Built-in Variant Generation and Unification, and Their Applications in Maude 2.7

  • Francisco Durán
  • Steven Eker
  • Santiago Escobar
  • Narciso Martí-Oliet
  • José Meseguer
  • Carolyn Talcott
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9706)

Abstract

This paper introduces some novel features of Maude 2.7. We have added support for: (i) built-in order-sorted unification modulo associativity, commutativity, and identity, (ii) built-in variant generation, (iii) built-in order-sorted unification modulo a finite variant theory, and (iv) symbolic reachability modulo a finite variant theory.

References

  1. 1.
    Bae, K., Escobar, S., Meseguer, J.: Abstract logical model checking of infinite-state systems using narrowing. In: van Raamsdonk, F., (ed.) 24th International Conference on Rewriting Techniques and Applications, RTA 2013, June 24–26, 2013, Eindhoven, The Netherlands. LIPIcs vol. 21, pp. 81–96. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)Google Scholar
  2. 2.
    Bouchard, C., Gero, K.A., Lynch, C., Narendran, P.: On forward closure and the finite variant property. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS, vol. 8152, pp. 327–342. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Cholewa, A., Meseguer, J., Escobar, S.: Variants of variants and the finite variant property. Technical report, University of Illinois at Urbana-Champaign (2014). http://hdl.handle.net/2142/47117
  4. 4.
    Clavel, M., Durán, F., Eker, S., Escobar, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: Unification and narrowing in maude 2.4. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 380–390. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)MATHGoogle Scholar
  6. 6.
    Comon-Lundh, H., Delaune, S.: The finite variant property: how to get rid of some algebraic properties. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 294–307. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Durán, F., Eker, S., Escobar, S., Meseguer, J., Talcott, C.L.: Variants, unification, narrowing, and symbolic reachability inMaude 2.6. In: Schmidt-Schauß, M., (ed.) Proceedings of the 22ndInternational Conference on Rewriting Techniques and Applications, RTA2011, May 30 - June 1, 2011, Novi Sad, Serbia. LIPIcs, vol. 10, pp. 31–40. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)Google Scholar
  8. 8.
    Durán, F., Lucas, S., Meseguer, J.: Termination modulo combinations of equational theories. In: Ghilardi, S., Sebastiani, R. (eds.) FroCoS 2009. LNCS, vol. 5749, pp. 246–262. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Durán, F., Meseguer, J.: On the Church-Rosser and coherence properties of conditional order-sorted rewrite theories. J. Logic Algebraic Program. 81(7–8), 816–850 (2012)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Escobar, S., Meadows, C., Meseguer, J.: Maude-NPA: Cryptographic protocol analysis modulo equationalproperties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Escobar, S., Meseguer, J.: Symbolic model checking of infinite-state systems using narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. J. Logic Algebraic Program. 81(7–8), 898–928 (2012)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Meier, S., Schmidt, B., Cremers, C., Basin, D.: The TAMARIN prover for the symbolic analysis of security protocols. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 696–701. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  14. 14.
    Meseguer, J.: Variant-based satisfiability in initial algebras. Technical report, University of Illinois at Urbana-Champaign (2015). http://hdl.handle.net/2142/88408
  15. 15.
    Meseguer, J., Thati, P.: Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols. High. Order Symbolic Comput. 20(1–2), 123–160 (2007)CrossRefMATHGoogle Scholar
  16. 16.
    Riesco, A.: Using big-step and small-step semantics in maude to perform declarative debugging. In: Codish, M., Sumii, E. (eds.) FLOPS 2014. LNCS, vol. 8475, pp. 52–68. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  17. 17.
    Rusu, V.: Combining theorem proving and narrowing for rewriting-logic specifications. In: Fraser, G., Gargantini, A. (eds.) TAP 2010. LNCS, vol. 6143, pp. 135–150. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Tushkanova, E., Giorgetti, A., Ringeissen, C., Kouchnarenko, O.: A rule-based system for automatic decidability and combinability. Sci. Comput. Program. 99, 3–23 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Francisco Durán
    • 1
  • Steven Eker
    • 2
  • Santiago Escobar
    • 3
  • Narciso Martí-Oliet
    • 4
  • José Meseguer
    • 5
  • Carolyn Talcott
    • 2
  1. 1.Universidad de MálagaMálagaSpain
  2. 2.SRI InternationalMenlo ParkUSA
  3. 3.Universitat Politècnica de ValènciaValenciaSpain
  4. 4.Universidad Complutense de MadridMadridSpain
  5. 5.University of Illinois at Urbana-ChampaignChampaignUSA

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