Document Open Access Logo

Completion for Logically Constrained Rewriting

Authors Sarah Winkler , Aart Middeldorp

PDF
Thumbnail PDF

File

LIPIcs.FSCD.2018.30.pdf
  • Filesize: 0.53 MB
  • 18 pages

Document Identifiers

Author Details

Sarah Winkler
  • Department of Computer Science, University of Innsbruck, Austria
Aart Middeldorp
  • Department of Computer Science, University of Innsbruck, Austria

Funding

This work is supported by FWF (Austrian Science Fund) project T789.

Cite As Get BibTex

Sarah Winkler and Aart Middeldorp. Completion for Logically Constrained Rewriting. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.FSCD.2018.30

Abstract

We propose an abstract completion procedure for logically constrained term rewrite systems (LCTRSs). This procedure can be instantiated to both standard Knuth-Bendix completion and ordered completion for LCTRSs, and we present a succinct and uniform correctness proof. A prototype implementation illustrates the viability of the new completion approach.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
  • Theory of computation → Equational logic and rewriting
  • Theory of computation → Automated reasoning
Keywords
  • Constrained rewriting
  • completion
  • automation
  • theorem proving

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. F. Baader and T. Nipkow. Term Rewriting and All That. Cambridge University Press, 1998. URL: http://dx.doi.org/10.1017/CBO9781139172752.
  2. L. Bachmair. Canonical Equational Proofs. Birkhäuser, 1991. Google Scholar
  3. L. Bachmair, N. Dershowitz, and D.A. Plaisted. Completion without failure. In H. Aït Kaci and M. Nivat, editors, Resolution of Equations in Algebraic Structures, volume 2: Rewriting Techniques of Progress in Theoretical Computer Science, pages 1-30. Academic Press, 1989. Google Scholar
  4. L. de Moura and N. Bjørner. Z3: An efficient SMT solver. In Proc. 14th TACAS, volume 4963 of LNCS, pages 337-340, 2008. URL: http://dx.doi.org/10.1007/978-3-540-78800-3_24.
  5. S. Falke and D. Kapur. Dependency pairs for rewriting with built-in numbers and semantic data structures. In Proc. 19th RTA, volume 5117 of LNCS, pages 94-109, 2008. URL: http://dx.doi.org/10.1007/978-3-540-70590-1_7.
  6. C. Fuhs, J. Giesl, M. Plücker, P. Schneider-Kamp, and S. Falke. Proving termination of integer term rewriting. In Proc. 20th RTA, volume 5595 of LNCS, pages 32-47, 2009. URL: http://dx.doi.org/10.1007/978-3-642-02348-4_3.
  7. C. Fuhs, C. Kop, and N. Nishida. Verifying procedural programs via constrained rewriting induction. ACM TOCL, 18(2):14:1-14:50, 2017. URL: http://dx.doi.org/10.1145/3060143.
  8. Y. Furuichi, N. Nishida, M. Sakai, K. Kusakari, and T. Sakabe. Approach to procedural-program verification based on implicit induction of constrained term rewriting systems. IPSJ Transactions on Programming, 1(2):100-121, 2008. In Japanese. Google Scholar
  9. N. Hirokawa, A. Middeldorp, and C. Sternagel. A new and formalized proof of abstract completion. In Proc. 5th ITP, volume 8558 of LNCS, pages 292-307, 2014. URL: http://dx.doi.org/10.1007/978-3-319-08970-6_19.
  10. K. Hoder, Z. Khasidashvili, K. Korovin, and A. Voronkov. Preprocessing techniques for first-order clausification. In Proc. 12th FMCAD, pages 44-51, 2012. Google Scholar
  11. D.E. Knuth and P. Bendix. Simple word problems in universal algebras. In J. Leech, editor, Computational Problems in Abstract Algebra, pages 263-297. Pergamon Press, 1970. URL: http://dx.doi.org/10.1016/B978-0-08-012975-4.
  12. C. Kop. Termination of LCTRSs. In Proc. 13th WST, pages 59-63, 2013. Google Scholar
  13. C. Kop and N. Nishida. Term rewriting with logical constraints. In Proc. 9th FroCoS, volume 8152 of LNAI, pages 343-358, 2013. Full version available at https://www.cs.ru.nl/~cynthiakop/frocos13.pdf. URL: http://dx.doi.org/10.1007/978-3-642-40885-4_24.
  14. C. Kop and N. Nishida. Constrained Term Rewriting tooL. In Proc. 20th LPAR, volume 9450 of LNAI, pages 549-557, 2015. URL: http://dx.doi.org/10.1007/978-3-662-48899-7_38.
  15. N. Lopes, D. Menendez, S. Nagarakatte, and J. Regehr. Provably correct peephole optimizations with Alive. In Proc. 36th PLDI, pages 22-32, 2015. URL: http://dx.doi.org/10.1145/2737924.2737965.
  16. N. Lopes, D. Menendez, S. Nagarakatte, and J. Regehr. Practical verification of peephole optimizations with Alive. Communications of the ACM, 61(2):84-91, 2018. URL: http://dx.doi.org/10.1145/3166064.
  17. A. Nadel. Bit-vector rewriting with automatic rule generation. In Proc. 16th CAV, pages 663-679, 2014. URL: http://dx.doi.org/10.1007/978-3-319-08867-9_44.
  18. P. Schultz and R. Wisnesky. Algebraic data integration. JFP, 27(e24):51 pages, 2017. URL: http://dx.doi.org/10.1017/S0956796817000168.
  19. I. Wehrman, A. Stump, and E.M. Westbrook. Slothrop: Knuth-Bendix completion with a modern termination checker. In Proc. 17th RTA, volume 4098 of LNCS, pages 287-296, 2006. URL: http://dx.doi.org/10.1007/11805618_22.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact