Torsor

The typeclasses provides in this module are equivalent to three of the typeclasses from the vector-space package. This package uses MPTCs with functional dependencies instead of type families in order to improved error messages.

Documentation

class Additive v where

Minimal complete definition

zero, invert, plus, minus

Methods

zero :: v

invert :: v -> v

plus :: v -> v -> v

minus :: v -> v -> v

Instances

Additive Double

Methods

zero :: Double

invert :: Double -> Double

plus :: Double -> Double -> Double

minus :: Double -> Double -> Double

Additive Int

Methods

zero :: Int

invert :: Int -> Int

plus :: Int -> Int -> Int

minus :: Int -> Int -> Int

Additive Int8

Methods

zero :: Int8

invert :: Int8 -> Int8

plus :: Int8 -> Int8 -> Int8

minus :: Int8 -> Int8 -> Int8

Additive Int16

Methods

zero :: Int16

invert :: Int16 -> Int16

plus :: Int16 -> Int16 -> Int16

minus :: Int16 -> Int16 -> Int16

Additive Int32

Methods

zero :: Int32

invert :: Int32 -> Int32

plus :: Int32 -> Int32 -> Int32

minus :: Int32 -> Int32 -> Int32

Additive Int64

Methods

zero :: Int64

invert :: Int64 -> Int64

plus :: Int64 -> Int64 -> Int64

minus :: Int64 -> Int64 -> Int64

Additive Word

Methods

zero :: Word

invert :: Word -> Word

plus :: Word -> Word -> Word

minus :: Word -> Word -> Word

Additive Word8

Methods

zero :: Word8

invert :: Word8 -> Word8

plus :: Word8 -> Word8 -> Word8

minus :: Word8 -> Word8 -> Word8

Additive Word16

Methods

zero :: Word16

invert :: Word16 -> Word16

plus :: Word16 -> Word16 -> Word16

minus :: Word16 -> Word16 -> Word16

Additive Word32

Methods

zero :: Word32

invert :: Word32 -> Word32

plus :: Word32 -> Word32 -> Word32

minus :: Word32 -> Word32 -> Word32

Additive Word64

Methods

zero :: Word64

invert :: Word64 -> Word64

plus :: Word64 -> Word64 -> Word64

minus :: Word64 -> Word64 -> Word64

class Additive v => Torsor p v | p -> v where

Minimal complete definition

add, difference

Methods

add :: v -> p -> p

difference :: p -> p -> v

Instances

Torsor Double Double

Methods

add :: Double -> Double -> Double

difference :: Double -> Double -> Double

Torsor Int Int

Methods

add :: Int -> Int -> Int

difference :: Int -> Int -> Int

Torsor Int8 Int8

Methods

add :: Int8 -> Int8 -> Int8

difference :: Int8 -> Int8 -> Int8

Torsor Int16 Int16

Methods

add :: Int16 -> Int16 -> Int16

difference :: Int16 -> Int16 -> Int16

Torsor Int32 Int32

Methods

add :: Int32 -> Int32 -> Int32

difference :: Int32 -> Int32 -> Int32

Torsor Int64 Int64

Methods

add :: Int64 -> Int64 -> Int64

difference :: Int64 -> Int64 -> Int64

Torsor Word Word

Methods

add :: Word -> Word -> Word

difference :: Word -> Word -> Word

Torsor Word8 Word8

Methods

add :: Word8 -> Word8 -> Word8

difference :: Word8 -> Word8 -> Word8

Torsor Word16 Word16

Methods

add :: Word16 -> Word16 -> Word16

difference :: Word16 -> Word16 -> Word16

Torsor Word32 Word32

Methods

add :: Word32 -> Word32 -> Word32

difference :: Word32 -> Word32 -> Word32

Torsor Word64 Word64

Methods

add :: Word64 -> Word64 -> Word64

difference :: Word64 -> Word64 -> Word64

class (Additive v, Additive s) => Scaling v s | v -> s where

Minimal complete definition

scale

Methods

scale :: s -> v -> v

Instances

Scaling Double Double

Methods

scale :: Double -> Double -> Double

Scaling Int Int

Methods

scale :: Int -> Int -> Int

Scaling Int8 Int8

Methods

scale :: Int8 -> Int8 -> Int8

Scaling Int16 Int16

Methods

scale :: Int16 -> Int16 -> Int16

Scaling Int32 Int32

Methods

scale :: Int32 -> Int32 -> Int32

Scaling Int64 Int64

Methods

scale :: Int64 -> Int64 -> Int64

Scaling Word Word

Methods

scale :: Word -> Word -> Word

Scaling Word8 Word8

Methods

scale :: Word8 -> Word8 -> Word8

Scaling Word16 Word16

Methods

scale :: Word16 -> Word16 -> Word16

Scaling Word32 Word32

Methods

scale :: Word32 -> Word32 -> Word32

Scaling Word64 Word64

Methods

scale :: Word64 -> Word64 -> Word64