semirings-0.7: two monoids as one, in holy haskimony
Safe HaskellNone
LanguageHaskell98

Data.Semiring

Description

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

Synopsis

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, with the first being commutative. In the documentation, you will often see the first monoid being referred to as additive, and the second monoid being referred to as multiplicative, a typical convention when talking about semirings.

For any type R with a Num instance, the additive monoid is (R, +, 0) and the multiplicative monoid is (R, *, 1).

For Bool, the additive monoid is (Bool, ||, False) and the multiplicative monoid is (Bool, &&, True).

Instances should satisfy the following laws:

additive left identity
zero + x = x
additive right identity
x + zero = x
additive associativity
x + (y + z) = (x + y) + z
additive commutativity
x + y = y + x
multiplicative left identity
one * x = x
multiplicative right identity
x * one = x
multiplicative associativity
x * (y * z) = (x * y) * z
left-distributivity of * over +
x * (y + z) = (x * y) + (x * z)
right-distributivity of * over +
(x + y) * z = (x * z) + (y * z)
annihilation
zero * x = x * zero = zero

Minimal complete definition

plus, times, (zero, one | fromNatural)

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

fromNatural Source #

Arguments

:: Natural 
-> a

Homomorphism of additive semigroups

Instances

Instances details
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 #

fromNatural :: Natural -> CChar 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 #

fromNatural :: Natural -> CClock 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 #

fromNatural :: Natural -> CDouble 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 #

fromNatural :: Natural -> CFloat 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 #

fromNatural :: Natural -> CInt 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 #

fromNatural :: Natural -> CIntMax 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 #

fromNatural :: Natural -> CIntPtr 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 #

fromNatural :: Natural -> CLLong 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 #

fromNatural :: Natural -> CLong 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 #

fromNatural :: Natural -> CPtrdiff 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 #

fromNatural :: Natural -> CSChar 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 #

fromNatural :: Natural -> CSUSeconds 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 #

fromNatural :: Natural -> CShort 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 #

fromNatural :: Natural -> CSigAtomic 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 #

fromNatural :: Natural -> CSize 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 #

fromNatural :: Natural -> CTime 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 #

fromNatural :: Natural -> CUChar 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 #

fromNatural :: Natural -> CUInt 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 #

fromNatural :: Natural -> CUIntMax 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 #

fromNatural :: Natural -> CUIntPtr 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 #

fromNatural :: Natural -> CULLong 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 #

fromNatural :: Natural -> CULong 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 #

fromNatural :: Natural -> CUSeconds 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 #

fromNatural :: Natural -> CUShort 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 #

fromNatural :: Natural -> CWchar 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 #

fromNatural :: Natural -> IntPtr 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 #

fromNatural :: Natural -> WordPtr 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> Int64 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 #

fromNatural :: Natural -> Int8 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 #

fromNatural :: Natural -> CCc 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 #

fromNatural :: Natural -> CDev 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 #

fromNatural :: Natural -> CGid 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> CMode 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 #

fromNatural :: Natural -> CNlink 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> CPid 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 #

fromNatural :: Natural -> CRLim 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 #

fromNatural :: Natural -> CSpeed 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 #

fromNatural :: Natural -> CSsize 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 #

fromNatural :: Natural -> CTcflag 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 #

fromNatural :: Natural -> CUid 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 #

fromNatural :: Natural -> Fd 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> Word64 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 #

fromNatural :: Natural -> Word8 Source #

Semiring Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: Mod2 -> Mod2 -> Mod2 Source #

zero :: Mod2 Source #

times :: Mod2 -> Mod2 -> Mod2 Source #

one :: Mod2 Source #

fromNatural :: Natural -> Mod2 Source #

Semiring Directed Source #

Since: 0.7

Instance details

Defined in Data.Semiring.Directed

Methods

plus :: Directed -> Directed -> Directed Source #

zero :: Directed Source #

times :: Directed -> Directed -> Directed Source #

one :: Directed Source #

fromNatural :: Natural -> Directed 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> Natural Source #

