Regular Expressions, Part 2
September 18, 2009
In the previous exercise, we decided on an intermediate representation for regular expressions and wrote a parser that produces the intermediate representation corresponding to a regular expression given as input.
Your task today is to write the corresponding matcher that takes an intermediate representation and a target string and returns a boolean indicating whether or not the regular expression matches the target string, using the same conventions as the prior exercise. Your matcher will be similar to Rob Pike’s matcher that we studied previously. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
I hope you’re planning on moving on to NFA-based regular expression matching, because the naive, exponential-time regex engine this series is developing is severely suboptimal. Automata, NFA and DFA, are beautiful, useful, and not difficult.
My Haskell solution (see http://bonsaicode.wordpress.com/2009/09/18/programming-praxis-regular-expressions-part-2/ for a version with comments):
import Data.List data Elem = Lit Char | Esc Char | Any | Set Bool [Elem] deriving Show data Chunk = Elem Elem | BoL | EoL | Star Elem deriving Show matchElem :: Elem -> Char -> Bool matchElem e c = case e of Lit l -> l == c Esc s -> show c == '\\':[s] Set b es -> b == any (`matchElem` c) es Any -> True matchHere :: [Chunk] -> String -> Bool matchHere (Elem r:rs) (x:xs) = matchElem r x && matchHere rs xs matchHere (Star e:r) xs = matchStar e r xs matchHere [EoL] xs = null xs matchHere r _ = null r matchStar :: Elem -> [Chunk] -> String -> Bool matchStar _ r xs | matchHere r xs = True matchStar e r (x:xs) = matchElem e x && matchStar e r xs matchStar _ _ _ = False match :: [Chunk] -> String -> Bool match (BoL:r) = matchHere r match r = any (matchHere r) . tailsOn a side note, the ‘HOWTO: Posting source code’ page no longer shows the actual tags required. You might want to fix that.
Also, the source code plugin now seems to htmlEncode characters like & and >, which screws up function types and such.
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kbob: This blog is getting programmers to write code, so that they can maintain and improve their coding skills. This blog is not about computer science or the comparative study of algorithms. It really doesn’t matter to me that I have the fastest algorithm that solves the particular programming problem I am discussing. I do have a two-part series regex->nfa, nfa->dfa on my idea list, but that doesn’t mean I’ll ever write it.
Remco: I fixed the ‘sourcecode’ tags on the HOWTOpage. And I sent a bug report to the WordPress support center. Thanks for pointing out the problems.
Sheri, from the WordPress Support Department, reports that the bug in the ‘sourcecode’ feature has now been fixed. I reported the bug on Friday evening and it was fixed by Sunday morning. Well done, WordPress!
Phil