Safe Haskell	None
Language	Haskell98

Data.Semiring

Contents

Semiring typeclass
Types
Ring typeclass

Description

A class for semirings (types with two binary operations, one commutative and one associative, and two respective identites), with various general-purpose instances.

Synopsis

class Semiring a where
(+) :: Semiring a => a -> a -> a
(*) :: Semiring a => a -> a -> a
(^) :: (Semiring a, Integral b) => a -> b -> a
foldMapP :: (Foldable t, Semiring s) => (a -> s) -> t a -> s
foldMapT :: (Foldable t, Semiring s) => (a -> s) -> t a -> s
sum :: (Foldable t, Semiring a) => t a -> a
product :: (Foldable t, Semiring a) => t a -> a
sum' :: (Foldable t, Semiring a) => t a -> a
product' :: (Foldable t, Semiring a) => t a -> a
newtype Add a = Add {
- getAdd :: a
}
newtype Mul a = Mul {
- getMul :: a
}
newtype WrappedNum a = WrapNum {
- unwrapNum :: a
}
class Semiring a => Ring a where
(-) :: Ring a => a -> a -> a
minus :: Ring a => a -> a -> a

Semiring typeclass

class Semiring a where Source #

The class of semirings (types with two binary operations and two respective identities). One can think of a semiring as two monoids of the same underlying type: A commutative monoid and an associative monoid. For any type R with a Num instance, the commutative monoid is (R, '(Prelude.+)', 0) and the associative monoid is (R, '(Prelude.*)', 1).

Instances should satisfy the following laws:

additive identity

x + zero = zero + x = x

additive associativity

x + (y + z) = (x + y) + z

additive commutativity

x + y = y + x

multiplicative identity

x * one = one * x = x

multiplicative associativity

x * (y * z) = (x * y) * z

left- and right-distributivity of * over +

x * (y + z) = (x * y) + (x * z) (x + y) * z = (x * z) + (y * z)

