Safe Haskell	None
Language	Haskell2010

Algebra.Structure.Semiring

Contents

Orphan instances

Description

A set with two binary operations, one for addition (srplus), one for multiplication (srmul). Together with a neutral element for srplus, named srzero, and one for srmul, named srone.

Synopsis

pattern V_Viterbi :: (Vector x) -> Vector (Viterbi x)
pattern V_MinPlus :: (Vector x) -> Vector (MinPlus x)
pattern V_MaxPlus :: (Vector x) -> Vector (MaxPlus x)
pattern MV_Viterbi :: (MVector s x) -> MVector s (Viterbi x)
pattern MV_MinPlus :: (MVector s x) -> MVector s (MinPlus x)
pattern MV_MaxPlus :: (MVector s x) -> MVector s (MaxPlus x)
newtype Viterbi x = Viterbi {
- getViterbi :: x
}
(⊕) :: Semiring a => a -> a -> a
(⊗) :: Semiring a => a -> a -> a
newtype MinPlus x = MinPlus {
- getMinPlus :: x
}
newtype MaxPlus x = MaxPlus {
- getMaxPlus :: x
}
newtype GSemiring (zeroMonoid :: * -> *) (oneMonoid :: * -> *) (x :: *) = GSemiring {
- getSemiring :: x
}
class Semiring a where
- plus :: a -> a -> a
- zero :: a
- times :: a -> a -> a
- one :: a

Documentation

pattern V_Viterbi :: (Vector x) -> Vector (Viterbi x) Source #

pattern V_MinPlus :: (Vector x) -> Vector (MinPlus x) Source #

pattern V_MaxPlus :: (Vector x) -> Vector (MaxPlus x) Source #

pattern MV_Viterbi :: (MVector s x) -> MVector s (Viterbi x) Source #

pattern MV_MinPlus :: (MVector s x) -> MVector s (MinPlus x) Source #

pattern MV_MaxPlus :: (MVector s x) -> MVector s (MaxPlus x) Source #

newtype Viterbi x Source #

The Viterbi SemiRing. It maximizes over the product.

Constructors

Viterbi
Fields getViterbi :: x

Instances

Unbox x => Vector Vector (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Viterbi x) -> m (Vector (Viterbi x)) # basicUnsafeThaw :: PrimMonad m => Vector (Viterbi x) -> m (Mutable Vector (PrimState m) (Viterbi x)) # basicLength :: Vector (Viterbi x) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Viterbi x) -> Vector (Viterbi x) # basicUnsafeIndexM :: Monad m => Vector (Viterbi x) -> Int -> m (Viterbi x) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Viterbi x) -> Vector (Viterbi x) -> m () # elemseq :: Vector (Viterbi x) -> Viterbi x -> b -> b #
Unbox x => MVector MVector (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods basicLength :: MVector s (Viterbi x) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Viterbi x) -> MVector s (Viterbi x) # basicOverlaps :: MVector s (Viterbi x) -> MVector s (Viterbi x) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Viterbi x)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Viterbi x -> m (MVector (PrimState m) (Viterbi x)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> Int -> m (Viterbi x) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> Int -> Viterbi x -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> Viterbi x -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> MVector (PrimState m) (Viterbi x) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> MVector (PrimState m) (Viterbi x) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Viterbi x) -> Int -> m (MVector (PrimState m) (Viterbi x)) #
Bounded x => Bounded (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods minBound :: Viterbi x # maxBound :: Viterbi x #
Eq x => Eq (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods (==) :: Viterbi x -> Viterbi x -> Bool # (/=) :: Viterbi x -> Viterbi x -> Bool #
Num x => Num (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods (+) :: Viterbi x -> Viterbi x -> Viterbi x # (-) :: Viterbi x -> Viterbi x -> Viterbi x # (*) :: Viterbi x -> Viterbi x -> Viterbi x # negate :: Viterbi x -> Viterbi x # abs :: Viterbi x -> Viterbi x # signum :: Viterbi x -> Viterbi x # fromInteger :: Integer -> Viterbi x #
Ord x => Ord (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods compare :: Viterbi x -> Viterbi x -> Ordering # (<) :: Viterbi x -> Viterbi x -> Bool # (<=) :: Viterbi x -> Viterbi x -> Bool # (>) :: Viterbi x -> Viterbi x -> Bool # (>=) :: Viterbi x -> Viterbi x -> Bool # max :: Viterbi x -> Viterbi x -> Viterbi x # min :: Viterbi x -> Viterbi x -> Viterbi x #
Read x => Read (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods readsPrec :: Int -> ReadS (Viterbi x) # readList :: ReadS [Viterbi x] # readPrec :: ReadPrec (Viterbi x) # readListPrec :: ReadPrec [Viterbi x] #
Show x => Show (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods showsPrec :: Int -> Viterbi x -> ShowS # show :: Viterbi x -> String # showList :: [Viterbi x] -> ShowS #
Generic (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Associated Types type Rep (Viterbi x) :: Type -> Type # Methods from :: Viterbi x -> Rep (Viterbi x) x0 # to :: Rep (Viterbi x) x0 -> Viterbi x #
NFData x => NFData (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods rnf :: Viterbi x -> () #
Unbox x => Unbox (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring
(Ord x, Semiring x) => Semiring (Viterbi x) Source #	TODO Shall we have generic instances, or specific ones like `SemiRing (Viterbi Prob)`? TODO Consider either a constraint `ProbLike x` or the above.
Instance details Defined in Algebra.Structure.Semiring Methods plus :: Viterbi x -> Viterbi x -> Viterbi x # zero :: Viterbi x # times :: Viterbi x -> Viterbi x -> Viterbi x # one :: Viterbi x #
Generic1 Viterbi Source #
Instance details Defined in Algebra.Structure.Semiring Associated Types type Rep1 Viterbi :: k -> Type # Methods from1 :: Viterbi a -> Rep1 Viterbi a # to1 :: Rep1 Viterbi a -> Viterbi a #
newtype MVector s (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring newtype MVector s (Viterbi x) = MV_Viterbi (MVector s x)
type Rep (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring type Rep (Viterbi x) = D1 (MetaData "Viterbi" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.0.0-8v1Wd4dQxf86ztFKnvLSrc" True) (C1 (MetaCons "Viterbi" PrefixI True) (S1 (MetaSel (Just "getViterbi") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))
newtype Vector (Viterbi x) Source #
Instance details Defined in Algebra.Structure.Semiring newtype Vector (Viterbi x) = V_Viterbi (Vector x)
type Rep1 Viterbi Source #
Instance details Defined in Algebra.Structure.Semiring type Rep1 Viterbi = D1 (MetaData "Viterbi" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.0.0-8v1Wd4dQxf86ztFKnvLSrc" True) (C1 (MetaCons "Viterbi" PrefixI True) (S1 (MetaSel (Just "getViterbi") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