Semiring () Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: () -> () -> () Source #

zero :: () Source #

times :: () -> () -> () Source #

one :: () Source #

fromNatural :: Natural -> () Source #

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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> Int 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 #

fromNatural :: Natural -> Word 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 #

fromNatural :: Natural -> Complex a Source #

Semiring a => Semiring (Equivalence a) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: Equivalence a -> Equivalence a -> Equivalence a Source #

zero :: Equivalence a Source #

times :: Equivalence a -> Equivalence a -> Equivalence a Source #

one :: Equivalence a Source #

fromNatural :: Natural -> Equivalence a Source #

Semiring (Predicate a) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: Predicate a -> Predicate a -> Predicate a Source #

zero :: Predicate a Source #

times :: Predicate a -> Predicate a -> Predicate a Source #

one :: Predicate a Source #

fromNatural :: Natural -> Predicate a Source #

(Ord a, Monoid a) => Semiring (Set a) Source #

The multiplication laws are satisfied for any underlying Monoid, so we require a Monoid constraint 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 #

fromNatural :: Natural -> Set 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 #

fromNatural :: Natural -> Identity 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 #

fromNatural :: Natural -> Down 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 #

fromNatural :: Natural -> Dual 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 #

fromNatural :: Natural -> 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 #

fromNatural :: Natural -> IO a Source #

Num a => Semiring (WrappedFractional a) Source # 
Instance details

Defined in Data.Euclidean

Methods

plus :: WrappedFractional a -> WrappedFractional a -> WrappedFractional a Source #

zero :: WrappedFractional a Source #

times :: WrappedFractional a -> WrappedFractional a -> WrappedFractional a Source #

one :: WrappedFractional a Source #

fromNatural :: Natural -> WrappedFractional a Source #

Num a => Semiring (WrappedIntegral a) Source # 
Instance details

Defined in Data.Euclidean

Methods

plus :: WrappedIntegral a -> WrappedIntegral a -> WrappedIntegral a Source #

zero :: WrappedIntegral a Source #

times :: WrappedIntegral a -> WrappedIntegral a -> WrappedIntegral a Source #

one :: WrappedIntegral a Source #

fromNatural :: Natural -> WrappedIntegral a Source #

Semiring (Modular Word16) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

plus :: Modular Word16 -> Modular Word16 -> Modular Word16 Source #

zero :: Modular Word16 Source #

times :: Modular Word16 -> Modular Word16 -> Modular Word16 Source #

one :: Modular Word16 Source #

fromNatural :: Natural -> Modular Word16 Source #

Semiring (Modular Word32) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

plus :: Modular Word32 -> Modular Word32 -> Modular Word32 Source #

zero :: Modular Word32 Source #

times :: Modular Word32 -> Modular Word32 -> Modular Word32 Source #

one :: Modular Word32 Source #

fromNatural :: Natural -> Modular Word32 Source #

Semiring (Modular Word64) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

plus :: Modular Word64 -> Modular Word64 -> Modular Word64 Source #

zero :: Modular Word64 Source #

times :: Modular Word64 -> Modular Word64 -> Modular Word64 Source #

one :: Modular Word64 Source #

fromNatural :: Natural -> Modular Word64 Source #

Semiring (Modular Word8) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

plus :: Modular Word8 -> Modular Word8 -> Modular Word8 Source #

zero :: Modular Word8 Source #

times :: Modular Word8 -> Modular Word8 -> Modular Word8 Source #

one :: Modular Word8 Source #

fromNatural :: Natural -> Modular Word8 Source #

Semiring (Modular Word) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

plus :: Modular Word -> Modular Word -> Modular Word Source #

zero :: Modular Word Source #

times :: Modular Word -> Modular Word -> Modular Word Source #

one :: Modular Word Source #

fromNatural :: Natural -> Modular Word Source #

(Coercible Int a, Monoid a) => Semiring (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: IntSetOf a -> IntSetOf a -> IntSetOf a Source #

zero :: IntSetOf a Source #

times :: IntSetOf a -> IntSetOf a -> IntSetOf a Source #

one :: IntSetOf a Source #

fromNatural :: Natural -> IntSetOf 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 #

fromNatural :: Natural -> WrappedNum a Source #

(Generic a, GSemiring (Rep a)) => Semiring (GenericSemiring a) Source # 
Instance details

