Algebra.Structure.Semiring

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.

Documentation

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

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

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

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

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

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

newtype Viterbi x

The Viterbi SemiRing. It maximizes over the product.

Constructors

Viterbi

Fields

• getViterbi :: x

Instances

Unbox x => Vector Vector (Viterbi x)

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)

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)

Defined in Algebra.Structure.Semiring

Methods

minBound :: Viterbi x

maxBound :: Viterbi x

Eq x => Eq (Viterbi x)

Defined in Algebra.Structure.Semiring

Methods

(==) :: Viterbi x -> Viterbi x -> Bool

(/=) :: Viterbi x -> Viterbi x -> Bool

Num x => Num (Viterbi x)

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)

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)

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)

Defined in Algebra.Structure.Semiring

Methods

showsPrec :: Int -> Viterbi x -> ShowS

show :: Viterbi x -> String

showList :: [Viterbi x] -> ShowS

Generic (Viterbi x)

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

ToJSON x => ToJSON (Viterbi x)

Defined in Algebra.Structure.Semiring

Methods

toJSON :: Viterbi x -> Value

toEncoding :: Viterbi x -> Encoding

toJSONList :: [Viterbi x] -> Value

toEncodingList :: [Viterbi x] -> Encoding

FromJSON x => FromJSON (Viterbi x)

Defined in Algebra.Structure.Semiring

Methods

parseJSON :: Value -> Parser (Viterbi x)

parseJSONList :: Value -> Parser [Viterbi x]

NFData x => NFData (Viterbi x)

Defined in Algebra.Structure.Semiring

Methods

rnf :: Viterbi x -> ()

Unbox x => Unbox (Viterbi x)

Defined in Algebra.Structure.Semiring

(Ord x, Semiring x) => Semiring (Viterbi x)

TODO Shall we have generic instances, or specific ones like SemiRing (Viterbi Prob)?

TODO Consider either a constraint ProbLike x or the above.

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

fromNatural :: Natural -> Viterbi x

Generic1 Viterbi

Defined in Algebra.Structure.Semiring

Associated Types

type Rep1 Viterbi :: k -> Type

Methods

from1 :: forall (a :: k). Viterbi a -> Rep1 Viterbi a

to1 :: forall (a :: k). Rep1 Viterbi a -> Viterbi a

newtype MVector s (Viterbi x)

Defined in Algebra.Structure.Semiring

newtype MVector s (Viterbi x) = MV_Viterbi (MVector s x)

type Rep (Viterbi x)

Defined in Algebra.Structure.Semiring

type Rep (Viterbi x) = D1 ('MetaData "Viterbi" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" 'True) (C1 ('MetaCons "Viterbi" 'PrefixI 'True) (S1 ('MetaSel ('Just "getViterbi") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 x)))

newtype Vector (Viterbi x)

Defined in Algebra.Structure.Semiring

newtype Vector (Viterbi x) = V_Viterbi (Vector x)

type Rep1 Viterbi

Defined in Algebra.Structure.Semiring

type Rep1 Viterbi = D1 ('MetaData "Viterbi" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" 'True) (C1 ('MetaCons "Viterbi" 'PrefixI 'True) (S1 ('MetaSel ('Just "getViterbi") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

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

Unicode variant of srplus.

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

Unicode variant of srmul.

nTimes :: Semiring a => Int -> a -> a

times but done n times.

TODO Include into type class to improve performance

newtype MinPlus x

The tropical MinPlus SemiRing. It minimizes over the sum.

Constructors

MinPlus

Fields

• getMinPlus :: x

Instances

Unbox x => Vector Vector (MinPlus x)

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)

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)

Defined in Algebra.Structure.Semiring

Methods

minBound :: MinPlus x

maxBound :: MinPlus x

Eq x => Eq (MinPlus x)

Defined in Algebra.Structure.Semiring

Methods

(==) :: MinPlus x -> MinPlus x -> Bool

(/=) :: MinPlus x -> MinPlus x -> Bool

Num x => Num (MinPlus x)

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)

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)

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)

Defined in Algebra.Structure.Semiring

Methods

showsPrec :: Int -> MinPlus x -> ShowS

show :: MinPlus x -> String

showList :: [MinPlus x] -> ShowS

Generic (MinPlus x)

