HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

Math.Algebra.Group.StringRewriting

Synopsis

# Documentation

rewrite :: Eq a => [([a], [a])] -> [a] -> [a] Source #

Given a list of rewrite rules of the form (left,right), and a word, rewrite it by repeatedly replacing any left substring in the word by the corresponding right

rewrite1 :: Eq a => ([a], [a]) -> [a] -> Maybe [a] Source #

splitSubstring :: Eq a => [a] -> [a] -> Maybe ([a], [a]) Source #

findOverlap :: Eq a => [a] -> [a] -> Maybe ([a], [a], [a]) Source #

knuthBendix1 :: Ord a => [([a], [a])] -> [([a], [a])] Source #

ordpair :: (Ord (t a), Foldable t) => t a -> t a -> Maybe (t a, t a) Source #

shortlex :: (Ord (t a), Foldable t) => t a -> t a -> Ordering Source #

knuthBendix2 :: Ord a => [([a], [a])] -> [([a], [a])] Source #

merge :: Ord a => [a] -> [a] -> [a] Source #

knuthBendix3 :: Ord a => [([a], [a])] -> [([a], [a])] Source #

knuthBendix :: Ord a => [([a], [a])] -> [([a], [a])] Source #

Implementation of the Knuth-Bendix algorithm. Given a list of relations, return a confluent rewrite system. The algorithm is not guaranteed to terminate.

nfs :: Ord a => ([a], [([a], [a])]) -> [[a]] Source #

Given generators and a confluent rewrite system, return (normal forms of) all elements

elts :: Ord a => ([a], [([a], [a])]) -> [[a]] Source #

Given generators and relations, return (normal forms of) all elements

newtype SGen Source #

Constructors

 S Int
Instances
 Source # Instance detailsDefined in Math.Algebra.Group.StringRewriting Methods(==) :: SGen -> SGen -> Bool #(/=) :: SGen -> SGen -> Bool # Source # Instance detailsDefined in Math.Algebra.Group.StringRewriting Methodscompare :: SGen -> SGen -> Ordering #(<) :: SGen -> SGen -> Bool #(<=) :: SGen -> SGen -> Bool #(>) :: SGen -> SGen -> Bool #(>=) :: SGen -> SGen -> Bool #max :: SGen -> SGen -> SGen #min :: SGen -> SGen -> SGen # Source # Instance detailsDefined in Math.Algebra.Group.StringRewriting MethodsshowsPrec :: Int -> SGen -> ShowS #show :: SGen -> String #showList :: [SGen] -> ShowS #

_S :: Int -> ([SGen], [([SGen], [a])]) Source #

_S' :: Int -> ([SGen], [([SGen], [SGen])]) Source #

tri :: Int -> Int -> Int -> ([Char], [([Char], [Char])]) Source #

_D :: Int -> Int -> Int -> ([Char], [([Char], [Char])]) Source #