Defined in Data.Semiring.Generic

Methods

plus :: GenericSemiring a -> GenericSemiring a -> GenericSemiring a Source #

zero :: GenericSemiring a Source #

times :: GenericSemiring a -> GenericSemiring a -> GenericSemiring a Source #

one :: GenericSemiring a Source #

fromNatural :: Natural -> GenericSemiring 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 constraint 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 #

fromNatural :: Natural -> HashSet 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 #

fromNatural :: Natural -> Maybe 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 #

fromNatural :: Natural -> Fixed a Source #

Semiring a => Semiring (Op a b) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: Op a b -> Op a b -> Op a b Source #

zero :: Op a b Source #

times :: Op a b -> Op a b -> Op a b Source #

one :: Op a b Source #

fromNatural :: Natural -> Op a b 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 constraint 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 #

fromNatural :: Natural -> Map k v 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 #

fromNatural :: Natural -> Proxy a Source #

(Coercible Int k, Monoid k, Semiring v) => Semiring (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v Source #

zero :: IntMapOf k v Source #

times :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v Source #

one :: IntMapOf k v Source #

fromNatural :: Natural -> IntMapOf k v Source #

(Ord a, Monoid a, Extremum e) => Semiring (Tropical e a) Source # 
Instance details

Defined in Data.Semiring.Tropical

Methods

plus :: Tropical e a -> Tropical e a -> Tropical e a Source #

zero :: Tropical e a Source #

times :: Tropical e a -> Tropical e a -> Tropical e a Source #

one :: Tropical e a Source #

fromNatural :: Natural -> Tropical e a 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 constraint 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 #

fromNatural :: Natural -> HashMap k v Source #

(Semiring a, 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 #

fromNatural :: Natural -> (a, b) 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 #

fromNatural :: Natural -> a -> b 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 #

fromNatural :: Natural -> Const a b Source #

(Semiring a, Applicative f) => Semiring (Ap f a) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: Ap f a -> Ap f a -> Ap f a Source #

zero :: Ap f a Source #

times :: Ap f a -> Ap f a -> Ap f a Source #

one :: Ap f a Source #

fromNatural :: Natural -> Ap f a Source #

(Semiring a, Semiring b, Semiring c) => Semiring (a, b, c) Source # 
Instance details

Defined in Data.Semiring

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 #

fromNatural :: Natural -> (a, b, c) Source #

(Semiring a, Semiring b, Semiring c, Semiring d) => Semiring (a, b, c, d) Source # 
Instance details

Defined in Data.Semiring

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 #

fromNatural :: Natural -> (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

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 #

fromNatural :: Natural -> (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

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 #

fromNatural :: Natural -> (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

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 #

fromNatural :: Natural -> (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 call error.

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.

isZero :: (Eq a, Semiring a) => a -> Bool Source #

Is the value zero?

isOne :: (Eq a, Semiring a) => a -> Bool Source #

Is the value one?

Types

newtype Add a Source #

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

Constructors

Add 

Fields

Instances

Instances details
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 #

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) #

Generic1 Add Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep1 Add 
Instance details

Defined in Data.Semiring

type Rep1 Add = D1 ('MetaData "Add" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Add" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAdd") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Add a -> Rep1 Add a #

to1 :: Rep1 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 #

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 #

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] #

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 () #

Generic (Add a) Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep (Add a) 
Instance details

Defined in Data.Semiring

type Rep (Add a) = D1 ('MetaData "Add" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Add" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAdd") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Add a -> Rep (Add a) x #

to :: Rep (Add a) x -> 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 #

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] #

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 #

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 #

Eq a => Eq (Add a) Source # 
Instance details

Defined in Data.Semiring

Methods

(==) :: Add a -> Add a -> Bool #

(/=) :: Add a -> Add a -> Bool #

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 #

type Rep1 Add Source # 
Instance details

Defined in Data.Semiring

type Rep1 Add = D1 ('MetaData "Add" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Add" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAdd") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Add a) Source # 
Instance details