annihilation

zero * x = x * zero = zero

Minimal complete definition

plus, zero, times, one

Methods

plus infixl 6 Source #

Arguments

:: a
-> a
-> a	Commutative Operation

zero Source #

Arguments

:: a	Commutative Unit

times infixl 7 Source #

Arguments

:: a
-> a
-> a	Associative Operation

one Source #

Arguments

:: a	Associative Unit

Instances

Semiring Bool Source #
Instance details Defined in Data.Semiring Methods plus :: Bool -> Bool -> Bool Source # zero :: Bool Source # times :: Bool -> Bool -> Bool Source # one :: Bool Source #
Semiring Double Source #
Instance details Defined in Data.Semiring Methods plus :: Double -> Double -> Double Source # zero :: Double Source # times :: Double -> Double -> Double Source # one :: Double Source #
Semiring Float Source #
Instance details Defined in Data.Semiring Methods plus :: Float -> Float -> Float Source # zero :: Float Source # times :: Float -> Float -> Float Source # one :: Float Source #
Semiring Int Source #
Instance details Defined in Data.Semiring Methods plus :: Int -> Int -> Int Source # zero :: Int Source # times :: Int -> Int -> Int Source # one :: Int Source #
Semiring Int8 Source #
Instance details Defined in Data.Semiring Methods plus :: Int8 -> Int8 -> Int8 Source # zero :: Int8 Source # times :: Int8 -> Int8 -> Int8 Source # one :: Int8 Source #
Semiring Int16 Source #
Instance details Defined in Data.Semiring Methods plus :: Int16 -> Int16 -> Int16 Source # zero :: Int16 Source # times :: Int16 -> Int16 -> Int16 Source # one :: Int16 Source #
Semiring Int32 Source #
Instance details Defined in Data.Semiring Methods plus :: Int32 -> Int32 -> Int32 Source # zero :: Int32 Source # times :: Int32 -> Int32 -> Int32 Source # one :: Int32 Source #
Semiring Int64 Source #
Instance details Defined in Data.Semiring Methods plus :: Int64 -> Int64 -> Int64 Source # zero :: Int64 Source # times :: Int64 -> Int64 -> Int64 Source # one :: Int64 Source #
Semiring Integer Source #
Instance details Defined in Data.Semiring Methods plus :: Integer -> Integer -> Integer Source # zero :: Integer Source # times :: Integer -> Integer -> Integer Source # one :: Integer Source #
Semiring Natural Source #
Instance details Defined in Data.Semiring Methods plus :: Natural -> Natural -> Natural Source # zero :: Natural Source # times :: Natural -> Natural -> Natural Source # one :: Natural Source #
Semiring Word Source #
Instance details Defined in Data.Semiring Methods plus :: Word -> Word -> Word Source # zero :: Word Source # times :: Word -> Word -> Word Source # one :: Word Source #
Semiring Word8 Source #
Instance details Defined in Data.Semiring Methods plus :: Word8 -> Word8 -> Word8 Source # zero :: Word8 Source # times :: Word8 -> Word8 -> Word8 Source # one :: Word8 Source #
Semiring Word16 Source #
Instance details Defined in Data.Semiring Methods plus :: Word16 -> Word16 -> Word16 Source # zero :: Word16 Source # times :: Word16 -> Word16 -> Word16 Source # one :: Word16 Source #
Semiring Word32 Source #
Instance details Defined in Data.Semiring Methods plus :: Word32 -> Word32 -> Word32 Source # zero :: Word32 Source # times :: Word32 -> Word32 -> Word32 Source # one :: Word32 Source #
Semiring Word64 Source #
Instance details Defined in Data.Semiring Methods plus :: Word64 -> Word64 -> Word64 Source # zero :: Word64 Source # times :: Word64 -> Word64 -> Word64 Source # one :: Word64 Source #
Semiring () Source #
Instance details Defined in Data.Semiring Methods plus :: () -> () -> () Source # zero :: () Source # times :: () -> () -> () Source # one :: () Source #
Semiring CDev Source #
Instance details Defined in Data.Semiring Methods plus :: CDev -> CDev -> CDev Source # zero :: CDev Source # times :: CDev -> CDev -> CDev Source # one :: CDev Source #
Semiring CIno Source #
Instance details Defined in Data.Semiring Methods plus :: CIno -> CIno -> CIno Source # zero :: CIno Source # times :: CIno -> CIno -> CIno Source # one :: CIno Source #
Semiring CMode Source #
Instance details Defined in Data.Semiring Methods plus :: CMode -> CMode -> CMode Source # zero :: CMode Source # times :: CMode -> CMode -> CMode Source # one :: CMode Source #
Semiring COff Source #
Instance details Defined in Data.Semiring Methods plus :: COff -> COff -> COff Source # zero :: COff Source # times :: COff -> COff -> COff Source # one :: COff Source #
Semiring CPid Source #
Instance details Defined in Data.Semiring Methods plus :: CPid -> CPid -> CPid Source # zero :: CPid Source # times :: CPid -> CPid -> CPid Source # one :: CPid Source #
Semiring CSsize Source #
Instance details Defined in Data.Semiring Methods plus :: CSsize -> CSsize -> CSsize Source # zero :: CSsize Source # times :: CSsize -> CSsize -> CSsize Source # one :: CSsize Source #
Semiring CGid Source #
Instance details Defined in Data.Semiring Methods plus :: CGid -> CGid -> CGid Source # zero :: CGid Source # times :: CGid -> CGid -> CGid Source # one :: CGid Source #
Semiring CNlink Source #
Instance details Defined in Data.Semiring Methods plus :: CNlink -> CNlink -> CNlink Source # zero :: CNlink Source # times :: CNlink -> CNlink -> CNlink Source # one :: CNlink Source #
Semiring CUid Source #
Instance details Defined in Data.Semiring Methods plus :: CUid -> CUid -> CUid Source # zero :: CUid Source # times :: CUid -> CUid -> CUid Source # one :: CUid Source #
Semiring CCc Source #
Instance details Defined in Data.Semiring Methods plus :: CCc -> CCc -> CCc Source # zero :: CCc Source # times :: CCc -> CCc -> CCc Source # one :: CCc Source #
Semiring CSpeed Source #
Instance details Defined in Data.Semiring Methods plus :: CSpeed -> CSpeed -> CSpeed Source # zero :: CSpeed Source # times :: CSpeed -> CSpeed -> CSpeed Source # one :: CSpeed Source #
Semiring CTcflag Source #
Instance details Defined in Data.Semiring Methods plus :: CTcflag -> CTcflag -> CTcflag Source # zero :: CTcflag Source # times :: CTcflag -> CTcflag -> CTcflag Source # one :: CTcflag Source #
Semiring CRLim Source #
Instance details Defined in Data.Semiring Methods plus :: CRLim -> CRLim -> CRLim Source # zero :: CRLim Source # times :: CRLim -> CRLim -> CRLim Source # one :: CRLim Source #
Semiring Fd Source #
Instance details Defined in Data.Semiring Methods plus :: Fd -> Fd -> Fd Source # zero :: Fd Source # times :: Fd -> Fd -> Fd Source # one :: Fd Source #
Semiring CChar Source #
Instance details Defined in Data.Semiring Methods plus :: CChar -> CChar -> CChar Source # zero :: CChar Source # times :: CChar -> CChar -> CChar Source # one :: CChar Source #
Semiring CSChar Source #
Instance details Defined in Data.Semiring Methods plus :: CSChar -> CSChar -> CSChar Source # zero :: CSChar Source # times :: CSChar -> CSChar -> CSChar Source # one :: CSChar Source #
Semiring CUChar Source #
Instance details Defined in Data.Semiring Methods plus :: CUChar -> CUChar -> CUChar Source # zero :: CUChar Source # times :: CUChar -> CUChar -> CUChar Source # one :: CUChar Source #
Semiring CShort Source #
