HaskellForMaths-0.4.5: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | Safe-Inferred

Math.Algebra.Group.StringRewriting

Synopsis

- rewrite :: Eq a => [([a], [a])] -> [a] -> [a]
- rewrite1 :: Eq a => ([a], [a]) -> [a] -> Maybe [a]
- splitSubstring :: Eq a => [a] -> [a] -> Maybe ([a], [a])
- findOverlap :: Eq a => [a] -> [a] -> Maybe ([a], [a], [a])
- knuthBendix1 :: Ord a => [([a], [a])] -> [([a], [a])]
- ordpair :: Ord a => [a] -> [a] -> Maybe ([a], [a])
- shortlex :: Ord a => [a] -> [a] -> Ordering
- knuthBendix2 :: Ord a => [([a], [a])] -> [([a], [a])]
- merge :: Ord a => [a] -> [a] -> [a]
- knuthBendix3 :: Ord a => [([a], [a])] -> [([a], [a])]
- knuthBendix :: Ord a => [([a], [a])] -> [([a], [a])]
- nfs :: Ord a => ([a], [([a], [a])]) -> [[a]]
- elts :: Ord a => ([a], [([a], [a])]) -> [[a]]
- newtype SGen = S Int
- s_ :: Int -> SGen
- s1 :: SGen
- s2 :: SGen
- s3 :: SGen
- _S :: Int -> ([SGen], [([SGen], [a])])
- _S' :: Int -> ([SGen], [([SGen], [SGen])])
- tri :: Int -> Int -> Int -> ([Char], [([Char], [Char])])
- _D :: Int -> Int -> Int -> ([Char], [([Char], [Char])])

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

shortlex :: Ord a => [a] -> [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

Eq SGen |
Ord SGen |
Show SGen |

s_ :: Int -> SGen Source

s1 :: SGen Source

s2 :: SGen Source

s3 :: SGen Source

_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