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

Unicode variant of srplus.

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

Unicode variant of srmul.

newtype MinPlus x Source #

The tropical MinPlus SemiRing. It minimizes over the sum.

Constructors

MinPlus
Fields getMinPlus :: x

Instances

Unbox x => Vector Vector (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (MinPlus x) -> m (Vector (MinPlus x)) # basicUnsafeThaw :: PrimMonad m => Vector (MinPlus x) -> m (Mutable Vector (PrimState m) (MinPlus x)) # basicLength :: Vector (MinPlus x) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (MinPlus x) -> Vector (MinPlus x) # basicUnsafeIndexM :: Monad m => Vector (MinPlus x) -> Int -> m (MinPlus x) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (MinPlus x) -> Vector (MinPlus x) -> m () # elemseq :: Vector (MinPlus x) -> MinPlus x -> b -> b #
Unbox x => MVector MVector (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods basicLength :: MVector s (MinPlus x) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (MinPlus x) -> MVector s (MinPlus x) # basicOverlaps :: MVector s (MinPlus x) -> MVector s (MinPlus x) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (MinPlus x)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> MinPlus x -> m (MVector (PrimState m) (MinPlus x)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> Int -> m (MinPlus x) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> Int -> MinPlus x -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> MinPlus x -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> MVector (PrimState m) (MinPlus x) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> MVector (PrimState m) (MinPlus x) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (MinPlus x) -> Int -> m (MVector (PrimState m) (MinPlus x)) #
Bounded x => Bounded (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods minBound :: MinPlus x # maxBound :: MinPlus x #
Eq x => Eq (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods (==) :: MinPlus x -> MinPlus x -> Bool # (/=) :: MinPlus x -> MinPlus x -> Bool #
Num x => Num (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods (+) :: MinPlus x -> MinPlus x -> MinPlus x # (-) :: MinPlus x -> MinPlus x -> MinPlus x # (*) :: MinPlus x -> MinPlus x -> MinPlus x # negate :: MinPlus x -> MinPlus x # abs :: MinPlus x -> MinPlus x # signum :: MinPlus x -> MinPlus x # fromInteger :: Integer -> MinPlus x #
Ord x => Ord (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods compare :: MinPlus x -> MinPlus x -> Ordering # (<) :: MinPlus x -> MinPlus x -> Bool # (<=) :: MinPlus x -> MinPlus x -> Bool # (>) :: MinPlus x -> MinPlus x -> Bool # (>=) :: MinPlus x -> MinPlus x -> Bool # max :: MinPlus x -> MinPlus x -> MinPlus x # min :: MinPlus x -> MinPlus x -> MinPlus x #
Read x => Read (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods readsPrec :: Int -> ReadS (MinPlus x) # readList :: ReadS [MinPlus x] # readPrec :: ReadPrec (MinPlus x) # readListPrec :: ReadPrec [MinPlus x] #
Show x => Show (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods showsPrec :: Int -> MinPlus x -> ShowS # show :: MinPlus x -> String # showList :: [MinPlus x] -> ShowS #
Generic (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Associated Types type Rep (MinPlus x) :: Type -> Type # Methods from :: MinPlus x -> Rep (MinPlus x) x0 # to :: Rep (MinPlus x) x0 -> MinPlus x #
NFData x => NFData (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods rnf :: MinPlus x -> () #
Unbox x => Unbox (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring
(Ord x, Semiring x, NumericLimits x) => Semiring (MinPlus x) Source #	Be careful, if the numeric limits are hits, underflows, etc will happen.
Instance details Defined in Algebra.Structure.Semiring Methods plus :: MinPlus x -> MinPlus x -> MinPlus x # zero :: MinPlus x # times :: MinPlus x -> MinPlus x -> MinPlus x # one :: MinPlus x #
NumericLimits x => NumericLimits (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods minFinite :: MinPlus x Source # maxFinite :: MinPlus x Source #
Generic1 MinPlus Source #
Instance details Defined in Algebra.Structure.Semiring Associated Types type Rep1 MinPlus :: k -> Type # Methods from1 :: MinPlus a -> Rep1 MinPlus a # to1 :: Rep1 MinPlus a -> MinPlus a #
newtype MVector s (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring newtype MVector s (MinPlus x) = MV_MinPlus (MVector s x)
type Rep (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring type Rep (MinPlus x) = D1 (MetaData "MinPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.0.0-8v1Wd4dQxf86ztFKnvLSrc" True) (C1 (MetaCons "MinPlus" PrefixI True) (S1 (MetaSel (Just "getMinPlus") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))
newtype Vector (MinPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring newtype Vector (MinPlus x) = V_MinPlus (Vector x)
type Rep1 MinPlus Source #
Instance details Defined in Algebra.Structure.Semiring type Rep1 MinPlus = D1 (MetaData "MinPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.0.0-8v1Wd4dQxf86ztFKnvLSrc" True) (C1 (MetaCons "MinPlus" PrefixI True) (S1 (MetaSel (Just "getMinPlus") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype MaxPlus x Source #