Instance details Defined in Data.Semiring Methods plus :: CShort -> CShort -> CShort Source # zero :: CShort Source # times :: CShort -> CShort -> CShort Source # one :: CShort Source #
Semiring CUShort Source #
Instance details Defined in Data.Semiring Methods plus :: CUShort -> CUShort -> CUShort Source # zero :: CUShort Source # times :: CUShort -> CUShort -> CUShort Source # one :: CUShort Source #
Semiring CInt Source #
Instance details Defined in Data.Semiring Methods plus :: CInt -> CInt -> CInt Source # zero :: CInt Source # times :: CInt -> CInt -> CInt Source # one :: CInt Source #
Semiring CUInt Source #
Instance details Defined in Data.Semiring Methods plus :: CUInt -> CUInt -> CUInt Source # zero :: CUInt Source # times :: CUInt -> CUInt -> CUInt Source # one :: CUInt Source #
Semiring CLong Source #
Instance details Defined in Data.Semiring Methods plus :: CLong -> CLong -> CLong Source # zero :: CLong Source # times :: CLong -> CLong -> CLong Source # one :: CLong Source #
Semiring CULong Source #
Instance details Defined in Data.Semiring Methods plus :: CULong -> CULong -> CULong Source # zero :: CULong Source # times :: CULong -> CULong -> CULong Source # one :: CULong Source #
Semiring CLLong Source #
Instance details Defined in Data.Semiring Methods plus :: CLLong -> CLLong -> CLLong Source # zero :: CLLong Source # times :: CLLong -> CLLong -> CLLong Source # one :: CLLong Source #
Semiring CULLong Source #
Instance details Defined in Data.Semiring Methods plus :: CULLong -> CULLong -> CULLong Source # zero :: CULLong Source # times :: CULLong -> CULLong -> CULLong Source # one :: CULLong Source #
Semiring CFloat Source #
Instance details Defined in Data.Semiring Methods plus :: CFloat -> CFloat -> CFloat Source # zero :: CFloat Source # times :: CFloat -> CFloat -> CFloat Source # one :: CFloat Source #
Semiring CDouble Source #
Instance details Defined in Data.Semiring Methods plus :: CDouble -> CDouble -> CDouble Source # zero :: CDouble Source # times :: CDouble -> CDouble -> CDouble Source # one :: CDouble Source #
Semiring CPtrdiff Source #
Instance details Defined in Data.Semiring Methods plus :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # zero :: CPtrdiff Source # times :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # one :: CPtrdiff Source #
Semiring CSize Source #
Instance details Defined in Data.Semiring Methods plus :: CSize -> CSize -> CSize Source # zero :: CSize Source # times :: CSize -> CSize -> CSize Source # one :: CSize Source #
Semiring CWchar Source #
Instance details Defined in Data.Semiring Methods plus :: CWchar -> CWchar -> CWchar Source # zero :: CWchar Source # times :: CWchar -> CWchar -> CWchar Source # one :: CWchar Source #
Semiring CSigAtomic Source #
Instance details Defined in Data.Semiring Methods plus :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # zero :: CSigAtomic Source # times :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # one :: CSigAtomic Source #
Semiring CClock Source #
Instance details Defined in Data.Semiring Methods plus :: CClock -> CClock -> CClock Source # zero :: CClock Source # times :: CClock -> CClock -> CClock Source # one :: CClock Source #
Semiring CTime Source #
Instance details Defined in Data.Semiring Methods plus :: CTime -> CTime -> CTime Source # zero :: CTime Source # times :: CTime -> CTime -> CTime Source # one :: CTime Source #
Semiring CUSeconds Source #
Instance details Defined in Data.Semiring Methods plus :: CUSeconds -> CUSeconds -> CUSeconds Source # zero :: CUSeconds Source # times :: CUSeconds -> CUSeconds -> CUSeconds Source # one :: CUSeconds Source #
Semiring CSUSeconds Source #
Instance details Defined in Data.Semiring Methods plus :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # zero :: CSUSeconds Source # times :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # one :: CSUSeconds Source #
Semiring CIntPtr Source #
Instance details Defined in Data.Semiring Methods plus :: CIntPtr -> CIntPtr -> CIntPtr Source # zero :: CIntPtr Source # times :: CIntPtr -> CIntPtr -> CIntPtr Source # one :: CIntPtr Source #
Semiring CUIntPtr Source #
Instance details Defined in Data.Semiring Methods plus :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # zero :: CUIntPtr Source # times :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # one :: CUIntPtr Source #
Semiring CIntMax Source #
Instance details Defined in Data.Semiring Methods plus :: CIntMax -> CIntMax -> CIntMax Source # zero :: CIntMax Source # times :: CIntMax -> CIntMax -> CIntMax Source # one :: CIntMax Source #
Semiring CUIntMax Source #
Instance details Defined in Data.Semiring Methods plus :: CUIntMax -> CUIntMax -> CUIntMax Source # zero :: CUIntMax Source # times :: CUIntMax -> CUIntMax -> CUIntMax Source # one :: CUIntMax Source #
Semiring WordPtr Source #
Instance details Defined in Data.Semiring Methods plus :: WordPtr -> WordPtr -> WordPtr Source # zero :: WordPtr Source # times :: WordPtr -> WordPtr -> WordPtr Source # one :: WordPtr Source #
Semiring IntPtr Source #
Instance details Defined in Data.Semiring Methods plus :: IntPtr -> IntPtr -> IntPtr Source # zero :: IntPtr Source # times :: IntPtr -> IntPtr -> IntPtr Source # one :: IntPtr Source #
Semiring a => Semiring [a] Source #
Instance details Defined in Data.Semiring Methods plus :: [a] -> [a] -> [a] Source # zero :: [a] Source # times :: [a] -> [a] -> [a] Source # one :: [a] Source #
Semiring a => Semiring (Maybe a) Source #
Instance details Defined in Data.Semiring Methods plus :: Maybe a -> Maybe a -> Maybe a Source # zero :: Maybe a Source # times :: Maybe a -> Maybe a -> Maybe a Source # one :: Maybe a Source #
Integral a => Semiring (Ratio a) Source #
Instance details Defined in Data.Semiring Methods plus :: Ratio a -> Ratio a -> Ratio a Source # zero :: Ratio a Source # times :: Ratio a -> Ratio a -> Ratio a Source # one :: Ratio a Source #
Semiring a => Semiring (IO a) Source #
Instance details Defined in Data.Semiring Methods plus :: IO a -> IO a -> IO a Source # zero :: IO a Source # times :: IO a -> IO a -> IO a Source # one :: IO a Source #
Ring a => Semiring (Complex a) Source #	This instance can suffer due to floating point arithmetic.
Instance details Defined in Data.Semiring Methods plus :: Complex a -> Complex a -> Complex a Source # zero :: Complex a Source # times :: Complex a -> Complex a -> Complex a Source # one :: Complex a Source #
HasResolution a => Semiring (Fixed a) Source #
Instance details Defined in Data.Semiring Methods plus :: Fixed a -> Fixed a -> Fixed a Source # zero :: Fixed a Source # times :: Fixed a -> Fixed a -> Fixed a Source # one :: Fixed a Source #
Semiring a => Semiring (Min a) Source #
Instance details Defined in Data.Semiring Methods plus :: Min a -> Min a -> Min a Source # zero :: Min a Source # times :: Min a -> Min a -> Min a Source # one :: Min a Source #
Semiring a => Semiring (Max a) Source #
Instance details Defined in Data.Semiring Methods plus :: Max a -> Max a -> Max a Source # zero :: Max a Source # times :: Max a -> Max a -> Max a Source # one :: Max a Source #