Defined in Data.Semiring

type Rep (Add a) = D1 ('MetaData "Add" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Add" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAdd") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Mul a Source #

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

Constructors

Mul 

Fields

Instances

Instances details
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 #

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) #

Generic1 Mul Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep1 Mul 
Instance details

Defined in Data.Semiring

type Rep1 Mul = D1 ('MetaData "Mul" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Mul" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMul") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Mul a -> Rep1 Mul a #

to1 :: Rep1 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 #

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 #

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] #

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 () #

Generic (Mul a) Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep (Mul a) 
Instance details

Defined in Data.Semiring

type Rep (Mul a) = D1 ('MetaData "Mul" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Mul" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMul") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Mul a -> Rep (Mul a) x #

to :: Rep (Mul a) x -> 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 #

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] #

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 #

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 #

Eq a => Eq (Mul a) Source # 
Instance details

Defined in Data.Semiring

Methods

(==) :: Mul a -> Mul a -> Bool #

(/=) :: Mul a -> Mul a -> Bool #

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 #

type Rep1 Mul Source # 
Instance details

Defined in Data.Semiring

type Rep1 Mul = D1 ('MetaData "Mul" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Mul" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMul") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Mul a) Source # 
Instance details

Defined in Data.Semiring

type Rep (Mul a) = D1 ('MetaData "Mul" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Mul" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMul") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

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

Instances

Instances details
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 #

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) #

Generic1 WrappedNum Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep1 WrappedNum 
Instance details

Defined in Data.Semiring

type Rep1 WrappedNum = D1 ('MetaData "WrappedNum" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "WrapNum" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapNum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: WrappedNum a -> Rep1 WrappedNum a #

to1 :: Rep1 WrappedNum a -> WrappedNum a #

Bits a => Bits (WrappedNum a) Source # 
Instance details

Defined in Data.Semiring

Methods

(.&.) :: WrappedNum a -> WrappedNum a -> WrappedNum a #

(.|.) :: WrappedNum a -> WrappedNum a -> WrappedNum a #

xor :: WrappedNum a -> WrappedNum a -> WrappedNum a #

complement :: WrappedNum a -> WrappedNum a #

shift :: WrappedNum a -> Int -> WrappedNum a #

rotate :: WrappedNum a -> Int -> WrappedNum a #

zeroBits :: WrappedNum a #

bit :: Int -> WrappedNum a #

setBit :: WrappedNum a -> Int -> WrappedNum a #

clearBit :: WrappedNum a -> Int -> WrappedNum a #

complementBit :: WrappedNum a -> Int -> WrappedNum a #

testBit :: WrappedNum a -> Int -> Bool #

bitSizeMaybe :: WrappedNum a -> Maybe Int #

bitSize :: WrappedNum a -> Int #

isSigned :: WrappedNum a -> Bool #

shiftL :: WrappedNum a -> Int -> WrappedNum a #

unsafeShiftL :: WrappedNum a -> Int -> WrappedNum a #

shiftR :: WrappedNum a -> Int -> WrappedNum a #

unsafeShiftR :: WrappedNum a -> Int -> WrappedNum a #

rotateL :: WrappedNum a -> Int -> WrappedNum a #

rotateR :: WrappedNum a -> Int -> WrappedNum a #

popCount :: WrappedNum a -> Int #

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] #

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 () #

Generic (WrappedNum a) Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep (WrappedNum a) 
Instance details

Defined in Data.Semiring

type Rep (WrappedNum a) = D1 ('MetaData "WrappedNum" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "WrapNum" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapNum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: WrappedNum a -> Rep (WrappedNum a) x #

to :: Rep (WrappedNum a) x -> 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 #

