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+<H2>POSIX Lexing with Derivatives of Regular Expressions (Proof Pearl)</H2>
+
+Fahad Ausaf, Roy Dyckhoff, Christian Urban
+<p>
+
+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.
+
+<H3>Theory Files for Isabelle 2016</H3>
+
+<ul>
+<li> <A HREF="http://talisker.inf.kcl.ac.uk/%7Eurbanc/cgi-bin/repos.cgi/lexing/raw-file/tip/thys/ReStar.thy">ReStar.thy</A>
+</u>
+
+
+<H3>Links</A>
+
+<ul>
+<li> <A HREF="http://talisker.inf.kcl.ac.uk/%7Eurbanc/cgi-bin/repos.cgi/lexing/raw-file/tip/Literature/sulzmann14-new.pdf">the paper</A> by Sulzmann and Lu
+</ul>
+
+</TABLE>
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