Article

E-Matching with free variables

Author:

Philipp RümmerAuthors Info & Claims

LPAR'12: Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning

Pages 359 - 374

https://doi.org/10.1007/978-3-642-28717-6_28

Published: 11 March 2012 Publication History

Abstract

E-matching is the most commonly used technique to handle quantifiers in SMT solvers. It works by identifying characteristic sub-expressions of quantified formulae, named triggers, which are matched during proof search on ground terms to discover relevant instantiations of the quantified formula. E-matching has proven to be an efficient and practical approach to handle quantifiers, in particular because triggers can be provided by the user to guide proof search; however, as it is heuristic in nature, e-matching alone is typically insufficient to establish a complete proof procedure. In contrast, free variable methods in tableau-like calculi are more robust and give rise to complete procedures, e.g., for first-order logic, but are not comparable to e-matching in terms of scalability. This paper discusses how e-matching can be combined with free variable approaches, leading to calculi that enjoy similar completeness properties as pure free variable procedures, but in which it is still possible for a user to provide domain-specific triggers to improve performance.

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Cited By

Murali APeña LBlanchard ELöding CMadhusudan P(2022)Model-guided synthesis of inductive lemmas for FOL with least fixpointsProceedings of the ACM on Programming Languages10.1145/35633546:OOPSLA2(1873-1902)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563354
Zhang YWang YWillsey MTatlock Z(2022)Relational e-matchingProceedings of the ACM on Programming Languages10.1145/34986966:POPL(1-22)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498696
Bugariu ATer-Gabrielyan AMüller P(2021)Identifying Overly Restrictive Matching Patterns in SMT-Based Program VerifiersFormal Methods10.1007/978-3-030-90870-6_15(273-291)Online publication date: 20-Nov-2021
https://dl.acm.org/doi/10.1007/978-3-030-90870-6_15
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E-Matching with free variables

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cover image Guide Proceedings

LPAR'12: Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning

March 2012

444 pages

ISBN:9783642287169

Editors:
Nikolaj Bjørner
Microsoft Research, One Microsoft Way, Redmond, WA
,
Andrei Voronkov
School of computer Science, University of Manchester, Kilburn Building, Oxford Road, Manchester, WA, UK

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Microsoft Research: Microsoft Research

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 11 March 2012

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Cited By

Murali APeña LBlanchard ELöding CMadhusudan P(2022)Model-guided synthesis of inductive lemmas for FOL with least fixpointsProceedings of the ACM on Programming Languages10.1145/35633546:OOPSLA2(1873-1902)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563354
Zhang YWang YWillsey MTatlock Z(2022)Relational e-matchingProceedings of the ACM on Programming Languages10.1145/34986966:POPL(1-22)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498696
Bugariu ATer-Gabrielyan AMüller P(2021)Identifying Overly Restrictive Matching Patterns in SMT-Based Program VerifiersFormal Methods10.1007/978-3-030-90870-6_15(273-291)Online publication date: 20-Nov-2021
https://dl.acm.org/doi/10.1007/978-3-030-90870-6_15
Brown CGauthier TKaliszyk CSutcliffe GUrban J(2019)GRUNGE: A Grand Unified ATP ChallengeAutomated Deduction – CADE 2710.1007/978-3-030-29436-6_8(123-141)Online publication date: 27-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-030-29436-6_8
Löding CMadhusudan PPeña L(2017)Foundations for natural proofs and quantifier instantiationProceedings of the ACM on Programming Languages10.1145/31580982:POPL(1-30)Online publication date: 27-Dec-2017
https://dl.acm.org/doi/10.1145/3158098
Barbosa HFontaine PReynolds A(2017)Congruence Closure with Free VariablesProceedings, Part II, of the 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems - Volume 1020610.1007/978-3-662-54580-5_13(214-230)Online publication date: 22-Apr-2017
https://dl.acm.org/doi/10.1007/978-3-662-54580-5_13
Voronkov A(2014)AVATARProceedings of the 16th International Conference on Computer Aided Verification - Volume 855910.1007/978-3-319-08867-9_46(696-710)Online publication date: 18-Jul-2014
https://dl.acm.org/doi/10.1007/978-3-319-08867-9_46

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