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

ToJSON x => ToJSON (MinPlus x)

Defined in Algebra.Structure.Semiring

Methods

toJSON :: MinPlus x -> Value

toEncoding :: MinPlus x -> Encoding

toJSONList :: [MinPlus x] -> Value

toEncodingList :: [MinPlus x] -> Encoding

FromJSON x => FromJSON (MinPlus x)

Defined in Algebra.Structure.Semiring

Methods

parseJSON :: Value -> Parser (MinPlus x)

parseJSONList :: Value -> Parser [MinPlus x]

NFData x => NFData (MinPlus x)

Defined in Algebra.Structure.Semiring

Methods

rnf :: MinPlus x -> ()

Unbox x => Unbox (MinPlus x)

Defined in Algebra.Structure.Semiring

(Ord x, Semiring x, NumericLimits x) => Semiring (MinPlus x)

Be careful, if the numeric limits are hits, underflows, etc will happen.

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

fromNatural :: Natural -> MinPlus x

NumericLimits x => NumericLimits (MinPlus x)

Defined in Algebra.Structure.Semiring

Methods

minFinite :: MinPlus x

maxFinite :: MinPlus x

Generic1 MinPlus

Defined in Algebra.Structure.Semiring

Associated Types

type Rep1 MinPlus :: k -> Type

Methods

from1 :: forall (a :: k). MinPlus a -> Rep1 MinPlus a

to1 :: forall (a :: k). Rep1 MinPlus a -> MinPlus a

newtype MVector s (MinPlus x)

Defined in Algebra.Structure.Semiring

newtype MVector s (MinPlus x) = MV_MinPlus (MVector s x)

type Rep (MinPlus x)

Defined in Algebra.Structure.Semiring

type Rep (MinPlus x) = D1 ('MetaData "MinPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" 'True) (C1 ('MetaCons "MinPlus" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMinPlus") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 x)))

newtype Vector (MinPlus x)

Defined in Algebra.Structure.Semiring

newtype Vector (MinPlus x) = V_MinPlus (Vector x)

type Rep1 MinPlus

Defined in Algebra.Structure.Semiring

type Rep1 MinPlus = D1 ('MetaData "MinPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" 'True) (C1 ('MetaCons "MinPlus" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMinPlus") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype MaxPlus x

The tropical MaxPlus SemiRing. It maximizes over the sum.

Constructors

MaxPlus

Fields

• getMaxPlus :: x

Instances

Unbox x => Vector Vector (MaxPlus x)

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)

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)

Defined in Algebra.Structure.Semiring

Methods

minBound :: MaxPlus x

maxBound :: MaxPlus x

Eq x => Eq (MaxPlus x)

Defined in Algebra.Structure.Semiring

Methods

(==) :: MaxPlus x -> MaxPlus x -> Bool

(/=) :: MaxPlus x -> MaxPlus x -> Bool

Num x => Num (MaxPlus x)

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)

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)

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)

Defined in Algebra.Structure.Semiring

Methods

showsPrec :: Int -> MaxPlus x -> ShowS

show :: MaxPlus x -> String

showList :: [MaxPlus x] -> ShowS

Generic (MaxPlus x)

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

Info x => Info (MaxPlus x)

Defined in Algebra.Structure.Semiring

Methods

info :: MaxPlus x -> String

ToJSON x => ToJSON (MaxPlus x)

Defined in Algebra.Structure.Semiring

Methods

toJSON :: MaxPlus x -> Value

toEncoding :: MaxPlus x -> Encoding

toJSONList :: [MaxPlus x] -> Value

toEncodingList :: [MaxPlus x] -> Encoding

FromJSON x => FromJSON (MaxPlus x)

Defined in Algebra.Structure.Semiring

Methods

parseJSON :: Value -> Parser (MaxPlus x)

parseJSONList :: Value -> Parser [MaxPlus x]

NFData x => NFData (MaxPlus x)

Defined in Algebra.Structure.Semiring

Methods

rnf :: MaxPlus x -> ()

Unbox x => Unbox (MaxPlus x)

Defined in Algebra.Structure.Semiring

(Ord x, Semiring x, NumericLimits x) => Semiring (MaxPlus x)

TODO Shall we have generic instances, or specific ones like SemiRing (Viterbi Prob)?