The tropical MaxPlus SemiRing. It maximizes over the sum.

Constructors

MaxPlus
Fields getMaxPlus :: x

Instances

Unbox x => Vector Vector (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (MaxPlus x) -> m (Vector (MaxPlus x)) # basicUnsafeThaw :: PrimMonad m => Vector (MaxPlus x) -> m (Mutable Vector (PrimState m) (MaxPlus x)) # basicLength :: Vector (MaxPlus x) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (MaxPlus x) -> Vector (MaxPlus x) # basicUnsafeIndexM :: Monad m => Vector (MaxPlus x) -> Int -> m (MaxPlus x) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (MaxPlus x) -> Vector (MaxPlus x) -> m () # elemseq :: Vector (MaxPlus x) -> MaxPlus x -> b -> b #
Unbox x => MVector MVector (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods basicLength :: MVector s (MaxPlus x) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (MaxPlus x) -> MVector s (MaxPlus x) # basicOverlaps :: MVector s (MaxPlus x) -> MVector s (MaxPlus x) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (MaxPlus x)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> MaxPlus x -> m (MVector (PrimState m) (MaxPlus x)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> Int -> m (MaxPlus x) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> Int -> MaxPlus x -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> MaxPlus x -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> MVector (PrimState m) (MaxPlus x) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> MVector (PrimState m) (MaxPlus x) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (MaxPlus x) -> Int -> m (MVector (PrimState m) (MaxPlus x)) #
Bounded x => Bounded (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods minBound :: MaxPlus x # maxBound :: MaxPlus x #
Eq x => Eq (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods (==) :: MaxPlus x -> MaxPlus x -> Bool # (/=) :: MaxPlus x -> MaxPlus x -> Bool #
Num x => Num (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods (+) :: MaxPlus x -> MaxPlus x -> MaxPlus x # (-) :: MaxPlus x -> MaxPlus x -> MaxPlus x # (*) :: MaxPlus x -> MaxPlus x -> MaxPlus x # negate :: MaxPlus x -> MaxPlus x # abs :: MaxPlus x -> MaxPlus x # signum :: MaxPlus x -> MaxPlus x # fromInteger :: Integer -> MaxPlus x #
Ord x => Ord (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods compare :: MaxPlus x -> MaxPlus x -> Ordering # (<) :: MaxPlus x -> MaxPlus x -> Bool # (<=) :: MaxPlus x -> MaxPlus x -> Bool # (>) :: MaxPlus x -> MaxPlus x -> Bool # (>=) :: MaxPlus x -> MaxPlus x -> Bool # max :: MaxPlus x -> MaxPlus x -> MaxPlus x # min :: MaxPlus x -> MaxPlus x -> MaxPlus x #
Read x => Read (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods readsPrec :: Int -> ReadS (MaxPlus x) # readList :: ReadS [MaxPlus x] # readPrec :: ReadPrec (MaxPlus x) # readListPrec :: ReadPrec [MaxPlus x] #
Show x => Show (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods showsPrec :: Int -> MaxPlus x -> ShowS # show :: MaxPlus x -> String # showList :: [MaxPlus x] -> ShowS #
Generic (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Associated Types type Rep (MaxPlus x) :: Type -> Type # Methods from :: MaxPlus x -> Rep (MaxPlus x) x0 # to :: Rep (MaxPlus x) x0 -> MaxPlus x #
NFData x => NFData (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods rnf :: MaxPlus x -> () #
Unbox x => Unbox (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring
(Ord x, Semiring x, NumericLimits x) => Semiring (MaxPlus x) Source #	TODO Shall we have generic instances, or specific ones like `SemiRing (Viterbi Prob)`? TODO Consider either a constraint `ProbLike x` or the above.
Instance details Defined in Algebra.Structure.Semiring Methods plus :: MaxPlus x -> MaxPlus x -> MaxPlus x # zero :: MaxPlus x # times :: MaxPlus x -> MaxPlus x -> MaxPlus x # one :: MaxPlus x #
NumericLimits x => NumericLimits (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods minFinite :: MaxPlus x Source # maxFinite :: MaxPlus x Source #
Generic1 MaxPlus Source #
Instance details Defined in Algebra.Structure.Semiring Associated Types type Rep1 MaxPlus :: k -> Type # Methods from1 :: MaxPlus a -> Rep1 MaxPlus a # to1 :: Rep1 MaxPlus a -> MaxPlus a #
newtype MVector s (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring newtype MVector s (MaxPlus x) = MV_MaxPlus (MVector s x)
type Rep (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring type Rep (MaxPlus x) = D1 (MetaData "MaxPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.0.0-8v1Wd4dQxf86ztFKnvLSrc" True) (C1 (MetaCons "MaxPlus" PrefixI True) (S1 (MetaSel (Just "getMaxPlus") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))
newtype Vector (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.Semiring newtype Vector (MaxPlus x) = V_MaxPlus (Vector x)
type Rep1 MaxPlus Source #
Instance details Defined in Algebra.Structure.Semiring type Rep1 MaxPlus = D1 (MetaData "MaxPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.0.0-8v1Wd4dQxf86ztFKnvLSrc" True) (C1 (MetaCons "MaxPlus" PrefixI True) (S1 (MetaSel (Just "getMaxPlus") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype GSemiring (zeroMonoid :: * -> *) (oneMonoid :: * -> *) (x :: *) Source #

