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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
The Coq Proof Assistant, http://coq.inria.fr/
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)
Barendregt, H.P.: The Lambda Calculus, Its Syntax and Semantics. Studies in Logic and the Foundation of Mathematics, vol. 103. Elsevier, Amsterdam (1984)
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
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)
Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. Journal of Automated Reasoning (2008)
Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting systems. Appl. Algebra Eng., Commun. Comput. 15(3), 149–171 (2004)
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)
Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 249–268. Springer, Heidelberg (2004)
Koprowski, A.: Termination of Rewriting and Its Certification. PhD thesis, Eindhoven University of Technology (2008)
Lucas, S.: Context-Sensitive Computations in Functional and Functional Logic Programs. Journal of Functional and Logic Programming 1998(1) (1998)
Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, New York (2002)
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)
Raffelsieper, M., Zantema, H.: A transformational approach to prove outermost termination automatically. Technical report, RISC-Linz Report Series (2008)
Terese: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)
Waldmann, J.: The combinator S. Information and Computation 159, 2–21 (2000)
Zantema, H.: Termination of term rewriting by semantic labelling. Fundamenta Informaticae 24, 89–105 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Endrullis, J., de Vrijer, R., Waldmann, J. (2009). Local Termination. In: Treinen, R. (eds) Rewriting Techniques and Applications. RTA 2009. Lecture Notes in Computer Science, vol 5595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02348-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-02348-4_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02347-7
Online ISBN: 978-3-642-02348-4
eBook Packages: Computer ScienceComputer Science (R0)