MTT: The Maude Termination Tool (System Description)

  • Francisco Durán
  • Salvador Lucas
  • José Meseguer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5195)


Despite the remarkable development of the theory of termination of rewriting, its application to high-level programming languages is far from being optimal. This is due to the need for features such as conditional equations and rules, types and subtypes, (possibly programmable) strategies for controlling the execution, matching modulo axioms, and so on, that are used in many programs and tend to place such programs outside the scope of current termination tools.The operational meaning of such features is often formalized in a proof-theoretic manner by means of an inference system (see, e.g., [2, 3, 17]) rather than just by a rewriting relation. In particular, Generalized Rewrite Theories (GRT) [3] are a recent generalization of rewrite theories at the heart of the most recent formulation of Maude [4].


Matching Condition Theory Transformation Termination Tool Termination Competition Conditional Rule 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Borovanský, P., Kirchner, C., Kirchner, H., Moreau, P.-E.: ELAN from a rewriting logic point of view. Theoretical Computer Science 285, 155–185 (2002)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bouhoula, A., Jouannaud, J.-P., Meseguer, J.: Specification and proof in membership equational logic. Theoretical Computer Science 236, 35–132 (2000)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bruni, R., Meseguer, J.: Semantic foundations for generalized rewrite theories. Theoretical Computer Science 351(1), 386–414 (2006)CrossRefMathSciNetGoogle Scholar
  4. 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)MATHGoogle Scholar
  5. 5.
    Durán, F., Lucas, S., Marché, C., Meseguer, J., Urbain, X.: Proving Termination of Membership Equational Programs. In: Sestoft, P., Heintze, N. (eds.) Proc. of ACM SIGPLAN 2004 Symposium on Partial Evaluation and Program Manipulation, PEPM 2004, pp. 147–158. ACM Press, New York (2004)CrossRefGoogle Scholar
  6. 6.
    Durán, F., Lucas, S., Marché, C., Meseguer, J., Urbain, X.: Proving Operational Termination of Membership Equational Programs. Higher-Order and Symbolic Computation (published online) (to appear, April 2008)Google Scholar
  7. 7.
    Durán, F., Lucas, S., Meseguer, J.: Operational Termination in Rewriting Logic. Technical Report 2008 (2008),
  8. 8.
    Futatsugi, K., Diaconescu, R.: CafeOBJ Report. AMAST Series. World Scientific (1998)Google Scholar
  9. 9.
    Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE1.2. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006), CrossRefGoogle Scholar
  10. 10.
    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)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Lucas, S.: Context-sensitive computations in functional and functional logic programs. Journal of Functional and Logic Programming 1998(1), 1–61 (1998)Google Scholar
  12. 12.
    Lucas, S.: Context-sensitive rewriting strategies. Information and Computation 178(1), 294–343 (2002)MATHMathSciNetGoogle Scholar
  13. 13.
    Lucas, S.: MU-TERM: A Tool for Proving Termination of Context-Sensitive Rewriting. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 200–209. Springer, Heidelberg (2004), Google Scholar
  14. 14.
    Lucas, S., Marché, C., Meseguer, J.: Operational termination of conditional term rewriting systems. Information Processing Letters 95(4), 446–453 (2005)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Lucas, S., Meseguer, J.: Operational Termination of Membership Equational Programs: the Order-Sorted Way. In: Rosu, G. (ed.) Proc. of the 7th International Workshop on Rewriting Logic and its Applications, WRLA 2008. Electronic Notes in Theoretical Computer Science (to appear, 2008)Google Scholar
  16. 16.
    Marché, C., Zantema, H.: The termination competition. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 303–313. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)Google Scholar
  18. 18.
    Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002)MATHGoogle Scholar
  19. 19.
    Ölveczky, P.C., Lysne, O.: Order-Sorted Termination: The Unsorted Way. In: Hanus, M., Rodríguez-Artalejo, M. (eds.) ALP 1996. LNCS, vol. 1139, pp. 92–106. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Francisco Durán
    • 1
  • Salvador Lucas
    • 2
  • José Meseguer
    • 3
  1. 1.LCCUniversidad de MálagaSpain
  2. 2.DSICUniversidad Politécnica de ValenciaSpain
  3. 3.CS Dept.University of Illinois at Urbana-ChampaignUSA

Personalised recommendations