public_html: lex/index.html~@1bb32ab3e90e (annotated)

415 f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1	<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2	"http://www.w3.org/TR/REC-html40/loose.dtd">
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	3	<HEAD>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	4	<TITLE>HGMP</TITLE>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	5	<BASE HREF="http://www.inf.kcl.ac.uk/staff/urbanc/">
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	6	</HEAD>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	7
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	8	<BODY TEXT="#000000"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	9	BGCOLOR="#4169E1"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	10	LINK="#0000EF"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	11	VLINK="#51188E"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	12	ALINK="#FF0000">
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	13
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	14	<TABLE WIDTH="100%"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	15	BGCOLOR="#4169E1"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	16	BORDER="0"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	17	FRAME="border"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	18	CELLPADDING="10"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	19	CELLSPACING="2"
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	20	RULES="all">
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	21
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	22	<!-- right column -->
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	23	<TR>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	24	<TD BGCOLOR="#FFFFFF" WIDTH="75%">
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	25	<H2>POSIX Lexing with Derivatives of Regular Expressions (Proof Pearl)</H2>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	26
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	27	Fahad Ausaf, Roy Dyckhoff, Christian Urban
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	28	<p>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	29
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	30	Brzozowski introduced the notion of derivatives for regular
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	31	expressions. They can be used for a very simple regular expression
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	32	matching algorithm. Sulzmann and Lu cleverly extended this algorithm
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	33	in order to deal with POSIX matching, which is the underlying
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	34	disambiguation strategy for regular expressions needed in lexers.
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	35	Sulzmann and Lu have made available on-line what they call a
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	36	''rigorous proof'' of the correctness of their algorithm w.r.t. their
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	37	specification; regrettably, it appears to us to have unfillable gaps.
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	38	In the first part of this paper we give our inductive definition of
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	39	what a POSIX value is and show (i) that such a value is unique (for
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	40	given regular expression and string being matched) and (ii) that
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	41	Sulzmann and Lu's algorithm always generates such a value (provided
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	42	that the regular expression matches the string). We also prove the
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	43	correctness of an optimised version of the POSIX matching
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	44	algorithm. Our definitions and proof are much simpler than those by
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	45	Sulzmann and Lu and can be easily formalised in Isabelle/HOL. In the
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	46	second part we analyse the correctness argument by Sulzmann and Lu and
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	47	explain why it seems hard to turn it into a proof rigorous enough to
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	48	be accepted by a system such as Isabelle/HOL.
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	49
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	50	<H3>Theory Files for Isabelle 2016</H3>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	51
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	52	<ul>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	53	<li> <A HREF="http://talisker.inf.kcl.ac.uk/%7Eurbanc/cgi-bin/repos.cgi/lexing/raw-file/tip/thys/ReStar.thy">ReStar.thy</A>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	54	<li> <A HREF="http://talisker.inf.kcl.ac.uk/%7Eurbanc/cgi-bin/repos.cgi/lexing/raw-file/tip/thys/Simplifying.thy">Simplifying.thy</A>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	55	<li> <A HREF="http://talisker.inf.kcl.ac.uk/%7Eurbanc/cgi-bin/repos.cgi/lexing/raw-file/tip/thys/Sulzmann.thy">Sulzmann.thy</A>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	56	</ul>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	57
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	58
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	59	<H3>Links</H3>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	60
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	61	<ul>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	62	<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
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	63	</ul>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	64
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	65	</TABLE>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	66	<P>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	67	<!-- hhmts start --> Last modified: Tue Mar 15 12:47:17 GMT 2016 <!-- hhmts end -->
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	68	<a href="http://validator.w3.org/check/referer">[Validate this page.]</a>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	69	</BODY>
f1be8028a4a9 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	70	</HTML>

author	Christian Urban <christian dot urban at kcl dot ac dot uk>
	Thu, 07 Apr 2016 23:14:26 +0100
changeset 424	1bb32ab3e90e
parent 415	f1be8028a4a9
permissions	-rw-r--r--