+POSIX Lexing with Derivatives of Regular Expressions (Proof Pearl)+ +Fahad Ausaf, Roy Dyckhoff, Christian Urban ++ +Brzozowski introduced the notion of derivatives for regular +expressions. They can be used for a very simple regular expression +matching algorithm. Sulzmann and Lu cleverly extended this algorithm +in order to deal with POSIX matching, which is the underlying +disambiguation strategy for regular expressions needed in lexers. +Sulzmann and Lu have made available on-line what they call a +''rigorous proof'' of the correctness of their algorithm w.r.t. their +specification; regrettably, it appears to us to have unfillable gaps. +In the first part of this paper we give our inductive definition of +what a POSIX value is and show (i) that such a value is unique (for +given regular expression and string being matched) and (ii) that +Sulzmann and Lu's algorithm always generates such a value (provided +that the regular expression matches the string). We also prove the +correctness of an optimised version of the POSIX matching +algorithm. Our definitions and proof are much simpler than those by +Sulzmann and Lu and can be easily formalised in Isabelle/HOL. In the +second part we analyse the correctness argument by Sulzmann and Lu and +explain why it seems hard to turn it into a proof rigorous enough to +be accepted by a system such as Isabelle/HOL. + + Theory Files for Isabelle 2016+ +
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+ Last modified: Tue Mar 15 12:47:17 GMT 2016 +[Validate this page.] + +