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] #

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 #

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 #

Eq a => Eq (WrappedNum a) Source # 
Instance details

Defined in Data.Semiring

Methods

(==) :: WrappedNum a -> WrappedNum a -> Bool #

(/=) :: WrappedNum a -> WrappedNum a -> Bool #

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 #

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 #

fromNatural :: Natural -> WrappedNum a Source #

type Rep1 WrappedNum Source # 
Instance details

Defined in Data.Semiring

type Rep1 WrappedNum = D1 ('MetaData "WrappedNum" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "WrapNum" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapNum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (WrappedNum a) Source # 
Instance details

Defined in Data.Semiring

type Rep (WrappedNum a) = D1 ('MetaData "WrappedNum" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "WrapNum" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapNum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Mod2 Source #

Mod2 represents the integers mod 2.

It is useful in the computing of Zhegalkin polynomials.

Constructors

Mod2 

Fields

Instances

Instances details
Bounded Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

minBound :: Mod2 #

maxBound :: Mod2 #

Enum Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

succ :: Mod2 -> Mod2 #

pred :: Mod2 -> Mod2 #

toEnum :: Int -> Mod2 #

fromEnum :: Mod2 -> Int #

enumFrom :: Mod2 -> [Mod2] #

enumFromThen :: Mod2 -> Mod2 -> [Mod2] #

enumFromTo :: Mod2 -> Mod2 -> [Mod2] #

enumFromThenTo :: Mod2 -> Mod2 -> Mod2 -> [Mod2] #

Generic Mod2 Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep Mod2 
Instance details

Defined in Data.Semiring

type Rep Mod2 = D1 ('MetaData "Mod2" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Mod2" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMod2") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Methods

from :: Mod2 -> Rep Mod2 x #

to :: Rep Mod2 x -> Mod2 #

Read Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

readsPrec :: Int -> ReadS Mod2 #

readList :: ReadS [Mod2] #

readPrec :: ReadPrec Mod2 #

readListPrec :: ReadPrec [Mod2] #

Show Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

showsPrec :: Int -> Mod2 -> ShowS #

show :: Mod2 -> String #

showList :: [Mod2] -> ShowS #

Eq Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

(==) :: Mod2 -> Mod2 -> Bool #

(/=) :: Mod2 -> Mod2 -> Bool #

Ord Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

compare :: Mod2 -> Mod2 -> Ordering #

(<) :: Mod2 -> Mod2 -> Bool #

(<=) :: Mod2 -> Mod2 -> Bool #

(>) :: Mod2 -> Mod2 -> Bool #

(>=) :: Mod2 -> Mod2 -> Bool #

max :: Mod2 -> Mod2 -> Mod2 #

min :: Mod2 -> Mod2 -> Mod2 #

Euclidean Mod2 Source # 
Instance details

Defined in Data.Euclidean

Methods

quotRem :: Mod2 -> Mod2 -> (Mod2, Mod2) Source #

quot :: Mod2 -> Mod2 -> Mod2 Source #

rem :: Mod2 -> Mod2 -> Mod2 Source #

degree :: Mod2 -> Natural Source #

Field Mod2 Source # 
Instance details

Defined in Data.Euclidean

GcdDomain Mod2 Source # 
Instance details

Defined in Data.Euclidean

Methods

divide :: Mod2 -> Mod2 -> Maybe Mod2 Source #

gcd :: Mod2 -> Mod2 -> Mod2 Source #

lcm :: Mod2 -> Mod2 -> Mod2 Source #

coprime :: Mod2 -> Mod2 -> Bool Source #

Ring Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Mod2 -> Mod2 Source #

Semiring Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: Mod2 -> Mod2 -> Mod2 Source #

zero :: Mod2 Source #

times :: Mod2 -> Mod2 -> Mod2 Source #

one :: Mod2 Source #

fromNatural :: Natural -> Mod2 Source #

Star Mod2 Source # 
Instance details

Defined in Data.Star

Methods

star :: Mod2 -> Mod2 Source #

aplus :: Mod2 -> Mod2 Source #

type Rep Mod2 Source # 
Instance details

Defined in Data.Semiring

type Rep Mod2 = D1 ('MetaData "Mod2" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "Mod2" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMod2") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype IntSetOf a Source #

Wrapper to mimic Set (Sum Int), Set (Product Int), etc., while having a more efficient underlying representation.

