Safe Haskell	None
Language	Haskell2010

Algebra.Structure.SemiRing

Contents

The SemiRing type class.
Newtype wrappers for SemiRing that make the semiring to use explicit.
Generic semiring structure encoding.
- Variants of Semigroup structures, that use NumericLimits instead of

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

class SemiRing a where
- srplus :: a -> a -> a
- srmul :: a -> a -> a
- srzero :: a
- srone :: a
(⊕) :: SemiRing a => a -> a -> a
(⊗) :: SemiRing a => a -> a -> a
newtype Viterbi x = Viterbi {
- getViterbi :: x
}
newtype MinPlus x = MinPlus {
- getMinPlus :: x
}
newtype MaxPlus x = MaxPlus {
- getMaxPlus :: x
}
newtype GSemiRing (zeroMonoid :: * -> *) (oneMonoid :: * -> *) (x :: *) = GSemiRing {
- getSemiRing :: x
}

The `SemiRing` type class.

class SemiRing a where Source #

The semiring operations and neutral elements.

Methods

srplus :: a -> a -> a infixl 6 Source #

srmul :: a -> a -> a infixl 7 Source #

srzero :: a Source #

srone :: a Source #

Instances

(Ord x, Num 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 srplus :: Viterbi x -> Viterbi x -> Viterbi x Source # srmul :: Viterbi x -> Viterbi x -> Viterbi x Source # srzero :: Viterbi x Source # srone :: Viterbi x Source #
(Ord x, Num x, NumericLimits x) => SemiRing (MinPlus 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 srplus :: MinPlus x -> MinPlus x -> MinPlus x Source # srmul :: MinPlus x -> MinPlus x -> MinPlus x Source # srzero :: MinPlus x Source # srone :: MinPlus x Source #
(Ord x, Num 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 srplus :: MaxPlus x -> MaxPlus x -> MaxPlus x Source # srmul :: MaxPlus x -> MaxPlus x -> MaxPlus x Source # srzero :: MaxPlus x Source # srone :: MaxPlus x Source #
Num r => SemiRing (Prob n r) Source #
Instance details Defined in Statistics.Probability Methods srplus :: Prob n r -> Prob n r -> Prob n r Source # srmul :: Prob n r -> Prob n r -> Prob n r Source # srzero :: Prob n r Source # srone :: Prob n r Source #
(Semigroup (zeroMonoid x), Monoid (zeroMonoid x), Semigroup (oneMonoid x), Monoid (oneMonoid x)) => SemiRing (GSemiRing zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.SemiRing Methods srplus :: GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x Source # srmul :: GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x Source # srzero :: GSemiRing zeroMonoid oneMonoid x Source # srone :: GSemiRing zeroMonoid oneMonoid x Source #

(⊕) :: 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 wrappers for `SemiRing` that make the semiring to use explicit.

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, Num 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 srplus :: Viterbi x -> Viterbi x -> Viterbi x Source # srmul :: Viterbi x -> Viterbi x -> Viterbi x Source # srzero :: Viterbi x Source # srone :: Viterbi x Source #
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 #
data MVector s (Viterbi x) Source #
Instance details Defined in Algebra.Structure.SemiRing data 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-0.0.0.1-MnwemAw82XA41vuhv62aH" True) (C1 (MetaCons "Viterbi" PrefixI True) (S1 (MetaSel (Just "getViterbi") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))
data Vector (Viterbi x) Source #
Instance details Defined in Algebra.Structure.SemiRing data 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-0.0.0.1-MnwemAw82XA41vuhv62aH" True) (C1 (MetaCons "Viterbi" PrefixI True) (S1 (MetaSel (Just "getViterbi") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

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, Num x, NumericLimits x) => SemiRing (MinPlus 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 srplus :: MinPlus x -> MinPlus x -> MinPlus x Source # srmul :: MinPlus x -> MinPlus x -> MinPlus x Source # srzero :: MinPlus x Source # srone :: 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 #
data MVector s (MinPlus x) Source #
Instance details Defined in Algebra.Structure.SemiRing data 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-0.0.0.1-MnwemAw82XA41vuhv62aH" True) (C1 (MetaCons "MinPlus" PrefixI True) (S1 (MetaSel (Just "getMinPlus") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))
data Vector (MinPlus x) Source #
Instance details Defined in Algebra.Structure.SemiRing data 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-0.0.0.1-MnwemAw82XA41vuhv62aH" 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
NumericLimits x => NumericLimits (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.SemiRing Methods minFinite :: MaxPlus x Source # maxFinite :: MaxPlus x Source #
(Ord x, Num 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 srplus :: MaxPlus x -> MaxPlus x -> MaxPlus x Source # srmul :: MaxPlus x -> MaxPlus x -> MaxPlus x Source # srzero :: MaxPlus x Source # srone :: 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 #
data MVector s (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.SemiRing data 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-0.0.0.1-MnwemAw82XA41vuhv62aH" True) (C1 (MetaCons "MaxPlus" PrefixI True) (S1 (MetaSel (Just "getMaxPlus") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))
data Vector (MaxPlus x) Source #
Instance details Defined in Algebra.Structure.SemiRing data 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-0.0.0.1-MnwemAw82XA41vuhv62aH" True) (C1 (MetaCons "MaxPlus" PrefixI True) (S1 (MetaSel (Just "getMaxPlus") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Generic semiring structure encoding.

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

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

It can be used like this: srzero ∷ GSemiRing Min Sum Int == maxBound srone ∷ 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)) => SemiRing (GSemiRing zeroMonoid oneMonoid x) Source #
Instance details Defined in Algebra.Structure.SemiRing Methods srplus :: GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x Source # srmul :: GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x -> GSemiRing zeroMonoid oneMonoid x Source # srzero :: GSemiRing zeroMonoid oneMonoid x Source # srone :: GSemiRing zeroMonoid oneMonoid x Source #
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-0.0.0.1-MnwemAw82XA41vuhv62aH" True) (C1 (MetaCons "GSemiRing" PrefixI True) (S1 (MetaSel (Just "getSemiRing") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 x)))

The SemiRing type class.

Newtype wrappers for SemiRing that make the semiring to use explicit.

Generic semiring structure encoding.

Variants of Semigroup structures, that use NumericLimits instead of

The `SemiRing` type class.

Newtype wrappers for `SemiRing` that make the semiring to use explicit.

Variants of `Semigroup` structures, that use `NumericLimits` instead of