Semiring a => Semiring (Identity a) Source #
Instance details Defined in Data.Semiring Methods plus :: Identity a -> Identity a -> Identity a Source # zero :: Identity a Source # times :: Identity a -> Identity a -> Identity a Source # one :: Identity a Source #
Semiring a => Semiring (Dual a) Source #
Instance details Defined in Data.Semiring Methods plus :: Dual a -> Dual a -> Dual a Source # zero :: Dual a Source # times :: Dual a -> Dual a -> Dual a Source # one :: Dual a Source #
Semiring a => Semiring (Sum a) Source #
Instance details Defined in Data.Semiring Methods plus :: Sum a -> Sum a -> Sum a Source # zero :: Sum a Source # times :: Sum a -> Sum a -> Sum a Source # one :: Sum a Source #
Semiring a => Semiring (Product a) Source #
Instance details Defined in Data.Semiring Methods plus :: Product a -> Product a -> Product a Source # zero :: Product a Source # times :: Product a -> Product a -> Product a Source # one :: Product a Source #
Semiring a => Semiring (Down a) Source #
Instance details Defined in Data.Semiring Methods plus :: Down a -> Down a -> Down a Source # zero :: Down a Source # times :: Down a -> Down a -> Down a Source # one :: Down a Source #
(Ord a, Monoid a) => Semiring (Set a) Source #	The multiplication laws are satisfied for any underlying `Monoid`, so we require a `Monoid` contraint instead of a `Semiring` constraint since `times` can use the context of either.
Instance details Defined in Data.Semiring Methods plus :: Set a -> Set a -> Set a Source # zero :: Set a Source # times :: Set a -> Set a -> Set a Source # one :: Set a Source #
(Eq a, Hashable a, Monoid a) => Semiring (HashSet a) Source #	The multiplication laws are satisfied for any underlying `Monoid`, so we require a `Monoid` contraint instead of a `Semiring` constraint since `times` can use the context of either.
Instance details Defined in Data.Semiring Methods plus :: HashSet a -> HashSet a -> HashSet a Source # zero :: HashSet a Source # times :: HashSet a -> HashSet a -> HashSet a Source # one :: HashSet a Source #
(Unbox a, Semiring a) => Semiring (Vector a) Source #
Instance details Defined in Data.Semiring Methods plus :: Vector a -> Vector a -> Vector a Source # zero :: Vector a Source # times :: Vector a -> Vector a -> Vector a Source # one :: Vector a Source #
(Storable a, Semiring a) => Semiring (Vector a) Source #
Instance details Defined in Data.Semiring Methods plus :: Vector a -> Vector a -> Vector a Source # zero :: Vector a Source # times :: Vector a -> Vector a -> Vector a Source # one :: Vector a Source #
Semiring a => Semiring (Vector a) Source #
Instance details Defined in Data.Semiring Methods plus :: Vector a -> Vector a -> Vector a Source # zero :: Vector a Source # times :: Vector a -> Vector a -> Vector a Source # one :: Vector a Source #
Num a => Semiring (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods plus :: WrappedNum a -> WrappedNum a -> WrappedNum a Source # zero :: WrappedNum a Source # times :: WrappedNum a -> WrappedNum a -> WrappedNum a Source # one :: WrappedNum a Source #
Semiring a => Semiring (Mul a) Source #
Instance details Defined in Data.Semiring Methods plus :: Mul a -> Mul a -> Mul a Source # zero :: Mul a Source # times :: Mul a -> Mul a -> Mul a Source # one :: Mul a Source #
Semiring a => Semiring (Add a) Source #
Instance details Defined in Data.Semiring Methods plus :: Add a -> Add a -> Add a Source # zero :: Add a Source # times :: Add a -> Add a -> Add a Source # one :: Add a Source #
Semiring b => Semiring (a -> b) Source #
Instance details Defined in Data.Semiring Methods plus :: (a -> b) -> (a -> b) -> a -> b Source # zero :: a -> b Source # times :: (a -> b) -> (a -> b) -> a -> b Source # one :: a -> b Source #
(Semiring a, Semiring b) => Semiring (a, b) Source #
Instance details Defined in Data.Semiring.Generic Methods plus :: (a, b) -> (a, b) -> (a, b) Source # zero :: (a, b) Source # times :: (a, b) -> (a, b) -> (a, b) Source # one :: (a, b) Source #
Semiring (Proxy a) Source #
Instance details Defined in Data.Semiring Methods plus :: Proxy a -> Proxy a -> Proxy a Source # zero :: Proxy a Source # times :: Proxy a -> Proxy a -> Proxy a Source # one :: Proxy a Source #
(Ord k, Monoid k, Semiring v) => Semiring (Map k v) Source #	The multiplication laws are satisfied for any underlying `Monoid` as the key type, so we require a `Monoid` contraint instead of a `Semiring` constraint since `times` can use the context of either.
Instance details Defined in Data.Semiring Methods plus :: Map k v -> Map k v -> Map k v Source # zero :: Map k v Source # times :: Map k v -> Map k v -> Map k v Source # one :: Map k v Source #
(Eq k, Hashable k, Monoid k, Semiring v) => Semiring (HashMap k v) Source #	The multiplication laws are satisfied for any underlying `Monoid` as the key type, so we require a `Monoid` contraint instead of a `Semiring` constraint since `times` can use the context of either.
Instance details Defined in Data.Semiring Methods plus :: HashMap k v -> HashMap k v -> HashMap k v Source # zero :: HashMap k v Source # times :: HashMap k v -> HashMap k v -> HashMap k v Source # one :: HashMap k v Source #
(Semiring a, Semiring b, Semiring c) => Semiring (a, b, c) Source #
Instance details Defined in Data.Semiring.Generic Methods plus :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # zero :: (a, b, c) Source # times :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # one :: (a, b, c) Source #
Semiring a => Semiring (Const a b) Source #
Instance details Defined in Data.Semiring Methods plus :: Const a b -> Const a b -> Const a b Source # zero :: Const a b Source # times :: Const a b -> Const a b -> Const a b Source # one :: Const a b Source #
(Semiring a, Semiring b, Semiring c, Semiring d) => Semiring (a, b, c, d) Source #
Instance details Defined in Data.Semiring.Generic Methods plus :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # zero :: (a, b, c, d) Source # times :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # one :: (a, b, c, d) Source #
(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e) => Semiring (a, b, c, d, e) Source #
Instance details Defined in Data.Semiring.Generic Methods plus :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # zero :: (a, b, c, d, e) Source # times :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # one :: (a, b, c, d, e) Source #
(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f) => Semiring (a, b, c, d, e, f) Source #
Instance details Defined in Data.Semiring.Generic Methods plus :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # zero :: (a, b, c, d, e, f) Source # times :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # one :: (a, b, c, d, e, f) Source #
(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g) => Semiring (a, b, c, d, e, f, g) Source #
Instance details Defined in Data.Semiring.Generic Methods plus :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # zero :: (a, b, c, d, e, f, g) Source # times :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # one :: (a, b, c, d, e, f, g) Source #