Constructors

IntSetOf 

Fields

Instances

Instances details
Generic1 IntSetOf Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep1 IntSetOf 
Instance details

Defined in Data.Semiring

type Rep1 IntSetOf = D1 ('MetaData "IntSetOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntSetOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntSet") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IntSet)))

Methods

from1 :: IntSetOf a -> Rep1 IntSetOf a #

to1 :: Rep1 IntSetOf a -> IntSetOf a #

Monoid (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

mempty :: IntSetOf a #

mappend :: IntSetOf a -> IntSetOf a -> IntSetOf a #

mconcat :: [IntSetOf a] -> IntSetOf a #

Semigroup (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

(<>) :: IntSetOf a -> IntSetOf a -> IntSetOf a #

sconcat :: NonEmpty (IntSetOf a) -> IntSetOf a #

stimes :: Integral b => b -> IntSetOf a -> IntSetOf a #

Generic (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep (IntSetOf a) 
Instance details

Defined in Data.Semiring

type Rep (IntSetOf a) = D1 ('MetaData "IntSetOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntSetOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntSet") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IntSet)))

Methods

from :: IntSetOf a -> Rep (IntSetOf a) x #

to :: Rep (IntSetOf a) x -> IntSetOf a #

Read (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

readsPrec :: Int -> ReadS (IntSetOf a) #

readList :: ReadS [IntSetOf a] #

readPrec :: ReadPrec (IntSetOf a) #

readListPrec :: ReadPrec [IntSetOf a] #

Show (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

showsPrec :: Int -> IntSetOf a -> ShowS #

show :: IntSetOf a -> String #

showList :: [IntSetOf a] -> ShowS #

Eq (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

(==) :: IntSetOf a -> IntSetOf a -> Bool #

(/=) :: IntSetOf a -> IntSetOf a -> Bool #

Ord (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

compare :: IntSetOf a -> IntSetOf a -> Ordering #

(<) :: IntSetOf a -> IntSetOf a -> Bool #

(<=) :: IntSetOf a -> IntSetOf a -> Bool #

(>) :: IntSetOf a -> IntSetOf a -> Bool #

(>=) :: IntSetOf a -> IntSetOf a -> Bool #

max :: IntSetOf a -> IntSetOf a -> IntSetOf a #

min :: IntSetOf a -> IntSetOf a -> IntSetOf a #

(Coercible Int a, Monoid a) => Semiring (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: IntSetOf a -> IntSetOf a -> IntSetOf a Source #

zero :: IntSetOf a Source #

times :: IntSetOf a -> IntSetOf a -> IntSetOf a Source #

one :: IntSetOf a Source #

fromNatural :: Natural -> IntSetOf a Source #

type Rep1 IntSetOf Source # 
Instance details

Defined in Data.Semiring

type Rep1 IntSetOf = D1 ('MetaData "IntSetOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntSetOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntSet") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IntSet)))
type Rep (IntSetOf a) Source # 
Instance details

Defined in Data.Semiring

type Rep (IntSetOf a) = D1 ('MetaData "IntSetOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntSetOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntSet") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 IntSet)))

newtype IntMapOf k v Source #

Wrapper to mimic Map (Sum Int) v, Map (Product Int) v, etc., while having a more efficient underlying representation.

