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A Maude Coherence Checker Tool for Conditional Order-Sorted Rewrite Theories

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Rewriting Logic and Its Applications (WRLA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6381))

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Abstract

For a rewrite theory to be executable, its equations E should be (ground) confluent and terminating modulo the given axioms A, and their rules should be (ground) coherent with E modulo A. The correctness of many important formal verification tasks, including search, LTL model checking, and the development of abstractions, crucially depends on the theory being ground coherent. Furthermore, many specifications of interest are typed, have equations E and rules R that are both conditional, have axioms A involving various combinations of associativity, commutativity and identity, and may contain frozenness restrictions. This makes it essential to extend the known coherence checking methods from the untyped, unconditional, and AC or free case, to this much more general setting. We present the mathematical foundations of the Maude ChC 3 tool, which provide such a generalization to support coherence and ground coherence checking for order-sorted rewrite theories under these general assumptions. We also explain and illustrate the use of the ChC 3 tool with a nontrivial example.

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References

  1. Avenhaus, J., Loría-Sáenz, C.: On conditional rewrite systems with extra variables and deterministic logic programs. In: Pfenning, F. (ed.) LPAR 1994. LNCS, vol. 822, pp. 215–229. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  2. Bruni, R., Meseguer, J.: Semantic foundations for generalized rewrite theories. Theoretical Computer Science 351(1), 286–414 (2006)

    MathSciNet  MATH  Google Scholar 

  3. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Quesada, J.: Maude: Specification and programming in rewriting logic. Theoretical Computer Science 285, 187–243 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. 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)

    MATH  Google Scholar 

  5. Clavel, M., Durán, F., Hendrix, J., Lucas, S., Meseguer, J., Ölveczky, P.: The Maude formal tool environment. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 173–178. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  7. Durán, F.: A Reflective Module Algebra with Applications to the Maude Language. PhD thesis, U. de Málaga, Spain (June 1999), http://maude.csl.sri.com/papers

  8. Durán, F.: The extensibility of Maude’s module algebra. In: Rus, T. (ed.) AMAST 2000. LNCS, vol. 1816, pp. 422–437. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  9. Durán, F., Lucas, S., Meseguer, J.: MTT: The Maude termination tool (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 313–319. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Durán, F., Lucas, S., Meseguer, J.: Termination modulo combinations of equational theories. In: Ghilardi, S. (ed.) FroCoS 2009. LNCS, vol. 5749, pp. 246–262. Springer, Heidelberg (2009)

    Google Scholar 

  11. Durán, F., Meseguer, J.: A Church-Rosser checker tool for Maude equational specifications. Technical Report ITI-2000-5, Dpto. de Lenguajes y Ciencias de la Computación, U. de Málaga (October 2000), http://maude.cs.uiuc.edu

  12. Durán, F., Meseguer, J.: Maude’s module algebra. Science of Computer Programming 66(2), 125–153 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Durán, F., Meseguer, J.: ChC 3: A coherence checker tool for conditional order-sorted rewrite Maude specifications (2009), http://maude.lcc.uma.es/CRChC

  14. Durán, F., Meseguer, J.: CRC 3: A Church-Rosser checker tool for conditional order-sorted equational Maude specifications (2009), http://maude.lcc.uma.es/CRChC

  15. Durán, F., Meseguer, J.: A Church-Rosser checker tool for conditional order-sorted equational Maude specifications. In: Ölveczky, P.C. (ed.) 8th Intl. Workshop on Rewriting Logic and its Applications (2010)

    Google Scholar 

  16. Durán, F., Meseguer, J.: A Maude coherence checker tool for conditional order-sorted rewrite theories, long version (2010), http://maude.lcc.uma.es/CRChC

  17. Durán, F., Ölveczky, P.C.: A guide to extending Full Maude illustrated with the implementation of Real-Time Maude. In: Roşu, G. (ed.) Proceedings 7th Intl. Workshop on Rewriting Logic and its Applications (WRLA 2008). Electronic Notes in Theoretical Computer Science. Elsevier, Amsterdam (2008)

    Google Scholar 

  18. Escobar, S., Meseguer, J., Sasse, R.: Variant narrowing and equational unification. In: Rosu, G. (ed.) Proc. 7th Intl. Workshop on Rewriting Logic and its Applications (WRLA 2008). Electronic Notes in Theoretical Computer Science, vol. 238, pp. 103–119. Elsevier, Amsterdam (2008)

    Google Scholar 

  19. Giesl, J., Kapur, D.: Dependency pairs for equational rewriting. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 93–108. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  20. Jouannaud, J.-P., Kirchner, H.: Completion of a set of rules modulo a set of equations. SIAM Journal of Computing 15(4), 1155–1194 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  21. Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science 96(1), 73–155 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  22. Meseguer, J.: A logical theory of concurrent objects and its realization in the Maude language. In: Agha, G., Wegner, P., Yonezawa, A. (eds.) Research Directions in Concurrent Object-Oriented Programming, pp. 314–390. The MIT Press, Cambridge (1993)

    Google Scholar 

  23. Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  24. Peterson, G., Stickel, M.: Complete sets of reductions for some equational theories. Journal of ACM 28(2), 233–264 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  25. Viry, P.: Equational rules for rewriting logic. Theoretical Computer Science 285(2), 487–517 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Universidad de Málaga, Spain

    Francisco Durán

  2. University of Illinois at Urbana-Champaign, IL, USA

    José Meseguer

Authors
  1. Francisco Durán
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  2. José Meseguer
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Editors and Affiliations

  1. Department of Informatics, University of Oslo, Gaustadalléen 23, 0373, Oslo, Norway

    Peter Csaba Ölveczky

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Durán, F., Meseguer, J. (2010). A Maude Coherence Checker Tool for Conditional Order-Sorted Rewrite Theories. In: Ölveczky, P.C. (eds) Rewriting Logic and Its Applications. WRLA 2010. Lecture Notes in Computer Science, vol 6381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16310-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-16310-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16309-8

  • Online ISBN: 978-3-642-16310-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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