TODO Consider either a constraint ProbLike x or the above.

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

fromNatural :: Natural -> MaxPlus x

NumericLimits x => NumericLimits (MaxPlus x)

Defined in Algebra.Structure.Semiring

Methods

minFinite :: MaxPlus x

maxFinite :: MaxPlus x

Generic1 MaxPlus

Defined in Algebra.Structure.Semiring

Associated Types

type Rep1 MaxPlus :: k -> Type

Methods

from1 :: forall (a :: k). MaxPlus a -> Rep1 MaxPlus a

to1 :: forall (a :: k). Rep1 MaxPlus a -> MaxPlus a

newtype MVector s (MaxPlus x)

Defined in Algebra.Structure.Semiring

newtype MVector s (MaxPlus x) = MV_MaxPlus (MVector s x)

type Rep (MaxPlus x)

Defined in Algebra.Structure.Semiring

type Rep (MaxPlus x) = D1 ('MetaData "MaxPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" 'True) (C1 ('MetaCons "MaxPlus" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMaxPlus") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 x)))

newtype Vector (MaxPlus x)

Defined in Algebra.Structure.Semiring

newtype Vector (MaxPlus x) = V_MaxPlus (Vector x)

type Rep1 MaxPlus

Defined in Algebra.Structure.Semiring

type Rep1 MaxPlus = D1 ('MetaData "MaxPlus" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" 'True) (C1 ('MetaCons "MaxPlus" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMaxPlus") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

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

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)

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)

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)

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)

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)

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

ToJSON x => ToJSON (GSemiring z o x)

Defined in Algebra.Structure.Semiring

Methods

toJSON :: GSemiring z o x -> Value

toEncoding :: GSemiring z o x -> Encoding

toJSONList :: [GSemiring z o x] -> Value

toEncodingList :: [GSemiring z o x] -> Encoding

FromJSON x => FromJSON (GSemiring z o x)

Defined in Algebra.Structure.Semiring

Methods

parseJSON :: Value -> Parser (GSemiring z o x)

parseJSONList :: Value -> Parser [GSemiring z o x]

NFData x => NFData (GSemiring zM oM x)

Defined in Algebra.Structure.Semiring

Methods

rnf :: GSemiring zM oM 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)

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

fromNatural :: Natural -> GSemiring zeroMonoid oneMonoid x

type Rep (GSemiring zeroMonoid oneMonoid x)

Defined in Algebra.Structure.Semiring

type Rep (GSemiring zeroMonoid oneMonoid x) = D1 ('MetaData "GSemiring" "Algebra.Structure.Semiring" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" '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, +, 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