(+) :: Semiring a => a -> a -> a infixl 6 Source #

Infix shorthand for plus.

(*) :: Semiring a => a -> a -> a infixl 7 Source #

Infix shorthand for times.

(^) :: (Semiring a, Integral b) => a -> b -> a infixr 8 Source #

Raise a number to a non-negative integral power. If the power is negative, this will return zero.

foldMapP :: (Foldable t, Semiring s) => (a -> s) -> t a -> s Source #

Map each element of the structure to a semiring, and combine the results using plus.

foldMapT :: (Foldable t, Semiring s) => (a -> s) -> t a -> s Source #

Map each element of the structure to a semiring, and combine the results using times.

sum :: (Foldable t, Semiring a) => t a -> a Source #

The sum function computes the additive sum of the elements in a structure. This function is lazy. For a strict version, see sum'.

product :: (Foldable t, Semiring a) => t a -> a Source #

The product function computes the product of the elements in a structure. This function is lazy. for a strict version, see product'.

sum' :: (Foldable t, Semiring a) => t a -> a Source #

The sum' function computes the additive sum of the elements in a structure. This function is strict. For a lazy version, see sum.

product' :: (Foldable t, Semiring a) => t a -> a Source #

The product' function computes the additive sum of the elements in a structure. This function is strict. For a lazy version, see product.

Types

newtype Add a Source #

Monoid under plus. Analogous to Sum, but uses the Semiring constraint rather than Num.