Constructors

IntMapOf 

Fields

Instances

Instances details
Generic1 (IntMapOf k :: Type -> Type) Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep1 (IntMapOf k :: Type -> Type) 
Instance details

Defined in Data.Semiring

type Rep1 (IntMapOf k :: Type -> Type) = D1 ('MetaData "IntMapOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntMapOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntMap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 IntMap)))

Methods

from1 :: IntMapOf k a -> Rep1 (IntMapOf k) a #

to1 :: Rep1 (IntMapOf k) a -> IntMapOf k a #

Monoid (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

mempty :: IntMapOf k v #

mappend :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v #

mconcat :: [IntMapOf k v] -> IntMapOf k v #

Semigroup (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

(<>) :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v #

sconcat :: NonEmpty (IntMapOf k v) -> IntMapOf k v #

stimes :: Integral b => b -> IntMapOf k v -> IntMapOf k v #

Generic (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Associated Types

type Rep (IntMapOf k v) 
Instance details

Defined in Data.Semiring

type Rep (IntMapOf k v) = D1 ('MetaData "IntMapOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntMapOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntMap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (IntMap v))))

Methods

from :: IntMapOf k v -> Rep (IntMapOf k v) x #

to :: Rep (IntMapOf k v) x -> IntMapOf k v #

Read v => Read (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

readsPrec :: Int -> ReadS (IntMapOf k v) #

readList :: ReadS [IntMapOf k v] #

readPrec :: ReadPrec (IntMapOf k v) #

readListPrec :: ReadPrec [IntMapOf k v] #

Show v => Show (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

showsPrec :: Int -> IntMapOf k v -> ShowS #

show :: IntMapOf k v -> String #

showList :: [IntMapOf k v] -> ShowS #

Eq v => Eq (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

(==) :: IntMapOf k v -> IntMapOf k v -> Bool #

(/=) :: IntMapOf k v -> IntMapOf k v -> Bool #

Ord v => Ord (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

compare :: IntMapOf k v -> IntMapOf k v -> Ordering #

(<) :: IntMapOf k v -> IntMapOf k v -> Bool #

(<=) :: IntMapOf k v -> IntMapOf k v -> Bool #

(>) :: IntMapOf k v -> IntMapOf k v -> Bool #

(>=) :: IntMapOf k v -> IntMapOf k v -> Bool #

max :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v #

min :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v #

(Coercible Int k, Monoid k, Semiring v) => Semiring (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

Methods

plus :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v Source #

zero :: IntMapOf k v Source #

times :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v Source #

one :: IntMapOf k v Source #

fromNatural :: Natural -> IntMapOf k v Source #

type Rep1 (IntMapOf k :: Type -> Type) Source # 
Instance details

Defined in Data.Semiring

type Rep1 (IntMapOf k :: Type -> Type) = D1 ('MetaData "IntMapOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntMapOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntMap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 IntMap)))
type Rep (IntMapOf k v) Source # 
Instance details

Defined in Data.Semiring

type Rep (IntMapOf k v) = D1 ('MetaData "IntMapOf" "Data.Semiring" "semirings-0.7-97kRgOWD5i9FFHSTrlNCn8" 'True) (C1 ('MetaCons "IntMapOf" 'PrefixI 'True) (S1 ('MetaSel ('Just "getIntMap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (IntMap v))))

Ring typeclass

class Semiring a => Ring a where Source #

The class of semirings with an additive inverse.

negate a + a = zero

Methods

negate :: a -> a Source #

Instances

Instances details
Ring CChar Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CChar -> CChar Source #

Ring CClock Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CClock -> CClock Source #

Ring CDouble Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CDouble -> CDouble Source #

Ring CFloat Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CFloat -> CFloat Source #

Ring CInt Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CInt -> CInt Source #

Ring CIntMax Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CIntMax -> CIntMax Source #

Ring CIntPtr Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CIntPtr -> CIntPtr Source #

Ring CLLong Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CLLong -> CLLong Source #

Ring CLong Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CLong -> CLong Source #

Ring CPtrdiff Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CPtrdiff -> CPtrdiff Source #

Ring CSChar Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CSChar -> CSChar Source #

Ring CSUSeconds Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CSUSeconds -> CSUSeconds Source #

Ring CShort Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CShort -> CShort Source #

Ring CSigAtomic Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CSigAtomic -> CSigAtomic Source #

Ring CSize Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CSize -> CSize Source #

Ring CTime Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CTime -> CTime Source #

