StarSemiring

Documentation

class Semiring a where

Minimal complete definition

zero, (<+>), one, (<.>)

Methods

zero :: a

(<+>) :: a -> a -> a infixl 6

one :: a

(<.>) :: a -> a -> a infixl 7

srsum :: [a] -> a

srprod :: [a] -> a

Instances

(Eq a, Num a) => Semiring (Compact a)

Methods

zero :: Compact a

(<+>) :: Compact a -> Compact a -> Compact a

one :: Compact a

(<.>) :: Compact a -> Compact a -> Compact a

srsum :: [Compact a] -> Compact a

srprod :: [Compact a] -> Compact a

Semiring (Language a)

Methods

zero :: Language a

(<+>) :: Language a -> Language a -> Language a

one :: Language a

(<.>) :: Language a -> Language a -> Language a

srsum :: [Language a] -> Language a

srprod :: [Language a] -> Language a

(Ord a, Num a) => Semiring (Tropical a)

Methods

zero :: Tropical a

(<+>) :: Tropical a -> Tropical a -> Tropical a

one :: Tropical a

(<.>) :: Tropical a -> Tropical a -> Tropical a

srsum :: [Tropical a] -> Tropical a

srprod :: [Tropical a] -> Tropical a

Semiring (RE a)

Methods

zero :: RE a

(<+>) :: RE a -> RE a -> RE a

one :: RE a

(<.>) :: RE a -> RE a -> RE a

srsum :: [RE a] -> RE a

srprod :: [RE a] -> RE a

Semiring (StarSemiringExpr a)

Methods

zero :: StarSemiringExpr a

(<+>) :: StarSemiringExpr a -> StarSemiringExpr a -> StarSemiringExpr a

one :: StarSemiringExpr a

(<.>) :: StarSemiringExpr a -> StarSemiringExpr a -> StarSemiringExpr a

srsum :: [StarSemiringExpr a] -> StarSemiringExpr a

srprod :: [StarSemiringExpr a] -> StarSemiringExpr a

(Ord a, Num a, Semiring b) => Semiring (ShortestPath a b)

Methods

zero :: ShortestPath a b

(<+>) :: ShortestPath a b -> ShortestPath a b -> ShortestPath a b

one :: ShortestPath a b

(<.>) :: ShortestPath a b -> ShortestPath a b -> ShortestPath a b

srsum :: [ShortestPath a b] -> ShortestPath a b

srprod :: [ShortestPath a b] -> ShortestPath a b

class Semiring a => StarSemiring a where

Methods

star :: a -> a

plus :: a -> a

Instances

(Eq a, Fractional a) => StarSemiring (Compact a)

Methods

star :: Compact a -> Compact a

plus :: Compact a -> Compact a

StarSemiring (Language a)

Methods

star :: Language a -> Language a

plus :: Language a -> Language a

(Ord a, Num a) => StarSemiring (Tropical a)

Methods

star :: Tropical a -> Tropical a

plus :: Tropical a -> Tropical a

StarSemiring (RE a)

Methods

star :: RE a -> RE a

plus :: RE a -> RE a

StarSemiring (StarSemiringExpr a)

Methods

star :: StarSemiringExpr a -> StarSemiringExpr a

plus :: StarSemiringExpr a -> StarSemiringExpr a

(Ord a, Num a, StarSemiring b) => StarSemiring (ShortestPath a b)

Methods

star :: ShortestPath a b -> ShortestPath a b

plus :: ShortestPath a b -> ShortestPath a b

class StarSemiring a => KleeneAlgebra a

Instances

(Ord a, Num a) => KleeneAlgebra (Tropical a)

(Ord a, Num a, KleeneAlgebra b) => KleeneAlgebra (ShortestPath a b)

data StarSemiringExpr a

Constructors

Var a

Or (StarSemiringExpr a) (StarSemiringExpr a)

Seq (StarSemiringExpr a) (StarSemiringExpr a)

Star (StarSemiringExpr a)

None

Empty

Instances

Show a => Show (StarSemiringExpr a)

Below you will find an appendix of functions that completes this module.

Methods

showsPrec :: Int -> StarSemiringExpr a -> ShowS

show :: StarSemiringExpr a -> String

showList :: [StarSemiringExpr a] -> ShowS

StarSemiring (StarSemiringExpr a)

Methods

star :: StarSemiringExpr a -> StarSemiringExpr a

plus :: StarSemiringExpr a -> StarSemiringExpr a

Semiring (StarSemiringExpr a)

Methods

zero :: StarSemiringExpr a

(<+>) :: StarSemiringExpr a -> StarSemiringExpr a -> StarSemiringExpr a

one :: StarSemiringExpr a

(<.>) :: StarSemiringExpr a -> StarSemiringExpr a -> StarSemiringExpr a

srsum :: [StarSemiringExpr a] -> StarSemiringExpr a

srprod :: [StarSemiringExpr a] -> StarSemiringExpr a

newtype RE a

Constructors

RE (StarSemiringExpr a)