Constructors

Add
Fields getAdd :: a

Instances

Functor Add Source #
Instance details Defined in Data.Semiring Methods fmap :: (a -> b) -> Add a -> Add b # (<$) :: a -> Add b -> Add a #
Foldable Add Source #
Instance details Defined in Data.Semiring Methods fold :: Monoid m => Add m -> m # foldMap :: Monoid m => (a -> m) -> Add a -> m # foldr :: (a -> b -> b) -> b -> Add a -> b # foldr' :: (a -> b -> b) -> b -> Add a -> b # foldl :: (b -> a -> b) -> b -> Add a -> b # foldl' :: (b -> a -> b) -> b -> Add a -> b # foldr1 :: (a -> a -> a) -> Add a -> a # foldl1 :: (a -> a -> a) -> Add a -> a # toList :: Add a -> [a] # null :: Add a -> Bool # length :: Add a -> Int # elem :: Eq a => a -> Add a -> Bool # maximum :: Ord a => Add a -> a # minimum :: Ord a => Add a -> a # sum :: Num a => Add a -> a # product :: Num a => Add a -> a #
Traversable Add Source #
Instance details Defined in Data.Semiring Methods traverse :: Applicative f => (a -> f b) -> Add a -> f (Add b) # sequenceA :: Applicative f => Add (f a) -> f (Add a) # mapM :: Monad m => (a -> m b) -> Add a -> m (Add b) # sequence :: Monad m => Add (m a) -> m (Add a) #
Bounded a => Bounded (Add a) Source #
Instance details Defined in Data.Semiring Methods minBound :: Add a # maxBound :: Add a #
Enum a => Enum (Add a) Source #
Instance details Defined in Data.Semiring Methods succ :: Add a -> Add a # pred :: Add a -> Add a # toEnum :: Int -> Add a # fromEnum :: Add a -> Int # enumFrom :: Add a -> [Add a] # enumFromThen :: Add a -> Add a -> [Add a] # enumFromTo :: Add a -> Add a -> [Add a] # enumFromThenTo :: Add a -> Add a -> Add a -> [Add a] #
Eq a => Eq (Add a) Source #
Instance details Defined in Data.Semiring Methods (==) :: Add a -> Add a -> Bool # (/=) :: Add a -> Add a -> Bool #
Fractional a => Fractional (Add a) Source #
Instance details Defined in Data.Semiring Methods (/) :: Add a -> Add a -> Add a # recip :: Add a -> Add a # fromRational :: Rational -> Add a #
Num a => Num (Add a) Source #
Instance details Defined in Data.Semiring Methods (+) :: Add a -> Add a -> Add a # (-) :: Add a -> Add a -> Add a # (*) :: Add a -> Add a -> Add a # negate :: Add a -> Add a # abs :: Add a -> Add a # signum :: Add a -> Add a # fromInteger :: Integer -> Add a #
Ord a => Ord (Add a) Source #
Instance details Defined in Data.Semiring Methods compare :: Add a -> Add a -> Ordering # (<) :: Add a -> Add a -> Bool # (<=) :: Add a -> Add a -> Bool # (>) :: Add a -> Add a -> Bool # (>=) :: Add a -> Add a -> Bool # max :: Add a -> Add a -> Add a # min :: Add a -> Add a -> Add a #
Read a => Read (Add a) Source #
Instance details Defined in Data.Semiring Methods readsPrec :: Int -> ReadS (Add a) # readList :: ReadS [Add a] # readPrec :: ReadPrec (Add a) # readListPrec :: ReadPrec [Add a] #
Real a => Real (Add a) Source #
Instance details Defined in Data.Semiring Methods toRational :: Add a -> Rational #
RealFrac a => RealFrac (Add a) Source #
Instance details Defined in Data.Semiring Methods properFraction :: Integral b => Add a -> (b, Add a) # truncate :: Integral b => Add a -> b # round :: Integral b => Add a -> b # ceiling :: Integral b => Add a -> b # floor :: Integral b => Add a -> b #
Show a => Show (Add a) Source #
Instance details Defined in Data.Semiring Methods showsPrec :: Int -> Add a -> ShowS # show :: Add a -> String # showList :: [Add a] -> ShowS #
Generic (Add a) Source #
Instance details Defined in Data.Semiring Associated Types type Rep (Add a) :: * -> * # Methods from :: Add a -> Rep (Add a) x # to :: Rep (Add a) x -> Add a #
Semiring a => Semigroup (Add a) Source #
Instance details Defined in Data.Semiring Methods (<>) :: Add a -> Add a -> Add a # sconcat :: NonEmpty (Add a) -> Add a # stimes :: Integral b => b -> Add a -> Add a #
Semiring a => Monoid (Add a) Source #
Instance details Defined in Data.Semiring Methods mempty :: Add a # mappend :: Add a -> Add a -> Add a # mconcat :: [Add a] -> Add a #
Storable a => Storable (Add a) Source #
Instance details Defined in Data.Semiring Methods sizeOf :: Add a -> Int # alignment :: Add a -> Int # peekElemOff :: Ptr (Add a) -> Int -> IO (Add a) # pokeElemOff :: Ptr (Add a) -> Int -> Add a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Add a) # pokeByteOff :: Ptr b -> Int -> Add a -> IO () # peek :: Ptr (Add a) -> IO (Add a) # poke :: Ptr (Add a) -> Add a -> IO () #
Semiring a => Semiring (Add a) Source #
Instance details Defined in Data.Semiring Methods plus :: Add a -> Add a -> Add a Source # zero :: Add a Source # times :: Add a -> Add a -> Add a Source # one :: Add a Source #
Generic1 Add Source #
Instance details Defined in Data.Semiring Associated Types type Rep1 Add :: k -> * # Methods from1 :: Add a -> Rep1 Add a # to1 :: Rep1 Add a -> Add a #
type Rep (Add a) Source #
Instance details Defined in Data.Semiring type Rep (Add a) = D1 (MetaData "Add" "Data.Semiring" "semirings-0.2.1.1-K4F9vEfdMGEFaB4LacyWRO" True) (C1 (MetaCons "Add" PrefixI True) (S1 (MetaSel (Just "getAdd") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Add Source #
Instance details Defined in Data.Semiring type Rep1 Add = D1 (MetaData "Add" "Data.Semiring" "semirings-0.2.1.1-K4F9vEfdMGEFaB4LacyWRO" True) (C1 (MetaCons "Add" PrefixI True) (S1 (MetaSel (Just "getAdd") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Mul a Source #

Monoid under times. Analogous to Product, but uses the Semiring constraint rather than Num.