Ring CUChar Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CUChar -> CUChar Source #

Ring CUInt Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CUInt -> CUInt Source #

Ring CUIntMax Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CUIntMax -> CUIntMax Source #

Ring CUIntPtr Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CUIntPtr -> CUIntPtr Source #

Ring CULLong Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CULLong -> CULLong Source #

Ring CULong Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CULong -> CULong Source #

Ring CUSeconds Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CUSeconds -> CUSeconds Source #

Ring CUShort Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CUShort -> CUShort Source #

Ring CWchar Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CWchar -> CWchar Source #

Ring IntPtr Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: IntPtr -> IntPtr Source #

Ring WordPtr Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: WordPtr -> WordPtr 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 Int8 Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Int8 -> Int8 Source #

Ring CCc Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CCc -> CCc Source #

Ring CDev Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CDev -> CDev Source #

Ring CGid Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CGid -> CGid 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 CNlink Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CNlink -> CNlink 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 CRLim Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CRLim -> CRLim Source #

Ring CSpeed Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CSpeed -> CSpeed Source #

Ring CSsize Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CSsize -> CSsize Source #

Ring CTcflag Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CTcflag -> CTcflag Source #

Ring CUid Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: CUid -> CUid Source #

Ring Fd Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Fd -> Fd 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 Word8 Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Word8 -> Word8 Source #

Ring Mod2 Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Mod2 -> Mod2 Source #

Ring Integer Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Integer -> Integer Source #

Ring () Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: () -> () 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 Word Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Word -> Word Source #

Ring a => Ring (Complex a) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Complex a -> Complex a Source #

Ring a => Ring (Identity a) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Identity a -> Identity a Source #

Ring a => Ring (Down a) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Down a -> Down a Source #

Ring a => Ring (Dual a) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Dual a -> Dual 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 #

Num a => Ring (WrappedFractional a) Source # 
Instance details

Defined in Data.Euclidean

Methods

negate :: WrappedFractional a -> WrappedFractional a Source #

Num a => Ring (WrappedIntegral a) Source # 
Instance details

Defined in Data.Euclidean

Methods

negate :: WrappedIntegral a -> WrappedIntegral a Source #

Ring (Modular Word16) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

negate :: Modular Word16 -> Modular Word16 Source #

Ring (Modular Word32) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

negate :: Modular Word32 -> Modular Word32 Source #

Ring (Modular Word64) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

negate :: Modular Word64 -> Modular Word64 Source #

Ring (Modular Word8) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

negate :: Modular Word8 -> Modular Word8 Source #

Ring (Modular Word) Source # 
Instance details

Defined in Data.Ring.Ordered

Methods

negate :: Modular Word -> Modular Word Source #

Num a => Ring (WrappedNum a) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: WrappedNum a -> WrappedNum a Source #

HasResolution a => Ring (Fixed a) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Fixed a -> Fixed a Source #

Ring a => Ring (Op a b) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Op a b -> Op a b Source #

(Ring a, Ring b) => Ring (a, b) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: (a, b) -> (a, b) Source #

Ring b => Ring (a -> b) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: (a -> b) -> a -> b 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, Applicative f) => Ring (Ap f a) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: Ap f a -> Ap f a Source #

(Ring a, Ring b, Ring c) => Ring (a, b, c) Source # 
Instance details

Defined in Data.Semiring

Methods

negate :: (a, b, c) -> (a, b, c) Source #

(Ring a, Ring b, Ring c, Ring d) => Ring (a, b, c, d) Source # 
Instance details

Defined in Data.Semiring

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

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

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

Methods

negate :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source #

fromInteger :: Ring a => Integer -> a Source #

Convert from integer to ring.

When {-# LANGUAGE RebindableSyntax #-} is enabled, this function is used for desugaring integer literals. This may be used to facilitate transition from Num to Ring: no need to replace 0 and 1 with one and zero or to cast numeric literals.

fromIntegral :: (Integral a, Ring b) => a -> b Source #

Convert from integral to ring.

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

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

x minus y = x + negate y

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

Infix shorthand for minus.