The generic semiring, defined over two Semigroup and Monoid constructions.

It can be used like this: zero ∷ GSemiring Min Sum Int == maxBound one ∷ GSemiring Min Sum Int == 0

It is generally useful to still provide explicit instances, since Min requires a Bounded instance.

Constructors

GSemiring
Fields getSemiring :: x

Instances

Eq x => Eq (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods (==) :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> Bool # (/=) :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> Bool #
Ord x => Ord (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods compare :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> Ordering # (<) :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> Bool # (<=) :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> Bool # (>) :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> Bool # (>=) :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> Bool # max :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x # min :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x #
Read x => Read (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods readsPrec :: Int -> ReadS (GSemiring zeroMonoid oneMonoid x) # readList :: ReadS [GSemiring zeroMonoid oneMonoid x] # readPrec :: ReadPrec (GSemiring zeroMonoid oneMonoid x) # readListPrec :: ReadPrec [GSemiring zeroMonoid oneMonoid x] #
Show x => Show (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods showsPrec :: Int -> GSemiring zeroMonoid oneMonoid x -> ShowS # show :: GSemiring zeroMonoid oneMonoid x -> String # showList :: [GSemiring zeroMonoid oneMonoid x] -> ShowS #
Generic (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring Associated Types type Rep (GSemiring zeroMonoid oneMonoid x) :: Type -> Type # Methods from :: GSemiring zeroMonoid oneMonoid x -> Rep (GSemiring zeroMonoid oneMonoid x) x0 # to :: Rep (GSemiring zeroMonoid oneMonoid x) x0 -> GSemiring zeroMonoid oneMonoid x #
(Semigroup (zeroMonoid x), Monoid (zeroMonoid x), Semigroup (oneMonoid x), Monoid (oneMonoid x), Coercible (zeroMonoid x) (GSemiring zeroMonoid oneMonoid x), Coercible (oneMonoid x) (GSemiring zeroMonoid oneMonoid x)) => Semiring (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods plus :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x # zero :: GSemiring zeroMonoid oneMonoid x # times :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x # one :: GSemiring zeroMonoid oneMonoid x #
type Rep (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring type Rep (GSemiring zeroMonoid oneMonoid x) = D1 (MetaData "GSemiring" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.0.0-8v1Wd4dQxf86ztFKnvLSrc" True) (C1 (MetaCons "GSemiring" PrefixI True) (S1 (MetaSel (Just "getSemiring") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))

class Semiring a where #

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, '(Prelude.+)', 0) and the multiplicative monoid is (R, '(Prelude.*)', 1).

