# HG changeset patch # User Christian Urban # Date 1463575530 -3600 # Node ID 99f91bb994181ff906a3d2df925e1a0828878e80 # Parent e53441994412fdda5dbf8307b35945393b338d8b updated diff -r e53441994412 -r 99f91bb99418 lex/index.html --- a/lex/index.html Wed May 18 11:50:59 2016 +0100 +++ b/lex/index.html Wed May 18 13:45:30 2016 +0100 @@ -33,7 +33,7 @@ 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 +``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 @@ -44,27 +44,27 @@ 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. +explain why the gaps in this argument cannot be filled easily. +

Theory Files for Isabelle 2016

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- Last modified: Tue Mar 15 12:48:13 GMT 2016 + Last modified: Wed May 18 13:44:30 BST 2016 [Validate this page.] diff -r e53441994412 -r 99f91bb99418 lex/index.html~ --- a/lex/index.html~ Wed May 18 11:50:59 2016 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,70 +0,0 @@ - - -HGMP - - - - - - - - - -
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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.] - -