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

fromNatural

Arguments

:: Natural

-> a

Homomorphism of additive semigroups

Instances

Semiring Bool

Defined in Data.Semiring

Methods

plus :: Bool -> Bool -> Bool

zero :: Bool

times :: Bool -> Bool -> Bool

one :: Bool

fromNatural :: Natural -> Bool

Semiring Double

Defined in Data.Semiring

Methods

plus :: Double -> Double -> Double

zero :: Double

times :: Double -> Double -> Double

one :: Double

fromNatural :: Natural -> Double

Semiring Float

Defined in Data.Semiring

Methods

plus :: Float -> Float -> Float

zero :: Float

times :: Float -> Float -> Float

one :: Float

fromNatural :: Natural -> Float

Semiring Int

Defined in Data.Semiring

Methods

plus :: Int -> Int -> Int

zero :: Int

times :: Int -> Int -> Int

one :: Int

fromNatural :: Natural -> Int

Semiring Int8

Defined in Data.Semiring

Methods

plus :: Int8 -> Int8 -> Int8

zero :: Int8

times :: Int8 -> Int8 -> Int8

one :: Int8

fromNatural :: Natural -> Int8

Semiring Int16

Defined in Data.Semiring

Methods

plus :: Int16 -> Int16 -> Int16

zero :: Int16

times :: Int16 -> Int16 -> Int16

one :: Int16

fromNatural :: Natural -> Int16

Semiring Int32

Defined in Data.Semiring

Methods

plus :: Int32 -> Int32 -> Int32

zero :: Int32

times :: Int32 -> Int32 -> Int32

one :: Int32

fromNatural :: Natural -> Int32

Semiring Int64

Defined in Data.Semiring

Methods

plus :: Int64 -> Int64 -> Int64

zero :: Int64

times :: Int64 -> Int64 -> Int64

one :: Int64

fromNatural :: Natural -> Int64

Semiring Integer

Defined in Data.Semiring

Methods

plus :: Integer -> Integer -> Integer

zero :: Integer

times :: Integer -> Integer -> Integer

one :: Integer

fromNatural :: Natural -> Integer

Semiring Natural

Defined in Data.Semiring

Methods

plus :: Natural -> Natural -> Natural

zero :: Natural

times :: Natural -> Natural -> Natural

one :: Natural

fromNatural :: Natural -> Natural

Semiring Word

Defined in Data.Semiring

Methods

plus :: Word -> Word -> Word

zero :: Word

times :: Word -> Word -> Word

one :: Word

fromNatural :: Natural -> Word

Semiring Word8

Defined in Data.Semiring

Methods

plus :: Word8 -> Word8 -> Word8

zero :: Word8

times :: Word8 -> Word8 -> Word8

one :: Word8

fromNatural :: Natural -> Word8

Semiring Word16

Defined in Data.Semiring

Methods

plus :: Word16 -> Word16 -> Word16

zero :: Word16

times :: Word16 -> Word16 -> Word16

one :: Word16

fromNatural :: Natural -> Word16

Semiring Word32

Defined in Data.Semiring

Methods

plus :: Word32 -> Word32 -> Word32

zero :: Word32

times :: Word32 -> Word32 -> Word32

one :: Word32

fromNatural :: Natural -> Word32

Semiring Word64

Defined in Data.Semiring

Methods

plus :: Word64 -> Word64 -> Word64

zero :: Word64

times :: Word64 -> Word64 -> Word64

one :: Word64

fromNatural :: Natural -> Word64

Semiring ()

Defined in Data.Semiring

Methods

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

zero :: ()

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

one :: ()

fromNatural :: Natural -> ()

