Advertisement

Local Termination

  • Jörg Endrullis
  • Roel de Vrijer
  • Johannes Waldmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5595)

Abstract

The characterization of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic characterization and most known termination methods are concerned with global termination, uniformly of all the terms of a term rewriting system (TRS). In this paper we consider local termination, of specific sets of terms within a given TRS.

The principal goal of this paper is generalizing the semantic characterization of global termination to local termination. This is made possible by admitting the well-founded monotone algebras to be partial. We show that our results can be applied in the development of techniques for proving local termination. We give several examples, among which a verifiable characterization of the terminating S-terms in CL.

Keywords

Normal Form Turing Machine Partial Model Global Termination Local Termination 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    The Coq Proof Assistant, http://coq.inria.fr/
  2. 2.
    Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Barendregt, H.P.: The Lambda Calculus, Its Syntax and Semantics. Studies in Logic and the Foundation of Mathematics, vol. 103. Elsevier, Amsterdam (1984)zbMATHGoogle Scholar
  4. 4.
    Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (2007), http://www.grappa.univ-lille3.fr/tata
  5. 5.
    Endrullis, J., Grabmayer, C., Hendriks, D., Klop, J.W., de Vrijer, R.C.: Proving Infinitary Normalization. In: Berardi, S., Damiani, F., de’Liguoro, U. (eds.) TYPES 2008. LNCS, vol. 5497, pp. 64–82. Springer, Heidelberg (2009)Google Scholar
  6. 6.
    Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. Journal of Automated Reasoning (2008)Google Scholar
  7. 7.
    Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting systems. Appl. Algebra Eng., Commun. Comput. 15(3), 149–171 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Giesl, J., Swiderski, S., Thiemann, R., Schneider-Kamp, P.: Automated termination analysis for Haskell: From term rewriting to programming languages. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 297–312. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 249–268. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Koprowski, A.: Termination of Rewriting and Its Certification. PhD thesis, Eindhoven University of Technology (2008)Google Scholar
  11. 11.
    Lucas, S.: Context-Sensitive Computations in Functional and Functional Logic Programs. Journal of Functional and Logic Programming 1998(1) (1998)Google Scholar
  12. 12.
    Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, New York (2002)CrossRefzbMATHGoogle Scholar
  13. 13.
    Panitz, S.E., Schmidt-Schauß, M.: TEA: Automatically proving termination of programs in a non-strict higher-order functional language. In: Van Hentenryck, P. (ed.) SAS 1997. LNCS, vol. 1302. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  14. 14.
    Raffelsieper, M., Zantema, H.: A transformational approach to prove outermost termination automatically. Technical report, RISC-Linz Report Series (2008)Google Scholar
  15. 15.
    Terese: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)Google Scholar
  16. 16.
    Waldmann, J.: The combinator S. Information and Computation 159, 2–21 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Zantema, H.: Termination of term rewriting by semantic labelling. Fundamenta Informaticae 24, 89–105 (1995)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jörg Endrullis
    • 1
  • Roel de Vrijer
    • 1
  • Johannes Waldmann
    • 2
  1. 1.Vrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Hochschule für Technik, Wirtschaft und Kultur (FH) LeipzigLeipzigGermany

Personalised recommendations