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

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

Methods

plus infixl 6 #

Arguments

:: a
-> a
-> a	Commutative Operation

zero #

Arguments

:: a	Commutative Unit

times infixl 7 #

Arguments

:: a
-> a
-> a	Associative Operation

one #

Arguments

:: a	Associative Unit

Instances

Semiring Bool
Instance details Defined in Data.Semiring Methods plus :: Bool -> Bool -> Bool # zero :: Bool # times :: Bool -> Bool -> Bool # one :: Bool #
Semiring Double
Instance details Defined in Data.Semiring Methods plus :: Double -> Double -> Double # zero :: Double # times :: Double -> Double -> Double # one :: Double #
Semiring Float
Instance details Defined in Data.Semiring Methods plus :: Float -> Float -> Float # zero :: Float # times :: Float -> Float -> Float # one :: Float #
Semiring Int
Instance details Defined in Data.Semiring Methods plus :: Int -> Int -> Int # zero :: Int # times :: Int -> Int -> Int # one :: Int #
Semiring Int8
Instance details Defined in Data.Semiring Methods plus :: Int8 -> Int8 -> Int8 # zero :: Int8 # times :: Int8 -> Int8 -> Int8 # one :: Int8 #
Semiring Int16
Instance details Defined in Data.Semiring Methods plus :: Int16 -> Int16 -> Int16 # zero :: Int16 # times :: Int16 -> Int16 -> Int16 # one :: Int16 #
Semiring Int32
Instance details Defined in Data.Semiring Methods plus :: Int32 -> Int32 -> Int32 # zero :: Int32 # times :: Int32 -> Int32 -> Int32 # one :: Int32 #
Semiring Int64
Instance details Defined in Data.Semiring Methods plus :: Int64 -> Int64 -> Int64 # zero :: Int64 # times :: Int64 -> Int64 -> Int64 # one :: Int64 #
Semiring Integer
Instance details Defined in Data.Semiring Methods plus :: Integer -> Integer -> Integer # zero :: Integer # times :: Integer -> Integer -> Integer # one :: Integer #
Semiring Natural
Instance details Defined in Data.Semiring Methods plus :: Natural -> Natural -> Natural # zero :: Natural # times :: Natural -> Natural -> Natural # one :: Natural #
Semiring Word
Instance details Defined in Data.Semiring Methods plus :: Word -> Word -> Word # zero :: Word # times :: Word -> Word -> Word # one :: Word #
Semiring Word8
Instance details Defined in Data.Semiring Methods plus :: Word8 -> Word8 -> Word8 # zero :: Word8 # times :: Word8 -> Word8 -> Word8 # one :: Word8 #
Semiring Word16
Instance details Defined in Data.Semiring Methods plus :: Word16 -> Word16 -> Word16 # zero :: Word16 # times :: Word16 -> Word16 -> Word16 # one :: Word16 #
Semiring Word32
Instance details Defined in Data.Semiring Methods plus :: Word32 -> Word32 -> Word32 # zero :: Word32 # times :: Word32 -> Word32 -> Word32 # one :: Word32 #
Semiring Word64
Instance details Defined in Data.Semiring Methods plus :: Word64 -> Word64 -> Word64 # zero :: Word64 # times :: Word64 -> Word64 -> Word64 # one :: Word64 #
Semiring ()
Instance details Defined in Data.Semiring Methods plus :: () -> () -> () # zero :: () # times :: () -> () -> () # one :: () #
Semiring CDev
Instance details Defined in Data.Semiring Methods plus :: CDev -> CDev -> CDev # zero :: CDev # times :: CDev -> CDev -> CDev # one :: CDev #
Semiring CIno
Instance details Defined in Data.Semiring Methods plus :: CIno -> CIno -> CIno # zero :: CIno # times :: CIno -> CIno -> CIno # one :: CIno #
Semiring CMode
Instance details Defined in Data.Semiring Methods plus :: CMode -> CMode -> CMode # zero :: CMode # times :: CMode -> CMode -> CMode # one :: CMode #
Semiring COff
Instance details Defined in Data.Semiring Methods plus :: COff -> COff -> COff # zero :: COff # times :: COff -> COff -> COff # one :: COff #
Semiring CPid
Instance details Defined in Data.Semiring Methods plus :: CPid -> CPid -> CPid # zero :: CPid # times :: CPid -> CPid -> CPid # one :: CPid #
Semiring CSsize
Instance details Defined in Data.Semiring Methods plus :: CSsize -> CSsize -> CSsize # zero :: CSsize # times :: CSsize -> CSsize -> CSsize # one :: CSsize #
Semiring CGid
Instance details Defined in Data.Semiring Methods plus :: CGid -> CGid -> CGid # zero :: CGid # times :: CGid -> CGid -> CGid # one :: CGid #
Semiring CNlink
Instance details Defined in Data.Semiring Methods plus :: CNlink -> CNlink -> CNlink # zero :: CNlink # times :: CNlink -> CNlink -> CNlink # one :: CNlink #
Semiring CUid
Instance details Defined in Data.Semiring Methods plus :: CUid -> CUid -> CUid # zero :: CUid # times :: CUid -> CUid -> CUid # one :: CUid #
Semiring CCc
Instance details Defined in Data.Semiring Methods plus :: CCc -> CCc -> CCc # zero :: CCc # times :: CCc -> CCc -> CCc # one :: CCc #
Semiring CSpeed
Instance details Defined in Data.Semiring Methods plus :: CSpeed -> CSpeed -> CSpeed # zero :: CSpeed # times :: CSpeed -> CSpeed -> CSpeed # one :: CSpeed #
Semiring CTcflag