Semiring CDev

Defined in Data.Semiring

Methods

plus :: CDev -> CDev -> CDev

zero :: CDev

times :: CDev -> CDev -> CDev

one :: CDev

fromNatural :: Natural -> CDev

Semiring CIno

Defined in Data.Semiring

Methods

plus :: CIno -> CIno -> CIno

zero :: CIno

times :: CIno -> CIno -> CIno

one :: CIno

fromNatural :: Natural -> CIno

Semiring CMode

Defined in Data.Semiring

Methods

plus :: CMode -> CMode -> CMode

zero :: CMode

times :: CMode -> CMode -> CMode

one :: CMode

fromNatural :: Natural -> CMode

Semiring COff

Defined in Data.Semiring

Methods

plus :: COff -> COff -> COff

zero :: COff

times :: COff -> COff -> COff

one :: COff

fromNatural :: Natural -> COff

Semiring CPid

Defined in Data.Semiring

Methods

plus :: CPid -> CPid -> CPid

zero :: CPid

times :: CPid -> CPid -> CPid

one :: CPid

fromNatural :: Natural -> CPid

Semiring CSsize

Defined in Data.Semiring

Methods

plus :: CSsize -> CSsize -> CSsize

zero :: CSsize

times :: CSsize -> CSsize -> CSsize

one :: CSsize

fromNatural :: Natural -> CSsize

Semiring CGid

Defined in Data.Semiring

Methods

plus :: CGid -> CGid -> CGid

zero :: CGid

times :: CGid -> CGid -> CGid

one :: CGid

fromNatural :: Natural -> CGid

Semiring CNlink

Defined in Data.Semiring

Methods

plus :: CNlink -> CNlink -> CNlink

zero :: CNlink

times :: CNlink -> CNlink -> CNlink

one :: CNlink

fromNatural :: Natural -> CNlink

Semiring CUid

Defined in Data.Semiring

Methods

plus :: CUid -> CUid -> CUid

zero :: CUid

times :: CUid -> CUid -> CUid

one :: CUid

fromNatural :: Natural -> CUid

Semiring CCc

Defined in Data.Semiring

Methods

plus :: CCc -> CCc -> CCc

zero :: CCc

times :: CCc -> CCc -> CCc

one :: CCc

fromNatural :: Natural -> CCc

Semiring CSpeed

Defined in Data.Semiring

Methods

plus :: CSpeed -> CSpeed -> CSpeed

zero :: CSpeed

times :: CSpeed -> CSpeed -> CSpeed

one :: CSpeed

fromNatural :: Natural -> CSpeed

Semiring CTcflag

Defined in Data.Semiring

Methods

plus :: CTcflag -> CTcflag -> CTcflag

zero :: CTcflag

times :: CTcflag -> CTcflag -> CTcflag

one :: CTcflag

fromNatural :: Natural -> CTcflag

Semiring CRLim

Defined in Data.Semiring

Methods

plus :: CRLim -> CRLim -> CRLim

zero :: CRLim

times :: CRLim -> CRLim -> CRLim

one :: CRLim

fromNatural :: Natural -> CRLim

Semiring Fd

Defined in Data.Semiring

Methods

plus :: Fd -> Fd -> Fd

zero :: Fd

times :: Fd -> Fd -> Fd

one :: Fd

fromNatural :: Natural -> Fd

Semiring CChar

Defined in Data.Semiring

Methods

plus :: CChar -> CChar -> CChar

zero :: CChar

times :: CChar -> CChar -> CChar

one :: CChar

fromNatural :: Natural -> CChar

Semiring CSChar

Defined in Data.Semiring

Methods

plus :: CSChar -> CSChar -> CSChar

zero :: CSChar

times :: CSChar -> CSChar -> CSChar

one :: CSChar

fromNatural :: Natural -> CSChar

Semiring CUChar

Defined in Data.Semiring

Methods

plus :: CUChar -> CUChar -> CUChar

zero :: CUChar

times :: CUChar -> CUChar -> CUChar

one :: CUChar

fromNatural :: Natural -> CUChar

Semiring CShort

Defined in Data.Semiring

Methods

plus :: CShort -> CShort -> CShort

zero :: CShort

times :: CShort -> CShort -> CShort

one :: CShort

fromNatural :: Natural -> CShort

Semiring CUShort

Defined in Data.Semiring

Methods

plus :: CUShort -> CUShort -> CUShort

zero :: CUShort

times :: CUShort -> CUShort -> CUShort

one :: CUShort

fromNatural :: Natural -> CUShort

Semiring CInt

Defined in Data.Semiring

Methods

plus :: CInt -> CInt -> CInt

zero :: CInt

times :: CInt -> CInt -> CInt

one :: CInt

fromNatural :: Natural -> CInt

Semiring CUInt

Defined in Data.Semiring

Methods

plus :: CUInt -> CUInt -> CUInt

zero :: CUInt

times :: CUInt -> CUInt -> CUInt

one :: CUInt

fromNatural :: Natural -> CUInt

Semiring CLong

Defined in Data.Semiring

Methods

plus :: CLong -> CLong -> CLong

zero :: CLong

times :: CLong -> CLong -> CLong

one :: CLong

fromNatural :: Natural -> CLong

Semiring CULong

Defined in Data.Semiring

Methods

plus :: CULong -> CULong -> CULong

zero :: CULong

times :: CULong -> CULong -> CULong

one :: CULong

fromNatural :: Natural -> CULong

Semiring CLLong

Defined in Data.Semiring

Methods

plus :: CLLong -> CLLong -> CLLong

zero :: CLLong

