Unification and Narrowing in Maude 2.4

  • Manuel Clavel
  • Francisco Durán
  • Steven Eker
  • Santiago Escobar
  • Patrick Lincoln
  • Narciso Martí-Oliet
  • José Meseguer
  • Carolyn Talcott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5595)


Maude is a high-performance reflective language and system supporting both equational and rewriting logic specification and programming for a wide range of applications, and has a relatively large worldwide user and open-source developer base. This paper introduces novel features of Maude 2.4 including support for unification and narrowing. Unification is supported in Core Maude, the core rewriting engine of Maude, with commands and metalevel functions for order-sorted unification modulo some frequently occurring equational axioms. Narrowing is currently supported in its Full Maude extension. We also give a brief summary of the most important features of Maude 2.4 that were not part of Maude 2.0 and earlier releases. These features include communication with external objects, a new implementation of its module algebra, and new predefined libraries. We also review some new Maude applications.


Equational Theory External Object Linear Temporal Logic Module Algebra Reachability Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alpuente, M., Escobar, S., Iborra, J.: Modular termination of basic narrowing. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 1–16. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Bae, K., Meseguer, J.: A rewriting-based model checker for the linear temporal logic of rewriting. In: Procs. of RULE 2008. ENTCS (to appear) (2008)Google Scholar
  3. 3.
    Boronat, A., Meseguer, J.: An Algebraic semantics for MOF. In: Fiadeiro, J.L., Inverardi, P. (eds.) FASE 2008. LNCS, vol. 4961, pp. 377–391. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Boudet, A., Contejean, E., Devie, H.: A new AC unification algorithm with an algorithm for solving systems of diophantine equations. In: Procs. of LICS 1990, pp. 289–299 (1990)Google Scholar
  5. 5.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Quesada, J.: The Maude system. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 240–243. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, J.: The Maude 2.0 system. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 14–29. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.L.: Maude Manual (v. 2.4), SRI Intl. & U. of Illinois at Urbana-Champaign (October 2008), http://maude.cs.uiuc.edu
  9. 9.
    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
  10. 10.
    Contejean, E., Devie, H.: An efficient incremental algorithm for solving systems of linear diophantine equations. Information and Computation 113(1), 143–172 (1994)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Contejean, E., Marché, C., Urbain, X.: CiME 3 (2004), http://cime.lri.fr/
  12. 12.
    Durán, F., Meseguer, J.: Maude’s module algebra. Sci. Comp. Progr. 66(2), 125–153 (2007)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Eker, S.: Unification in Maude. Talk at the Protocol eXchange Seminar, Naval Postgraduate School (January 2007), http://maude.cs.uiuc.edu/talks/eker-unification.pdf
  14. 14.
    Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL Protocol Analyzer and its meta-logical properties. Theor. Comput. Sci. 367(1-2), 162–202 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    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
  16. 16.
    Escobar, S., Meseguer, J., Sasse, R.: Effectively checking the finite variant property. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 79–93. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Escobar, S., Meseguer, J., Sasse, R.: Variant narrowing and equational unification. In: Procs. of WRLA 2008, pp. 88–102. ENTCS (2008)Google Scholar
  18. 18.
    Jouannaud, J.-P., Kirchner, C., Kirchner, H.: Incremental construction of unification algorithms in equational theories. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 361–373. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  19. 19.
    Hullot, J.-M.: Canonical forms and unification. In: Bibel, W. (ed.) CADE 1980. LNCS, vol. 87, pp. 318–334. Springer, Heidelberg (1980)Google Scholar
  20. 20.
    Martí-Oliet, N., Meseguer, J., Verdejo, A.: Towards a strategy language for Maude. In: Procs. of WRLA 2004. ENTCS, vol. 117, pp. 417–441 (2005)Google Scholar
  21. 21.
    Meseguer, J., Roşu, G.: The rewriting logic semantics project. Theor. Comput. Sci. 373(3), 213–237 (2007)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Meseguer, J., Thati, P.: Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols. High.-Ord. Symb. Comp. 20(1-2), 123–160 (2007)CrossRefMATHGoogle Scholar
  23. 23.
    Rivera, J.E., Vallecillo, A.: Adding behavioral semantics to models. In: Procs. of EDOC 2007, pp. 169–180 (2007)Google Scholar
  24. 24.
    Şerbănuţă, T.F., Roşu, G., Meseguer, J.: A rewriting logic approach to operational semantics. Information and Computation. (available online December 6, 2008) (in press)Google Scholar
  25. 25.
    Viola, E.: E-unifiability via narrowing. In: Restivo, A., Ronchi Della Rocca, S., Roversi, L. (eds.) ICTCS 2001. LNCS, vol. 2202, pp. 426–438. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Manuel Clavel
    • 1
    • 2
  • Francisco Durán
    • 3
  • Steven Eker
    • 4
  • Santiago Escobar
    • 5
  • Patrick Lincoln
    • 4
  • Narciso Martí-Oliet
    • 2
  • José Meseguer
    • 6
  • Carolyn Talcott
    • 4
  1. 1.IMDEA SoftwareMadridSpain
  2. 2.Universidad Complutense de MadridSpain
  3. 3.Universidad de MálagaSpain
  4. 4.SRI InternationalUSA
  5. 5.Universidad Politécnica de ValenciaSpain
  6. 6.University of Illinois at Urbana-ChampaignUSA

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