Instance details Defined in Data.Semiring Methods plus :: CTcflag -> CTcflag -> CTcflag # zero :: CTcflag # times :: CTcflag -> CTcflag -> CTcflag # one :: CTcflag #
Semiring CRLim
Instance details Defined in Data.Semiring Methods plus :: CRLim -> CRLim -> CRLim # zero :: CRLim # times :: CRLim -> CRLim -> CRLim # one :: CRLim #
Semiring Fd
Instance details Defined in Data.Semiring Methods plus :: Fd -> Fd -> Fd # zero :: Fd # times :: Fd -> Fd -> Fd # one :: Fd #
Semiring CChar
Instance details Defined in Data.Semiring Methods plus :: CChar -> CChar -> CChar # zero :: CChar # times :: CChar -> CChar -> CChar # one :: CChar #
Semiring CSChar
Instance details Defined in Data.Semiring Methods plus :: CSChar -> CSChar -> CSChar # zero :: CSChar # times :: CSChar -> CSChar -> CSChar # one :: CSChar #
Semiring CUChar
Instance details Defined in Data.Semiring Methods plus :: CUChar -> CUChar -> CUChar # zero :: CUChar # times :: CUChar -> CUChar -> CUChar # one :: CUChar #
Semiring CShort
Instance details Defined in Data.Semiring Methods plus :: CShort -> CShort -> CShort # zero :: CShort # times :: CShort -> CShort -> CShort # one :: CShort #
Semiring CUShort
Instance details Defined in Data.Semiring Methods plus :: CUShort -> CUShort -> CUShort # zero :: CUShort # times :: CUShort -> CUShort -> CUShort # one :: CUShort #
Semiring CInt
Instance details Defined in Data.Semiring Methods plus :: CInt -> CInt -> CInt # zero :: CInt # times :: CInt -> CInt -> CInt # one :: CInt #
Semiring CUInt
Instance details Defined in Data.Semiring Methods plus :: CUInt -> CUInt -> CUInt # zero :: CUInt # times :: CUInt -> CUInt -> CUInt # one :: CUInt #
Semiring CLong
Instance details Defined in Data.Semiring Methods plus :: CLong -> CLong -> CLong # zero :: CLong # times :: CLong -> CLong -> CLong # one :: CLong #
Semiring CULong
Instance details Defined in Data.Semiring Methods plus :: CULong -> CULong -> CULong # zero :: CULong # times :: CULong -> CULong -> CULong # one :: CULong #
Semiring CLLong
Instance details Defined in Data.Semiring Methods plus :: CLLong -> CLLong -> CLLong # zero :: CLLong # times :: CLLong -> CLLong -> CLLong # one :: CLLong #
Semiring CULLong
Instance details Defined in Data.Semiring Methods plus :: CULLong -> CULLong -> CULLong # zero :: CULLong # times :: CULLong -> CULLong -> CULLong # one :: CULLong #
Semiring CFloat
Instance details Defined in Data.Semiring Methods plus :: CFloat -> CFloat -> CFloat # zero :: CFloat # times :: CFloat -> CFloat -> CFloat # one :: CFloat #
Semiring CDouble
Instance details Defined in Data.Semiring Methods plus :: CDouble -> CDouble -> CDouble # zero :: CDouble # times :: CDouble -> CDouble -> CDouble # one :: CDouble #
Semiring CPtrdiff
Instance details Defined in Data.Semiring Methods plus :: CPtrdiff -> CPtrdiff -> CPtrdiff # zero :: CPtrdiff # times :: CPtrdiff -> CPtrdiff -> CPtrdiff # one :: CPtrdiff #
Semiring CSize
Instance details Defined in Data.Semiring Methods plus :: CSize -> CSize -> CSize # zero :: CSize # times :: CSize -> CSize -> CSize # one :: CSize #
Semiring CWchar
Instance details Defined in Data.Semiring Methods plus :: CWchar -> CWchar -> CWchar # zero :: CWchar # times :: CWchar -> CWchar -> CWchar # one :: CWchar #
Semiring CSigAtomic
Instance details Defined in Data.Semiring Methods plus :: CSigAtomic -> CSigAtomic -> CSigAtomic # zero :: CSigAtomic # times :: CSigAtomic -> CSigAtomic -> CSigAtomic # one :: CSigAtomic #
Semiring CClock
Instance details Defined in Data.Semiring Methods plus :: CClock -> CClock -> CClock # zero :: CClock # times :: CClock -> CClock -> CClock # one :: CClock #
Semiring CTime
Instance details Defined in Data.Semiring Methods plus :: CTime -> CTime -> CTime # zero :: CTime # times :: CTime -> CTime -> CTime # one :: CTime #
Semiring CUSeconds
Instance details Defined in Data.Semiring Methods plus :: CUSeconds -> CUSeconds -> CUSeconds # zero :: CUSeconds # times :: CUSeconds -> CUSeconds -> CUSeconds # one :: CUSeconds #
Semiring CSUSeconds
Instance details Defined in Data.Semiring Methods plus :: CSUSeconds -> CSUSeconds -> CSUSeconds # zero :: CSUSeconds # times :: CSUSeconds -> CSUSeconds -> CSUSeconds # one :: CSUSeconds #
Semiring CIntPtr
Instance details Defined in Data.Semiring Methods plus :: CIntPtr -> CIntPtr -> CIntPtr # zero :: CIntPtr # times :: CIntPtr -> CIntPtr -> CIntPtr # one :: CIntPtr #
Semiring CUIntPtr
Instance details Defined in Data.Semiring Methods plus :: CUIntPtr -> CUIntPtr -> CUIntPtr # zero :: CUIntPtr # times :: CUIntPtr -> CUIntPtr -> CUIntPtr # one :: CUIntPtr #
Semiring CIntMax
Instance details Defined in Data.Semiring Methods plus :: CIntMax -> CIntMax -> CIntMax # zero :: CIntMax # times :: CIntMax -> CIntMax -> CIntMax # one :: CIntMax #
Semiring CUIntMax