times :: CLLong -> CLLong -> CLLong

one :: CLLong

fromNatural :: Natural -> CLLong

Semiring CULLong

Defined in Data.Semiring

Methods

plus :: CULLong -> CULLong -> CULLong

zero :: CULLong

times :: CULLong -> CULLong -> CULLong

one :: CULLong

fromNatural :: Natural -> CULLong

Semiring CFloat

Defined in Data.Semiring

Methods

plus :: CFloat -> CFloat -> CFloat

zero :: CFloat

times :: CFloat -> CFloat -> CFloat

one :: CFloat

fromNatural :: Natural -> CFloat

Semiring CDouble

Defined in Data.Semiring

Methods

plus :: CDouble -> CDouble -> CDouble

zero :: CDouble

times :: CDouble -> CDouble -> CDouble

one :: CDouble

fromNatural :: Natural -> CDouble

Semiring CPtrdiff

Defined in Data.Semiring

Methods

plus :: CPtrdiff -> CPtrdiff -> CPtrdiff

zero :: CPtrdiff

times :: CPtrdiff -> CPtrdiff -> CPtrdiff

one :: CPtrdiff

fromNatural :: Natural -> CPtrdiff

Semiring CSize

Defined in Data.Semiring

Methods

plus :: CSize -> CSize -> CSize

zero :: CSize

times :: CSize -> CSize -> CSize

one :: CSize

fromNatural :: Natural -> CSize

Semiring CWchar

Defined in Data.Semiring

Methods

plus :: CWchar -> CWchar -> CWchar

zero :: CWchar

times :: CWchar -> CWchar -> CWchar

one :: CWchar

fromNatural :: Natural -> CWchar

Semiring CSigAtomic

Defined in Data.Semiring

Methods

plus :: CSigAtomic -> CSigAtomic -> CSigAtomic

zero :: CSigAtomic

times :: CSigAtomic -> CSigAtomic -> CSigAtomic

one :: CSigAtomic

fromNatural :: Natural -> CSigAtomic

Semiring CClock

Defined in Data.Semiring

Methods

plus :: CClock -> CClock -> CClock

zero :: CClock

times :: CClock -> CClock -> CClock

one :: CClock

fromNatural :: Natural -> CClock

Semiring CTime

Defined in Data.Semiring

Methods

plus :: CTime -> CTime -> CTime

zero :: CTime

times :: CTime -> CTime -> CTime

one :: CTime

fromNatural :: Natural -> CTime

Semiring CUSeconds

Defined in Data.Semiring

Methods

plus :: CUSeconds -> CUSeconds -> CUSeconds

zero :: CUSeconds

times :: CUSeconds -> CUSeconds -> CUSeconds

one :: CUSeconds

fromNatural :: Natural -> CUSeconds

Semiring CSUSeconds

Defined in Data.Semiring

Methods

plus :: CSUSeconds -> CSUSeconds -> CSUSeconds

zero :: CSUSeconds

times :: CSUSeconds -> CSUSeconds -> CSUSeconds

one :: CSUSeconds

fromNatural :: Natural -> CSUSeconds

Semiring CIntPtr

Defined in Data.Semiring

Methods

plus :: CIntPtr -> CIntPtr -> CIntPtr

zero :: CIntPtr

times :: CIntPtr -> CIntPtr -> CIntPtr

one :: CIntPtr

fromNatural :: Natural -> CIntPtr

Semiring CUIntPtr

Defined in Data.Semiring

Methods

plus :: CUIntPtr -> CUIntPtr -> CUIntPtr

zero :: CUIntPtr

times :: CUIntPtr -> CUIntPtr -> CUIntPtr

one :: CUIntPtr

fromNatural :: Natural -> CUIntPtr

Semiring CIntMax

Defined in Data.Semiring

Methods

plus :: CIntMax -> CIntMax -> CIntMax

zero :: CIntMax

times :: CIntMax -> CIntMax -> CIntMax

one :: CIntMax

fromNatural :: Natural -> CIntMax

Semiring CUIntMax

Defined in Data.Semiring

Methods

plus :: CUIntMax -> CUIntMax -> CUIntMax

zero :: CUIntMax

times :: CUIntMax -> CUIntMax -> CUIntMax

one :: CUIntMax

fromNatural :: Natural -> CUIntMax

Semiring WordPtr

Defined in Data.Semiring

Methods

plus :: WordPtr -> WordPtr -> WordPtr

zero :: WordPtr

times :: WordPtr -> WordPtr -> WordPtr

one :: WordPtr

fromNatural :: Natural -> WordPtr

Semiring IntPtr

Defined in Data.Semiring

Methods

plus :: IntPtr -> IntPtr -> IntPtr

zero :: IntPtr

times :: IntPtr -> IntPtr -> IntPtr

one :: IntPtr

fromNatural :: Natural -> IntPtr

Semiring Mod2

Defined in Data.Semiring

Methods

plus :: Mod2 -> Mod2 -> Mod2

zero :: Mod2

times :: Mod2 -> Mod2 -> Mod2

one :: Mod2

fromNatural :: Natural -> Mod2

Semiring Odds

Defined in Statistics.Odds

Methods

plus :: Odds -> Odds -> Odds

zero :: Odds

times :: Odds -> Odds -> Odds

one :: Odds

fromNatural :: Natural -> Odds

Semiring a => Semiring (Maybe a)

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

fromNatural :: Natural -> Maybe a

Integral a => Semiring (Ratio a)

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

fromNatural :: Natural -> Ratio a

Semiring a => Semiring (IO a)

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

fromNatural :: Natural -> IO a

Ring a => Semiring (Complex a)

