Article

A decision procedure for regular expression equivalence in type theory

Authors:

Thierry Coquand,

Vincent SilesAuthors Info & Claims

CPP'11: Proceedings of the First international conference on Certified Programs and Proofs

Pages 119 - 134

https://doi.org/10.1007/978-3-642-25379-9_11

Published: 07 December 2011 Publication History

Abstract

We describe and formally verify a procedure to decide regular expressions equivalence: two regular expressions are equivalent if and only if they recognize the same language. Our approach to this problem is inspired by Brzozowski's algorithm using derivatives of regular expressions, with a new definition of finite sets. In this paper, we detail a complete formalization of Brzozowki's derivatives, a new definition of finite sets along with its basic meta-theory, and a decidable equivalence procedure correctly proved using Coq and Ssreflect.

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Cited By

Chattopadhyay ALi AMamouras KStark KTimany ABlazy STabareau N(2025)Verified and Efficient Matching of Regular Expressions with LookaroundProceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3703595.3705884(198-213)Online publication date: 10-Jan-2025
https://dl.acm.org/doi/10.1145/3703595.3705884
Mamouras KChattopadhyay A(2024)Efficient Matching of Regular Expressions with Lookaround AssertionsProceedings of the ACM on Programming Languages10.1145/36329348:POPL(2761-2791)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632934
Egolf DLasser SFisher KPopescu AZdancewic S(2022)Verbatim++: verified, optimized, and semantically rich lexing with derivativesProceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3497775.3503694(27-39)Online publication date: 17-Jan-2022
https://dl.acm.org/doi/10.1145/3497775.3503694
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A decision procedure for regular expression equivalence in type theory
1. Theory of computation
  1. Models of computation
  2. Semantics and reasoning

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Published In

cover image Guide Proceedings

CPP'11: Proceedings of the First international conference on Certified Programs and Proofs

December 2011

400 pages

ISBN:9783642253782

Editors:
Jean-Pierre Jouannaud
Tsinghua University, Beijing, China
,
Zhong Shao
Department of Computer Science, Yale University, 51 Prospect Street, New Haven, CT, China

Sponsors

Tsinghua University: TsingHua University Philips Research
Academia Sinica: Academia Sinica
Advances in image and video technology: Advances in image and video technology
National Science Council: National Science Council (Taiwan)

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 07 December 2011

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Cited By

Chattopadhyay ALi AMamouras KStark KTimany ABlazy STabareau N(2025)Verified and Efficient Matching of Regular Expressions with LookaroundProceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3703595.3705884(198-213)Online publication date: 10-Jan-2025
https://dl.acm.org/doi/10.1145/3703595.3705884
Mamouras KChattopadhyay A(2024)Efficient Matching of Regular Expressions with Lookaround AssertionsProceedings of the ACM on Programming Languages10.1145/36329348:POPL(2761-2791)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632934
Egolf DLasser SFisher KPopescu AZdancewic S(2022)Verbatim++: verified, optimized, and semantically rich lexing with derivativesProceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3497775.3503694(27-39)Online publication date: 17-Jan-2022
https://dl.acm.org/doi/10.1145/3497775.3503694
Doczkal CSmolka G(2018)Regular Language Representations in the Constructive Type Theory of CoqJournal of Automated Reasoning10.1007/s10817-018-9460-x61:1-4(521-553)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1007/s10817-018-9460-x
Asăvoae Ide Boer FBonsangue MLucanu DRot J(2015)Model checking recursive programs interacting via the heapScience of Computer Programming10.1016/j.scico.2014.09.009100:C(61-83)Online publication date: 15-Mar-2015
https://dl.acm.org/doi/10.1016/j.scico.2014.09.009
Traytel DNipkow T(2013)Verified decision procedures for MSO on words based on derivatives of regular expressionsACM SIGPLAN Notices10.1145/2544174.250061248:9(3-12)Online publication date: 25-Sep-2013
https://dl.acm.org/doi/10.1145/2544174.2500612
Traytel DNipkow TMorrisett GUustalu T(2013)Verified decision procedures for MSO on words based on derivatives of regular expressionsProceedings of the 18th ACM SIGPLAN international conference on Functional programming10.1145/2500365.2500612(3-12)Online publication date: 25-Sep-2013
https://dl.acm.org/doi/10.1145/2500365.2500612
Pous D(2013)Kleene algebra with tests and coq tools for while programsProceedings of the 4th international conference on Interactive Theorem Proving10.1007/978-3-642-39634-2_15(180-196)Online publication date: 22-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39634-2_15
Firsov DUustalu T(2013)Certified Parsing of Regular LanguagesCertified Programs and Proofs10.1007/978-3-319-03545-1_7(98-113)Online publication date: 11-Dec-2013
https://dl.acm.org/doi/10.1007/978-3-319-03545-1_7
Doczkal CKaiser JSmolka G(2013)A Constructive Theory of Regular Languages in CoqCertified Programs and Proofs10.1007/978-3-319-03545-1_6(82-97)Online publication date: 11-Dec-2013
https://dl.acm.org/doi/10.1007/978-3-319-03545-1_6
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