Instance details Defined in Data.Semiring Methods plus :: CUIntMax -> CUIntMax -> CUIntMax # zero :: CUIntMax # times :: CUIntMax -> CUIntMax -> CUIntMax # one :: CUIntMax #
Semiring WordPtr
Instance details Defined in Data.Semiring Methods plus :: WordPtr -> WordPtr -> WordPtr # zero :: WordPtr # times :: WordPtr -> WordPtr -> WordPtr # one :: WordPtr #
Semiring IntPtr
Instance details Defined in Data.Semiring Methods plus :: IntPtr -> IntPtr -> IntPtr # zero :: IntPtr # times :: IntPtr -> IntPtr -> IntPtr # one :: IntPtr #
Semiring Odds Source #
Instance details Defined in Statistics.Odds Methods plus :: Odds -> Odds -> Odds # zero :: Odds # times :: Odds -> Odds -> Odds # one :: Odds #
Semiring a => Semiring [a]	The `Semiring` instance for '[a]' can be interpreted as treating each element of the list as coefficients to a polynomial in one variable. Examples Expand `poly1 = [1,2,3] :: [Int]` `poly2 = [ 2,1] :: [Int]` `poly1 * poly2 = [2,5,8,3]` fromList [2,5,8,3]
Instance details Defined in Data.Semiring Methods plus :: [a] -> [a] -> [a] # zero :: [a] # times :: [a] -> [a] -> [a] # one :: [a] #
Semiring a => Semiring (Maybe a)
Instance details Defined in Data.Semiring Methods plus :: Maybe a -> Maybe a -> Maybe a # zero :: Maybe a # times :: Maybe a -> Maybe a -> Maybe a # one :: Maybe a #
Integral a => Semiring (Ratio a)
Instance details Defined in Data.Semiring Methods plus :: Ratio a -> Ratio a -> Ratio a # zero :: Ratio a # times :: Ratio a -> Ratio a -> Ratio a # one :: Ratio a #
Semiring a => Semiring (IO a)
Instance details Defined in Data.Semiring Methods plus :: IO a -> IO a -> IO a # zero :: IO a # times :: IO a -> IO a -> IO a # one :: IO a #
Ring a => Semiring (Complex a)	This instance can suffer due to floating point arithmetic.
Instance details Defined in Data.Semiring Methods plus :: Complex a -> Complex a -> Complex a # zero :: Complex a # times :: Complex a -> Complex a -> Complex a # one :: Complex a #
HasResolution a => Semiring (Fixed a)
Instance details Defined in Data.Semiring Methods plus :: Fixed a -> Fixed a -> Fixed a # zero :: Fixed a # times :: Fixed a -> Fixed a -> Fixed a # one :: Fixed a #
Semiring (Predicate a)
Instance details Defined in Data.Semiring Methods plus :: Predicate a -> Predicate a -> Predicate a # zero :: Predicate a # times :: Predicate a -> Predicate a -> Predicate a # one :: Predicate a #
Semiring a => Semiring (Equivalence a)
Instance details Defined in Data.Semiring Methods plus :: Equivalence a -> Equivalence a -> Equivalence a # zero :: Equivalence a # times :: Equivalence a -> Equivalence a -> Equivalence a # one :: Equivalence a #
Semiring a => Semiring (Identity a)
Instance details Defined in Data.Semiring Methods plus :: Identity a -> Identity a -> Identity a # zero :: Identity a # times :: Identity a -> Identity a -> Identity a # one :: Identity a #
Semiring a => Semiring (Dual a)
Instance details Defined in Data.Semiring Methods plus :: Dual a -> Dual a -> Dual a # zero :: Dual a # times :: Dual a -> Dual a -> Dual a # one :: Dual a #
Semiring a => Semiring (Down a)
Instance details Defined in Data.Semiring Methods plus :: Down a -> Down a -> Down a # zero :: Down a # times :: Down a -> Down a -> Down a # one :: Down a #
(Ord a, Monoid a) => Semiring (Set a)	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 # zero :: Set a # times :: Set a -> Set a -> Set a # one :: Set a #
(Storable a, Semiring a) => Semiring (Vector a)
Instance details Defined in Data.Semiring Methods plus :: Vector a -> Vector a -> Vector a # zero :: Vector a # times :: Vector a -> Vector a -> Vector a # one :: Vector a #
(Unbox a, Semiring a) => Semiring (Vector a)
Instance details Defined in Data.Semiring Methods plus :: Vector a -> Vector a -> Vector a # zero :: Vector a # times :: Vector a -> Vector a -> Vector a # one :: Vector a #
(Eq a, Hashable a, Monoid a) => Semiring (HashSet a)	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 # zero :: HashSet a # times :: HashSet a -> HashSet a -> HashSet a # one :: HashSet a #
Semiring a => Semiring (Vector a)	The `Semiring` instance for 'Vector a' can be interpreted as treating each element of the list as coefficients to a polynomial in one variable. Examples Expand `poly1 = Vector.fromList [1,2,3 :: Int]` `poly2 = Vector.fromList [ 2,1 :: Int]` `poly1 * poly2` fromList [2,5,8,3]
Instance details Defined in Data.Semiring Methods plus :: Vector a -> Vector a -> Vector a # zero :: Vector a # times :: Vector a -> Vector a -> Vector a # one :: Vector a #
(Precise a, RealFloat a) => Semiring (Log a) Source #
Instance details Defined in Algebra.Structure.Semiring Methods plus :: Log a -> Log a -> Log a # zero :: Log a # times :: Log a -> Log a -> Log a # one :: Log a #
Num a => Semiring (WrappedNum a)
Instance details Defined in Data.Semiring Methods plus :: WrappedNum a -> WrappedNum a -> WrappedNum a # zero :: WrappedNum a # times :: WrappedNum a -> WrappedNum a -> WrappedNum a # one :: WrappedNum a #