This instance can suffer due to floating point arithmetic.

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

fromNatural :: Natural -> Complex a

Semiring (Predicate a)

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

fromNatural :: Natural -> Predicate a

Semiring a => Semiring (Equivalence a)

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

fromNatural :: Natural -> Equivalence a

Semiring a => Semiring (Identity a)

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

fromNatural :: Natural -> Identity a

Semiring a => Semiring (Dual a)

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

fromNatural :: Natural -> Dual a

Semiring a => Semiring (Down a)

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

fromNatural :: Natural -> 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.

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

fromNatural :: Natural -> Set 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.

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

fromNatural :: Natural -> HashSet a

RealFloat a => Semiring (Log a)

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

fromNatural :: Natural -> Log a

Num a => Semiring (WrappedNum a)

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

fromNatural :: Natural -> WrappedNum a

(Coercible Int a, Monoid a) => Semiring (IntSetOf a)

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

fromNatural :: Natural -> IntSetOf a

(Ord x, Semiring x) => Semiring (Viterbi x)

TODO Shall we have generic instances, or specific ones like SemiRing (Viterbi Prob)?

TODO Consider either a constraint ProbLike x or the above.

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

fromNatural :: Natural -> Viterbi x

(Ord x, Semiring x, NumericLimits x) => Semiring (MinPlus x)

Be careful, if the numeric limits are hits, underflows, etc will happen.

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

fromNatural :: Natural -> MinPlus x

(Ord x, Semiring x, NumericLimits x) => Semiring (MaxPlus x)

TODO Shall we have generic instances, or specific ones like SemiRing (Viterbi Prob)?

TODO Consider either a constraint ProbLike x or the above.

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

fromNatural :: Natural -> MaxPlus x

Semiring b => Semiring (a -> b)

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

fromNatural :: Natural -> a -> b

Semiring a => Semiring (Op a b)

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

fromNatural :: Natural -> 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.

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

fromNatural :: Natural -> 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.

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

fromNatural :: Natural -> Map k v

HasResolution a => Semiring (Fixed a)

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

fromNatural :: Natural -> Fixed a

Semiring (Proxy a)

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

fromNatural :: Natural -> Proxy a

(Coercible Int k, Monoid k, Semiring v) => Semiring (IntMapOf k v)

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

fromNatural :: Natural -> IntMapOf k v

Num (Discretized k2) => Semiring (Discretized k2)

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

fromNatural :: Natural -> Discretized k2

Semiring (Discretized t) => Semiring (DiscLogOdds t)

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

fromNatural :: Natural -> DiscLogOdds t

Num r => Semiring (Probability n r)

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

fromNatural :: Natural -> Probability n r

Semiring a => Semiring (Const a b)

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

fromNatural :: Natural -> Const a b

(Semiring a, Applicative f) => Semiring (Ap f a)

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

fromNatural :: Natural -> 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)

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

fromNatural :: Natural -> GSemiring zeroMonoid oneMonoid x

Orphan instances

RealFloat a => Semiring (Log a)

Methods

plus :: Log a -> Log a -> Log a

zero :: Log a

times :: Log a -> Log a -> Log a

one :: Log a

fromNatural :: Natural -> Log a