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International Workshop on Rewriting Logic and its Applications

WRLA 2010: Rewriting Logic and Its Applications pp 69–85Cite as

A Church-Rosser Checker Tool for Conditional Order-Sorted Equational Maude Specifications

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

Abstract

The Church-Rosser property, together with termination, is essential for an equational specification to have good executability conditions, and also for having a complete agreement between the specification’s initial algebra, mathematical semantics, and its operational semantics by rewriting. Checking this property for expressive specifications that are order-sorted, conditional with possibly extra variables in their condition, and whose equations can be applied modulo different combinations of associativity, commutativity and identity axioms is challenging. In particular, the resulting conditional critical pairs that cannot be joined have often an intuitively unsatisfiable condition or seem intuitively joinable, so that sophisticated tool support is needed to eliminate them. Another challenge is the presence of different combinations of associativity, commutativity and identity axioms, including the very challenging case of associativity without commutativity for which no finitary unification algorithms exist. In this paper we present the foundations and illustrate the design and use of a completely new version of the Maude Church-Rosser Checker tool that addresses all the above-mentioned challenges and can deal effectively with complex conditional specifications modulo axioms.

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References

  1. Avenhaus, J., Hillenbrand, T., Löchner, B.: On using ground joinable equations in equational theorem proving. Journal of Symbolic Computation 36(1-2), 217–233 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. 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 

  3. Bachmair, L., Dershowitz, N., Plaisted, D.A.: Completion without failure. In: Kaci, A.H., Nivat, M. (eds.) Resolution of Equations in Algebraic Structures. Rewriting Techniques, vol. 2, pp. 1–30. Academic Press, New York (1989)

    Google Scholar 

  4. Becker, K.: Proving ground confluence and inductive validity in constructor based equational specifications. In: Gaudel, M.-C., Jouannaud, J.-P. (eds.) CAAP 1993, FASE 1993, and TAPSOFT 1993. LNCS, vol. 668, pp. 46–60. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  5. Bergstra, J., Tucker, J.: Characterization of computable data types by means of a finite equational specification method. In: de Bakker, J.W., van Leeuwen, J. (eds.) Seventh Colloquium on Automata, Languages and Programming. LNCS, vol. 81, pp. 76–90. Springer, Heidelberg (1980)

    Chapter  Google Scholar 

  6. Bouhoula, A.: Simultaneous checking of completeness and ground confluence for algebraic specifications. ACM Transactions on Computational Logic 10(3) (2009)

    Google Scholar 

  7. Bouhoula, A., Jouannaud, J.-P., Meseguer, J.: Specification and proof in membership equational logic. Theoretical Computer Science 236(1), 35–132 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  9. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C. (eds.): All About Maude - A High-Performance Logical Framework: How to Specify, Program, and Verify Systems in Rewriting Logic. LNCS, vol. 4350. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  10. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: Maude 2.4 manual (November 2008), http://maude.cs.uiuc.edu

  11. 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 

  12. Clavel, M., Palomino, M., Riesco, A.: Introducing the ITP tool: a tutorial. Journal of Universal Computer Science 12(11), 1618–1650 (2006)

    Google Scholar 

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

  14. 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 

  15. 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)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. 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

  18. Durán, F., Meseguer, J.: A Maude coherence checker tool for conditional order-sorted rewrite theories. In: Olveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 86–103. Springer, Heidelberg (2010)

    Google Scholar 

  19. 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 

  20. 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 International Workshop on Rewriting Logic and its Applications (WRLA 2008). Electronic Notes in Theoretical Computer Science. Elsevier, Amsterdam (2008)

    Google Scholar 

  21. 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 

  22. Gnaedig, I., Kirchner, C., Kirchner, H.: Equational completion in order-sorted algebras. Theoretical Computer Science 72, 169–202 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  23. Goguen, J., Meseguer, J.: Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science 105, 217–273 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hendrix, J., Meseguer, J., Ohsaki, H.: A sufficient completeness checker for linear order-sorted specifications modulo axioms. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 151–155. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  25. 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 

  26. Kapur, D., Narendran, P., Otto, F.: On ground-confluence of term rewriting systems. Information and Computation 86(1), 14–31 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  27. Kirchner, C., Kirchner, H., Meseguer, J.: Operational semantics of OBJ3. In: Lepistö, T., Salomaa, A. (eds.) ICALP 1988. LNCS, vol. 317, pp. 287–301. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  28. Martin, U., Nipkow, T.: Ordered rewriting and confluence. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 366–380. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

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

    Book  MATH  Google Scholar 

  30. 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 

  31. Plaisted, D.: Semantic confluence tests and completion methods. Information and Control 65, 182–215 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  32. Rocha, C., Meseguer, J.: Constructors, sufficient completeness, deadlock states of rewrite theories. Technical Report 2010-05-1, CS Dept., University of Illinois at Urbana-Champaign (May 2010), http://ideals.illinois.edu

  33. 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 Church-Rosser Checker Tool for Conditional Order-Sorted Equational Maude Specifications. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-16310-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16309-8

  • Online ISBN: 978-3-642-16310-4

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