

azero :: CIntMax

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

scale :: IsNatural n => n -> CIntMax -> CIntMax

Additive CUIntMax

Methods

azero :: CUIntMax

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

scale :: IsNatural n => n -> CUIntMax -> CUIntMax

Additive Word128

Methods

azero :: Word128

(+) :: Word128 -> Word128 -> Word128

scale :: IsNatural n => n -> Word128 -> Word128

Additive Word256

Methods

azero :: Word256

(+) :: Word256 -> Word256 -> Word256

scale :: IsNatural n => n -> Word256 -> Word256

KnownNat n => Additive (Zn n)

Methods

azero :: Zn n

(+) :: Zn n -> Zn n -> Zn n

scale :: IsNatural n => n -> Zn n -> Zn n

(KnownNat n, NatWithinBound Word64 n) => Additive (Zn64 n)

Methods

azero :: Zn64 n

(+) :: Zn64 n -> Zn64 n -> Zn64 n

scale :: IsNatural n => n -> Zn64 n -> Zn64 n

Additive (CountOf ty)

Methods

azero :: CountOf ty

(+) :: CountOf ty -> CountOf ty -> CountOf ty

scale :: IsNatural n => n -> CountOf ty -> CountOf ty

Additive (Offset ty)

Methods

azero :: Offset ty

(+) :: Offset ty -> Offset ty -> Offset ty

scale :: IsNatural n => n -> Offset ty -> Offset ty

SizeValid n => Additive (Bits n)

Methods

azero :: Bits n

(+) :: Bits n -> Bits n -> Bits n

scale :: IsNatural n => n -> Bits n -> Bits n