Instances

Eq a => Eq (RE a)

Methods

(==) :: RE a -> RE a -> Bool

(/=) :: RE a -> RE a -> Bool

Show a => Show (RE a)

Methods

showsPrec :: Int -> RE a -> ShowS

show :: RE a -> String

showList :: [RE a] -> ShowS

StarSemiring (RE a)

Methods

star :: RE a -> RE a

plus :: RE a -> RE a

Semiring (RE a)

Methods

zero :: RE a

(<+>) :: RE a -> RE a -> RE a

one :: RE a

(<.>) :: RE a -> RE a -> RE a

srsum :: [RE a] -> RE a

srprod :: [RE a] -> RE a

re :: a -> RE a

data Tropical a

Constructors

Tropical a

Infinity

Instances

Eq a => Eq (Tropical a)

Methods

(==) :: Tropical a -> Tropical a -> Bool

(/=) :: Tropical a -> Tropical a -> Bool

Ord a => Ord (Tropical a)

Methods

compare :: Tropical a -> Tropical a -> Ordering

(<) :: Tropical a -> Tropical a -> Bool

(<=) :: Tropical a -> Tropical a -> Bool

(>) :: Tropical a -> Tropical a -> Bool

(>=) :: Tropical a -> Tropical a -> Bool

max :: Tropical a -> Tropical a -> Tropical a

min :: Tropical a -> Tropical a -> Tropical a

Show a => Show (Tropical a)

Methods

showsPrec :: Int -> Tropical a -> ShowS

show :: Tropical a -> String

showList :: [Tropical a] -> ShowS

(Ord a, Num a) => KleeneAlgebra (Tropical a)

(Ord a, Num a) => StarSemiring (Tropical a)

Methods

star :: Tropical a -> Tropical a

plus :: Tropical a -> Tropical a

(Ord a, Num a) => Semiring (Tropical a)

Methods

zero :: Tropical a

(<+>) :: Tropical a -> Tropical a -> Tropical a

one :: Tropical a

(<.>) :: Tropical a -> Tropical a -> Tropical a

srsum :: [Tropical a] -> Tropical a

srprod :: [Tropical a] -> Tropical a

data ShortestPath a b

Constructors

ShortestPath (Tropical a) b

Instances

Functor (ShortestPath a)

Methods

fmap :: (a -> b) -> ShortestPath a a -> ShortestPath a b

(<$) :: a -> ShortestPath a b -> ShortestPath a a

(Show a, Show b) => Show (ShortestPath a b)

Methods

showsPrec :: Int -> ShortestPath a b -> ShowS

show :: ShortestPath a b -> String

showList :: [ShortestPath a b] -> ShowS

(Ord a, Num a, KleeneAlgebra b) => KleeneAlgebra (ShortestPath a b)

(Ord a, Num a, StarSemiring b) => StarSemiring (ShortestPath a b)

Methods

star :: ShortestPath a b -> ShortestPath a b

plus :: ShortestPath a b -> ShortestPath a b

(Ord a, Num a, Semiring b) => Semiring (ShortestPath a b)

Methods

zero :: ShortestPath a b

(<+>) :: ShortestPath a b -> ShortestPath a b -> ShortestPath a b

one :: ShortestPath a b

(<.>) :: ShortestPath a b -> ShortestPath a b -> ShortestPath a b

srsum :: [ShortestPath a b] -> ShortestPath a b

srprod :: [ShortestPath a b] -> ShortestPath a b

extract :: ShortestPath a b -> b

newtype Language a

Constructors

Language [[a]]

Instances

StarSemiring (Language a)

Methods

star :: Language a -> Language a

plus :: Language a -> Language a

Semiring (Language a)

Methods

zero :: Language a

(<+>) :: Language a -> Language a -> Language a

one :: Language a

(<.>) :: Language a -> Language a -> Language a

srsum :: [Language a] -> Language a

srprod :: [Language a] -> Language a

letter :: a -> Language a

someWord :: Language a -> Maybe [a]

evalRE :: KleeneAlgebra a => (l -> a) -> RE l -> a

data Compact a

Constructors

Real a

Inf

Instances

Show a => Show (Compact a)

Methods

showsPrec :: Int -> Compact a -> ShowS

show :: Compact a -> String

showList :: [Compact a] -> ShowS

(Eq a, Fractional a) => StarSemiring (Compact a)

Methods

star :: Compact a -> Compact a

plus :: Compact a -> Compact a

(Eq a, Num a) => Semiring (Compact a)

Methods

zero :: Compact a

(<+>) :: Compact a -> Compact a -> Compact a

one :: Compact a

(<.>) :: Compact a -> Compact a -> Compact a

srsum :: [Compact a] -> Compact a

srprod :: [Compact a] -> Compact a

evalSSE :: StarSemiring a => (l -> a) -> StarSemiringExpr l -> a

todo :: a