Data.Semiring

Documentation

class Semiring a where

Minimal complete definition

plus, zero, times, one

Methods

plus

Arguments

:: a

-> a

-> a

Additive Magma

zero

Arguments

:: a

Additive Unital

times

Arguments

:: a

-> a

-> a

Multiplicative Magma

one

Arguments

:: a

Multiplicative Unital

Instances

Semiring Bool

Methods

plus :: Bool -> Bool -> Bool

zero :: Bool

times :: Bool -> Bool -> Bool

one :: Bool

Semiring Double

Methods

plus :: Double -> Double -> Double

zero :: Double

times :: Double -> Double -> Double

one :: Double

Semiring Float

Methods

plus :: Float -> Float -> Float

zero :: Float

times :: Float -> Float -> Float

one :: Float

Semiring Int

Methods

plus :: Int -> Int -> Int

zero :: Int

times :: Int -> Int -> Int

one :: Int

Semiring Int8

Methods

plus :: Int8 -> Int8 -> Int8

zero :: Int8

times :: Int8 -> Int8 -> Int8

one :: Int8

Semiring Int16

Methods

plus :: Int16 -> Int16 -> Int16

zero :: Int16

times :: Int16 -> Int16 -> Int16

one :: Int16

Semiring Int32

Methods

plus :: Int32 -> Int32 -> Int32

zero :: Int32

times :: Int32 -> Int32 -> Int32

one :: Int32

Semiring Int64

Methods

plus :: Int64 -> Int64 -> Int64

zero :: Int64

times :: Int64 -> Int64 -> Int64

one :: Int64

Semiring Word

Methods

plus :: Word -> Word -> Word

zero :: Word

times :: Word -> Word -> Word

one :: Word

Semiring Word8

Methods

plus :: Word8 -> Word8 -> Word8

zero :: Word8

times :: Word8 -> Word8 -> Word8

one :: Word8

Semiring Word16

Methods

plus :: Word16 -> Word16 -> Word16

zero :: Word16

times :: Word16 -> Word16 -> Word16

one :: Word16

Semiring Word32

Methods

plus :: Word32 -> Word32 -> Word32

zero :: Word32

times :: Word32 -> Word32 -> Word32

one :: Word32

Semiring Word64

Methods

plus :: Word64 -> Word64 -> Word64

zero :: Word64

times :: Word64 -> Word64 -> Word64

one :: Word64

Semiring ()

Methods

plus :: () -> () -> ()

zero :: ()

times :: () -> () -> ()

one :: ()

Semiring a => Semiring [a]

Methods

plus :: [a] -> [a] -> [a]

zero :: [a]

times :: [a] -> [a] -> [a]

one :: [a]

Semiring b => Semiring (a -> b)

Methods

plus :: (a -> b) -> (a -> b) -> a -> b

zero :: a -> b

times :: (a -> b) -> (a -> b) -> a -> b

one :: a -> b

(Semiring a, Semiring b) => Semiring (a, b)

Methods

plus :: (a, b) -> (a, b) -> (a, b)

zero :: (a, b)

times :: (a, b) -> (a, b) -> (a, b)

one :: (a, b)

(Semiring a, Semiring b, Semiring c) => Semiring (a, b, c)

Methods

plus :: (a, b, c) -> (a, b, c) -> (a, b, c)

zero :: (a, b, c)

times :: (a, b, c) -> (a, b, c) -> (a, b, c)

one :: (a, b, c)

(Semiring a, Semiring b, Semiring c, Semiring d) => Semiring (a, b, c, d)

Methods

plus :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

zero :: (a, b, c, d)

times :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

one :: (a, b, c, d)

(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e) => Semiring (a, b, c, d, e)

Methods

plus :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

zero :: (a, b, c, d, e)

times :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

one :: (a, b, c, d, e)

(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f) => Semiring (a, b, c, d, e, f)

Methods

plus :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)

zero :: (a, b, c, d, e, f)

times :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)

one :: (a, b, c, d, e, f)

(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g) => Semiring (a, b, c, d, e, f, g)

Methods

plus :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)

zero :: (a, b, c, d, e, f, g)

times :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)

one :: (a, b, c, d, e, f, g)

(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g, Semiring h) => Semiring (a, b, c, d, e, f, g, h)

Methods

plus :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h)

zero :: (a, b, c, d, e, f, g, h)

times :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h)

one :: (a, b, c, d, e, f, g, h)

(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g, Semiring h, Semiring i) => Semiring (a, b, c, d, e, f, g, h, i)

Methods

plus :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i)

zero :: (a, b, c, d, e, f, g, h, i)

times :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i)

one :: (a, b, c, d, e, f, g, h, i)

(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g, Semiring h, Semiring i, Semiring j) => Semiring (a, b, c, d, e, f, g, h, i, j)

Methods

plus :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j)

zero :: (a, b, c, d, e, f, g, h, i, j)

times :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j)

one :: (a, b, c, d, e, f, g, h, i, j)