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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>
-<li> <A HREF="http://talisker.inf.kcl.ac.uk/%7Eurbanc/cgi-bin/repos.cgi/lexing/raw-file/tip/thys/Simplifying.thy">Simplifying.thy</A>
-<li> <A HREF="http://talisker.inf.kcl.ac.uk/%7Eurbanc/cgi-bin/repos.cgi/lexing/raw-file/tip/thys/Sulzmann.thy">Sulzmann.thy</A>
-</ul>
-
-
-<H3>Links</H3>
-
-<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>
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