Constructors

Mul
Fields getMul :: a

Instances

Functor Mul Source #
Instance details Defined in Data.Semiring Methods fmap :: (a -> b) -> Mul a -> Mul b # (<$) :: a -> Mul b -> Mul a #
Foldable Mul Source #
Instance details Defined in Data.Semiring Methods fold :: Monoid m => Mul m -> m # foldMap :: Monoid m => (a -> m) -> Mul a -> m # foldr :: (a -> b -> b) -> b -> Mul a -> b # foldr' :: (a -> b -> b) -> b -> Mul a -> b # foldl :: (b -> a -> b) -> b -> Mul a -> b # foldl' :: (b -> a -> b) -> b -> Mul a -> b # foldr1 :: (a -> a -> a) -> Mul a -> a # foldl1 :: (a -> a -> a) -> Mul a -> a # toList :: Mul a -> [a] # null :: Mul a -> Bool # length :: Mul a -> Int # elem :: Eq a => a -> Mul a -> Bool # maximum :: Ord a => Mul a -> a # minimum :: Ord a => Mul a -> a # sum :: Num a => Mul a -> a # product :: Num a => Mul a -> a #
Traversable Mul Source #
Instance details Defined in Data.Semiring Methods traverse :: Applicative f => (a -> f b) -> Mul a -> f (Mul b) # sequenceA :: Applicative f => Mul (f a) -> f (Mul a) # mapM :: Monad m => (a -> m b) -> Mul a -> m (Mul b) # sequence :: Monad m => Mul (m a) -> m (Mul a) #
Bounded a => Bounded (Mul a) Source #
Instance details Defined in Data.Semiring Methods minBound :: Mul a # maxBound :: Mul a #
Enum a => Enum (Mul a) Source #
Instance details Defined in Data.Semiring Methods succ :: Mul a -> Mul a # pred :: Mul a -> Mul a # toEnum :: Int -> Mul a # fromEnum :: Mul a -> Int # enumFrom :: Mul a -> [Mul a] # enumFromThen :: Mul a -> Mul a -> [Mul a] # enumFromTo :: Mul a -> Mul a -> [Mul a] # enumFromThenTo :: Mul a -> Mul a -> Mul a -> [Mul a] #
Eq a => Eq (Mul a) Source #
Instance details Defined in Data.Semiring Methods (==) :: Mul a -> Mul a -> Bool # (/=) :: Mul a -> Mul a -> Bool #
Fractional a => Fractional (Mul a) Source #
Instance details Defined in Data.Semiring Methods (/) :: Mul a -> Mul a -> Mul a # recip :: Mul a -> Mul a # fromRational :: Rational -> Mul a #
Num a => Num (Mul a) Source #
Instance details Defined in Data.Semiring Methods (+) :: Mul a -> Mul a -> Mul a # (-) :: Mul a -> Mul a -> Mul a # (*) :: Mul a -> Mul a -> Mul a # negate :: Mul a -> Mul a # abs :: Mul a -> Mul a # signum :: Mul a -> Mul a # fromInteger :: Integer -> Mul a #
Ord a => Ord (Mul a) Source #
Instance details Defined in Data.Semiring Methods compare :: Mul a -> Mul a -> Ordering # (<) :: Mul a -> Mul a -> Bool # (<=) :: Mul a -> Mul a -> Bool # (>) :: Mul a -> Mul a -> Bool # (>=) :: Mul a -> Mul a -> Bool # max :: Mul a -> Mul a -> Mul a # min :: Mul a -> Mul a -> Mul a #
Read a => Read (Mul a) Source #
Instance details Defined in Data.Semiring Methods readsPrec :: Int -> ReadS (Mul a) # readList :: ReadS [Mul a] # readPrec :: ReadPrec (Mul a) # readListPrec :: ReadPrec [Mul a] #
Real a => Real (Mul a) Source #
Instance details Defined in Data.Semiring Methods toRational :: Mul a -> Rational #
RealFrac a => RealFrac (Mul a) Source #
Instance details Defined in Data.Semiring Methods properFraction :: Integral b => Mul a -> (b, Mul a) # truncate :: Integral b => Mul a -> b # round :: Integral b => Mul a -> b # ceiling :: Integral b => Mul a -> b # floor :: Integral b => Mul a -> b #
Show a => Show (Mul a) Source #
Instance details Defined in Data.Semiring Methods showsPrec :: Int -> Mul a -> ShowS # show :: Mul a -> String # showList :: [Mul a] -> ShowS #
Generic (Mul a) Source #
Instance details Defined in Data.Semiring Associated Types type Rep (Mul a) :: * -> * # Methods from :: Mul a -> Rep (Mul a) x # to :: Rep (Mul a) x -> Mul a #
Semiring a => Semigroup (Mul a) Source #
Instance details Defined in Data.Semiring Methods (<>) :: Mul a -> Mul a -> Mul a # sconcat :: NonEmpty (Mul a) -> Mul a # stimes :: Integral b => b -> Mul a -> Mul a #
Semiring a => Monoid (Mul a) Source #
Instance details Defined in Data.Semiring Methods mempty :: Mul a # mappend :: Mul a -> Mul a -> Mul a # mconcat :: [Mul a] -> Mul a #
Storable a => Storable (Mul a) Source #
Instance details Defined in Data.Semiring Methods sizeOf :: Mul a -> Int # alignment :: Mul a -> Int # peekElemOff :: Ptr (Mul a) -> Int -> IO (Mul a) # pokeElemOff :: Ptr (Mul a) -> Int -> Mul a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Mul a) # pokeByteOff :: Ptr b -> Int -> Mul a -> IO () # peek :: Ptr (Mul a) -> IO (Mul a) # poke :: Ptr (Mul a) -> Mul a -> IO () #
Semiring a => Semiring (Mul a) Source #
Instance details Defined in Data.Semiring Methods plus :: Mul a -> Mul a -> Mul a Source # zero :: Mul a Source # times :: Mul a -> Mul a -> Mul a Source # one :: Mul a Source #
Generic1 Mul Source #
Instance details Defined in Data.Semiring Associated Types type Rep1 Mul :: k -> * # Methods from1 :: Mul a -> Rep1 Mul a # to1 :: Rep1 Mul a -> Mul a #
type Rep (Mul a) Source #
Instance details Defined in Data.Semiring type Rep (Mul a) = D1 (MetaData "Mul" "Data.Semiring" "semirings-0.2.1.1-K4F9vEfdMGEFaB4LacyWRO" True) (C1 (MetaCons "Mul" PrefixI True) (S1 (MetaSel (Just "getMul") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Mul Source #
Instance details Defined in Data.Semiring type Rep1 Mul = D1 (MetaData "Mul" "Data.Semiring" "semirings-0.2.1.1-K4F9vEfdMGEFaB4LacyWRO" True) (C1 (MetaCons "Mul" PrefixI True) (S1 (MetaSel (Just "getMul") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype WrappedNum a Source #

Provide Semiring and Ring for an arbitrary Num. It is useful with GHC 8.6+'s DerivingVia extension.

Constructors

WrapNum
Fields unwrapNum :: a

Instances

Functor WrappedNum Source #
Instance details Defined in Data.Semiring Methods fmap :: (a -> b) -> WrappedNum a -> WrappedNum b # (<$) :: a -> WrappedNum b -> WrappedNum a #
Foldable WrappedNum Source #
Instance details Defined in Data.Semiring Methods fold :: Monoid m => WrappedNum m -> m # foldMap :: Monoid m => (a -> m) -> WrappedNum a -> m # foldr :: (a -> b -> b) -> b -> WrappedNum a -> b # foldr' :: (a -> b -> b) -> b -> WrappedNum a -> b # foldl :: (b -> a -> b) -> b -> WrappedNum a -> b # foldl' :: (b -> a -> b) -> b -> WrappedNum a -> b # foldr1 :: (a -> a -> a) -> WrappedNum a -> a # foldl1 :: (a -> a -> a) -> WrappedNum a -> a # toList :: WrappedNum a -> [a] # null :: WrappedNum a -> Bool # length :: WrappedNum a -> Int # elem :: Eq a => a -> WrappedNum a -> Bool # maximum :: Ord a => WrappedNum a -> a # minimum :: Ord a => WrappedNum a -> a # sum :: Num a => WrappedNum a -> a # product :: Num a => WrappedNum a -> a #
Traversable WrappedNum Source #
Instance details Defined in Data.Semiring Methods traverse :: Applicative f => (a -> f b) -> WrappedNum a -> f (WrappedNum b) # sequenceA :: Applicative f => WrappedNum (f a) -> f (WrappedNum a) # mapM :: Monad m => (a -> m b) -> WrappedNum a -> m (WrappedNum b) # sequence :: Monad m => WrappedNum (m a) -> m (WrappedNum a) #
Bounded a => Bounded (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods minBound :: WrappedNum a # maxBound :: WrappedNum a #
Enum a => Enum (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods succ :: WrappedNum a -> WrappedNum a # pred :: WrappedNum a -> WrappedNum a # toEnum :: Int -> WrappedNum a # fromEnum :: WrappedNum a -> Int # enumFrom :: WrappedNum a -> [WrappedNum a] # enumFromThen :: WrappedNum a -> WrappedNum a -> [WrappedNum a] # enumFromTo :: WrappedNum a -> WrappedNum a -> [WrappedNum a] # enumFromThenTo :: WrappedNum a -> WrappedNum a -> WrappedNum a -> [WrappedNum a] #
Eq a => Eq (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods (==) :: WrappedNum a -> WrappedNum a -> Bool # (/=) :: WrappedNum a -> WrappedNum a -> Bool #
Fractional a => Fractional (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods (/) :: WrappedNum a -> WrappedNum a -> WrappedNum a # recip :: WrappedNum a -> WrappedNum a # fromRational :: Rational -> WrappedNum a #
Num a => Num (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods (+) :: WrappedNum a -> WrappedNum a -> WrappedNum a # (-) :: WrappedNum a -> WrappedNum a -> WrappedNum a # (*) :: WrappedNum a -> WrappedNum a -> WrappedNum a # negate :: WrappedNum a -> WrappedNum a # abs :: WrappedNum a -> WrappedNum a # signum :: WrappedNum a -> WrappedNum a # fromInteger :: Integer -> WrappedNum a #
Ord a => Ord (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods compare :: WrappedNum a -> WrappedNum a -> Ordering # (<) :: WrappedNum a -> WrappedNum a -> Bool # (<=) :: WrappedNum a -> WrappedNum a -> Bool # (>) :: WrappedNum a -> WrappedNum a -> Bool # (>=) :: WrappedNum a -> WrappedNum a -> Bool # max :: WrappedNum a -> WrappedNum a -> WrappedNum a # min :: WrappedNum a -> WrappedNum a -> WrappedNum a #
Read a => Read (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods readsPrec :: Int -> ReadS (WrappedNum a) # readList :: ReadS [WrappedNum a] # readPrec :: ReadPrec (WrappedNum a) # readListPrec :: ReadPrec [WrappedNum a] #
Real a => Real (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods toRational :: WrappedNum a -> Rational #
RealFrac a => RealFrac (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods properFraction :: Integral b => WrappedNum a -> (b, WrappedNum a) # truncate :: Integral b => WrappedNum a -> b # round :: Integral b => WrappedNum a -> b # ceiling :: Integral b => WrappedNum a -> b # floor :: Integral b => WrappedNum a -> b #
Show a => Show (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods showsPrec :: Int -> WrappedNum a -> ShowS # show :: WrappedNum a -> String # showList :: [WrappedNum a] -> ShowS #
Generic (WrappedNum a) Source #
Instance details Defined in Data.Semiring Associated Types type Rep (WrappedNum a) :: * -> * # Methods from :: WrappedNum a -> Rep (WrappedNum a) x # to :: Rep (WrappedNum a) x -> WrappedNum a #
Storable a => Storable (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods sizeOf :: WrappedNum a -> Int # alignment :: WrappedNum a -> Int # peekElemOff :: Ptr (WrappedNum a) -> Int -> IO (WrappedNum a) # pokeElemOff :: Ptr (WrappedNum a) -> Int -> WrappedNum a -> IO () # peekByteOff :: Ptr b -> Int -> IO (WrappedNum a) # pokeByteOff :: Ptr b -> Int -> WrappedNum a -> IO () # peek :: Ptr (WrappedNum a) -> IO (WrappedNum a) # poke :: Ptr (WrappedNum a) -> WrappedNum a -> IO () #
Num a => Ring (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods negate :: WrappedNum a -> WrappedNum a Source #
Num a => Semiring (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods plus :: WrappedNum a -> WrappedNum a -> WrappedNum a Source # zero :: WrappedNum a Source # times :: WrappedNum a -> WrappedNum a -> WrappedNum a Source # one :: WrappedNum a Source #
Generic1 WrappedNum Source #
Instance details Defined in Data.Semiring Associated Types type Rep1 WrappedNum :: k -> * # Methods from1 :: WrappedNum a -> Rep1 WrappedNum a # to1 :: Rep1 WrappedNum a -> WrappedNum a #
type Rep (WrappedNum a) Source #
Instance details Defined in Data.Semiring type Rep (WrappedNum a) = D1 (MetaData "WrappedNum" "Data.Semiring" "semirings-0.2.1.1-K4F9vEfdMGEFaB4LacyWRO" True) (C1 (MetaCons "WrapNum" PrefixI True) (S1 (MetaSel (Just "unwrapNum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 WrappedNum Source #
Instance details Defined in Data.Semiring type Rep1 WrappedNum = D1 (MetaData "WrappedNum" "Data.Semiring" "semirings-0.2.1.1-K4F9vEfdMGEFaB4LacyWRO" True) (C1 (MetaCons "WrapNum" PrefixI True) (S1 (MetaSel (Just "unwrapNum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Ring typeclass