(Coercible Int a, Monoid a) => Semiring (IntSetOf a)
Instance details Defined in Data.Semiring Methods plus :: IntSetOf a -> IntSetOf a -> IntSetOf a # zero :: IntSetOf a # times :: IntSetOf a -> IntSetOf a -> IntSetOf a # one :: IntSetOf a #
(Ord x, Semiring x) => Semiring (Viterbi x) Source #	TODO Shall we have generic instances, or specific ones like `SemiRing (Viterbi Prob)`? TODO Consider either a constraint `ProbLike x` or the above.
Instance details Defined in Algebra.Structure.Semiring Methods plus :: Viterbi x -> Viterbi x -> Viterbi x # zero :: Viterbi x # times :: Viterbi x -> Viterbi x -> Viterbi x # one :: Viterbi x #
(Ord x, Semiring x, NumericLimits x) => Semiring (MinPlus x) Source #	Be careful, if the numeric limits are hits, underflows, etc will happen.
Instance details Defined in Algebra.Structure.Semiring Methods plus :: MinPlus x -> MinPlus x -> MinPlus x # zero :: MinPlus x # times :: MinPlus x -> MinPlus x -> MinPlus x # one :: MinPlus x #
(Ord x, Semiring x, NumericLimits x) => Semiring (MaxPlus x) Source #	TODO Shall we have generic instances, or specific ones like `SemiRing (Viterbi Prob)`? TODO Consider either a constraint `ProbLike x` or the above.
Instance details Defined in Algebra.Structure.Semiring Methods plus :: MaxPlus x -> MaxPlus x -> MaxPlus x # zero :: MaxPlus x # times :: MaxPlus x -> MaxPlus x -> MaxPlus x # one :: MaxPlus x #
Semiring b => Semiring (a -> b)
Instance details Defined in Data.Semiring Methods plus :: (a -> b) -> (a -> b) -> a -> b # zero :: a -> b # times :: (a -> b) -> (a -> b) -> a -> b # one :: a -> b #
Semiring a => Semiring (Op a b)
Instance details Defined in Data.Semiring Methods plus :: Op a b -> Op a b -> Op a b # zero :: Op a b # times :: Op a b -> Op a b -> Op a b # one :: Op a b #
(Eq k, Hashable k, Monoid k, Semiring v) => Semiring (HashMap k v)	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 # zero :: HashMap k v # times :: HashMap k v -> HashMap k v -> HashMap k v # one :: HashMap k v #
(Ord k, Monoid k, Semiring v) => Semiring (Map k v)	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 # zero :: Map k v # times :: Map k v -> Map k v -> Map k v # one :: Map k v #
Semiring (Proxy a)
Instance details Defined in Data.Semiring Methods plus :: Proxy a -> Proxy a -> Proxy a # zero :: Proxy a # times :: Proxy a -> Proxy a -> Proxy a # one :: Proxy a #
(Coercible Int k, Monoid k, Semiring v) => Semiring (IntMapOf k v)
Instance details Defined in Data.Semiring Methods plus :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v # zero :: IntMapOf k v # times :: IntMapOf k v -> IntMapOf k v -> IntMapOf k v # one :: IntMapOf k v #
Num (Discretized k2) => Semiring (Discretized k2) Source #
Instance details Defined in Numeric.Discretized Methods plus :: Discretized k2 -> Discretized k2 -> Discretized k2 # zero :: Discretized k2 # times :: Discretized k2 -> Discretized k2 -> Discretized k2 # one :: Discretized k2 #
Semiring (Discretized t) => Semiring (DiscLogOdds t) Source #
Instance details Defined in Statistics.Odds Methods plus :: DiscLogOdds t -> DiscLogOdds t -> DiscLogOdds t # zero :: DiscLogOdds t # times :: DiscLogOdds t -> DiscLogOdds t -> DiscLogOdds t # one :: DiscLogOdds t #
Num r => Semiring (Probability n r) Source #
Instance details Defined in Statistics.Probability Methods plus :: Probability n r -> Probability n r -> Probability n r # zero :: Probability n r # times :: Probability n r -> Probability n r -> Probability n r # one :: Probability n r #
Semiring a => Semiring (Const a b)
Instance details Defined in Data.Semiring Methods plus :: Const a b -> Const a b -> Const a b # zero :: Const a b # times :: Const a b -> Const a b -> Const a b # one :: Const a b #
(Semiring a, Applicative f) => Semiring (Ap f a)
Instance details Defined in Data.Semiring Methods plus :: Ap f a -> Ap f a -> Ap f a # zero :: Ap f a # times :: Ap f a -> Ap f a -> Ap f a # one :: Ap f a #
(Semigroup (zeroMonoid x), Monoid (zeroMonoid x), Semigroup (oneMonoid x), Monoid (oneMonoid x), Coercible (zeroMonoid x) (GSemiring zeroMonoid oneMonoid x), Coercible (oneMonoid x) (GSemiring zeroMonoid oneMonoid x)) => Semiring (GSemiring zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.Semiring Methods plus :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x # zero :: GSemiring zeroMonoid oneMonoid x # times :: GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x -> GSemiring zeroMonoid oneMonoid x # one :: GSemiring zeroMonoid oneMonoid x #

Orphan instances

(Precise a, RealFloat a) => Semiring (Log a) Source #
Instance details Methods plus :: Log a -> Log a -> Log a # zero :: Log a # times :: Log a -> Log a -> Log a # one :: Log a #

Documentation

Examples

Examples

Orphan instances