class Semiring a => Ring a where Source #

The class of semirings with an additive inverse.

negate a + a = zero

Minimal complete definition

negate

Methods

negate :: a -> a Source #

Instances

Ring Bool Source #
Instance details Defined in Data.Semiring Methods negate :: Bool -> Bool Source #
Ring Double Source #
Instance details Defined in Data.Semiring Methods negate :: Double -> Double Source #
Ring Float Source #
Instance details Defined in Data.Semiring Methods negate :: Float -> Float Source #
Ring Int Source #
Instance details Defined in Data.Semiring Methods negate :: Int -> Int Source #
Ring Int8 Source #
Instance details Defined in Data.Semiring Methods negate :: Int8 -> Int8 Source #
Ring Int16 Source #
Instance details Defined in Data.Semiring Methods negate :: Int16 -> Int16 Source #
Ring Int32 Source #
Instance details Defined in Data.Semiring Methods negate :: Int32 -> Int32 Source #
Ring Int64 Source #
Instance details Defined in Data.Semiring Methods negate :: Int64 -> Int64 Source #
Ring Integer Source #
Instance details Defined in Data.Semiring Methods negate :: Integer -> Integer Source #
Ring Natural Source #
Instance details Defined in Data.Semiring Methods negate :: Natural -> Natural Source #
Ring Word Source #
Instance details Defined in Data.Semiring Methods negate :: Word -> Word Source #
Ring Word8 Source #
Instance details Defined in Data.Semiring Methods negate :: Word8 -> Word8 Source #
Ring Word16 Source #
Instance details Defined in Data.Semiring Methods negate :: Word16 -> Word16 Source #
Ring Word32 Source #
Instance details Defined in Data.Semiring Methods negate :: Word32 -> Word32 Source #
Ring Word64 Source #
Instance details Defined in Data.Semiring Methods negate :: Word64 -> Word64 Source #
Ring () Source #
Instance details Defined in Data.Semiring Methods negate :: () -> () Source #
Ring CDev Source #
Instance details Defined in Data.Semiring Methods negate :: CDev -> CDev Source #
Ring CIno Source #
Instance details Defined in Data.Semiring Methods negate :: CIno -> CIno Source #
Ring CMode Source #
Instance details Defined in Data.Semiring Methods negate :: CMode -> CMode Source #
Ring COff Source #
Instance details Defined in Data.Semiring Methods negate :: COff -> COff Source #
Ring CPid Source #
Instance details Defined in Data.Semiring Methods negate :: CPid -> CPid Source #
Ring CSsize Source #
Instance details Defined in Data.Semiring Methods negate :: CSsize -> CSsize Source #
Ring CGid Source #
Instance details Defined in Data.Semiring Methods negate :: CGid -> CGid Source #
Ring CNlink Source #
Instance details Defined in Data.Semiring Methods negate :: CNlink -> CNlink Source #
Ring CUid Source #
Instance details Defined in Data.Semiring Methods negate :: CUid -> CUid Source #
Ring CCc Source #
Instance details Defined in Data.Semiring Methods negate :: CCc -> CCc Source #
Ring CSpeed Source #
Instance details Defined in Data.Semiring Methods negate :: CSpeed -> CSpeed Source #
Ring CTcflag Source #
Instance details Defined in Data.Semiring Methods negate :: CTcflag -> CTcflag Source #
Ring CRLim Source #
Instance details Defined in Data.Semiring Methods negate :: CRLim -> CRLim Source #
Ring Fd Source #
Instance details Defined in Data.Semiring Methods negate :: Fd -> Fd Source #
Ring CChar Source #
Instance details Defined in Data.Semiring Methods negate :: CChar -> CChar Source #
Ring CSChar Source #
Instance details Defined in Data.Semiring Methods negate :: CSChar -> CSChar Source #
Ring CUChar Source #
Instance details Defined in Data.Semiring Methods negate :: CUChar -> CUChar Source #
Ring CShort Source #
Instance details Defined in Data.Semiring Methods negate :: CShort -> CShort Source #
Ring CUShort Source #
Instance details Defined in Data.Semiring Methods negate :: CUShort -> CUShort Source #
Ring CInt Source #
Instance details Defined in Data.Semiring Methods negate :: CInt -> CInt Source #
Ring CUInt Source #
Instance details Defined in Data.Semiring Methods negate :: CUInt -> CUInt Source #
Ring CLong Source #
Instance details Defined in Data.Semiring Methods negate :: CLong -> CLong Source #
Ring CULong Source #
Instance details Defined in Data.Semiring Methods negate :: CULong -> CULong Source #
Ring CLLong Source #
Instance details Defined in Data.Semiring Methods negate :: CLLong -> CLLong Source #
Ring CULLong Source #
Instance details Defined in Data.Semiring Methods negate :: CULLong -> CULLong Source #
Ring CFloat Source #
Instance details Defined in Data.Semiring Methods negate :: CFloat -> CFloat Source #
Ring CDouble Source #
Instance details Defined in Data.Semiring Methods negate :: CDouble -> CDouble Source #
Ring CPtrdiff Source #
Instance details Defined in Data.Semiring Methods negate :: CPtrdiff -> CPtrdiff Source #
Ring CSize Source #
Instance details Defined in Data.Semiring Methods negate :: CSize -> CSize Source #
Ring CWchar Source #
Instance details Defined in Data.Semiring Methods negate :: CWchar -> CWchar Source #
Ring CSigAtomic Source #
Instance details Defined in Data.Semiring Methods negate :: CSigAtomic -> CSigAtomic Source #
Ring CClock Source #
Instance details Defined in Data.Semiring Methods negate :: CClock -> CClock Source #
Ring CTime Source #
Instance details Defined in Data.Semiring Methods negate :: CTime -> CTime Source #
Ring CUSeconds Source #
Instance details Defined in Data.Semiring Methods negate :: CUSeconds -> CUSeconds Source #
Ring CSUSeconds Source #
Instance details Defined in Data.Semiring Methods negate :: CSUSeconds -> CSUSeconds Source #
Ring CIntPtr Source #
Instance details Defined in Data.Semiring Methods negate :: CIntPtr -> CIntPtr Source #
Ring CUIntPtr Source #
Instance details Defined in Data.Semiring Methods negate :: CUIntPtr -> CUIntPtr Source #
Ring CIntMax Source #
Instance details Defined in Data.Semiring Methods negate :: CIntMax -> CIntMax Source #
Ring CUIntMax Source #
Instance details Defined in Data.Semiring Methods negate :: CUIntMax -> CUIntMax Source #
Ring WordPtr Source #
Instance details Defined in Data.Semiring Methods negate :: WordPtr -> WordPtr Source #
Ring IntPtr Source #
Instance details Defined in Data.Semiring Methods negate :: IntPtr -> IntPtr Source #
Ring a => Ring [a] Source #
Instance details Defined in Data.Semiring Methods negate :: [a] -> [a] Source #
Ring a => Ring (Maybe a) Source #
Instance details Defined in Data.Semiring Methods negate :: Maybe a -> Maybe a Source #
Integral a => Ring (Ratio a) Source #
Instance details Defined in Data.Semiring Methods negate :: Ratio a -> Ratio a Source #
Ring a => Ring (IO a) Source #
Instance details Defined in Data.Semiring Methods negate :: IO a -> IO a Source #
Ring a => Ring (Complex a) Source #
Instance details Defined in Data.Semiring Methods negate :: Complex a -> Complex a Source #
HasResolution a => Ring (Fixed a) Source #
Instance details Defined in Data.Semiring Methods negate :: Fixed a -> Fixed a Source #
Ring a => Ring (Min a) Source #
Instance details Defined in Data.Semiring Methods negate :: Min a -> Min a Source #
Ring a => Ring (Max a) Source #
Instance details Defined in Data.Semiring Methods negate :: Max a -> Max a Source #
Ring a => Ring (Identity a) Source #
Instance details Defined in Data.Semiring Methods negate :: Identity a -> Identity a Source #
Ring a => Ring (Dual a) Source #
Instance details Defined in Data.Semiring Methods negate :: Dual a -> Dual a Source #
Ring a => Ring (Sum a) Source #
Instance details Defined in Data.Semiring Methods negate :: Sum a -> Sum a Source #
Ring a => Ring (Product a) Source #
Instance details Defined in Data.Semiring Methods negate :: Product a -> Product a Source #
Ring a => Ring (Down a) Source #
Instance details Defined in Data.Semiring Methods negate :: Down a -> Down a Source #
(Unbox a, Ring a) => Ring (Vector a) Source #
Instance details Defined in Data.Semiring Methods negate :: Vector a -> Vector a Source #
(Storable a, Ring a) => Ring (Vector a) Source #
Instance details Defined in Data.Semiring Methods negate :: Vector a -> Vector a Source #
Ring a => Ring (Vector a) Source #
Instance details Defined in Data.Semiring Methods negate :: Vector a -> Vector a Source #
Num a => Ring (WrappedNum a) Source #
Instance details Defined in Data.Semiring Methods negate :: WrappedNum a -> WrappedNum a Source #
Ring b => Ring (a -> b) Source #
Instance details Defined in Data.Semiring Methods negate :: (a -> b) -> a -> b Source #
(Ring a, Ring b) => Ring (a, b) Source #
Instance details Defined in Data.Semiring.Generic Methods negate :: (a, b) -> (a, b) Source #
(Ring a, Ring b, Ring c) => Ring (a, b, c) Source #
Instance details Defined in Data.Semiring.Generic Methods negate :: (a, b, c) -> (a, b, c) Source #
Ring a => Ring (Const a b) Source #
Instance details Defined in Data.Semiring Methods negate :: Const a b -> Const a b Source #
(Ring a, Ring b, Ring c, Ring d) => Ring (a, b, c, d) Source #
Instance details Defined in Data.Semiring.Generic Methods negate :: (a, b, c, d) -> (a, b, c, d) Source #
(Ring a, Ring b, Ring c, Ring d, Ring e) => Ring (a, b, c, d, e) Source #
Instance details Defined in Data.Semiring.Generic Methods negate :: (a, b, c, d, e) -> (a, b, c, d, e) Source #
(Ring a, Ring b, Ring c, Ring d, Ring e, Ring f) => Ring (a, b, c, d, e, f) Source #
Instance details Defined in Data.Semiring.Generic Methods negate :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source #
(Ring a, Ring b, Ring c, Ring d, Ring e, Ring f, Ring g) => Ring (a, b, c, d, e, f, g) Source #
Instance details Defined in Data.Semiring.Generic Methods negate :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source #

(-) :: Ring a => a -> a -> a infixl 6 Source #

Infix shorthand for minus.

minus :: Ring a => a -> a -> a infixl 6 Source #

Substract two Ring values. For any type R with a Num instance, this is the same as '(Prelude.-)'.

x minus y = x + negate y