Abstract
We give a short constructive proof of the fact that certain binary relations > are well-founded, given a lifting ≫ á la Ferreira-Zantema and a well-founded relation>. This construction generalizes several variants of the recursive path ordering on terms and of the Knuth-Bendix ordering. It also applies to other domains, of graphs, of infinite terms, of word and tree automata notably. We then extend this construction further; the resulting family of well-founded relations generalizes Jouannaud and Rubio’s higher-order recursive path orderings.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
B. Barras, S. Boutin, C. Cornes, J. Courant, Y. Coscoy, D. Delahaye, D. de Rauglaudre, J.-C. Filliâtre, E. Giménez, H. Herbelin, G. Huet, H. Laulhère, C. Muñoz, C. Murthy, C. Parent-Vigouroux, P. Loiseleur, C. Paulin-Mohring, A. Saïbi, and B. Werner. The Coq proof assistant-reference manual. Available at http://coq.inria.fr/doc/main.html., Dec. 1999. Version 6.3.1.
P. Cousot. Semantic foundations of program analysis. In S. Muchnick and N. Jones, editors, Program Flow Analysis: Theory and Applications, chapter 10, pages 303–342. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1981.
N. Dershowitz. Orderings for term rewriting systems. Theoretical Computer Science, 17(3):279–301, 1982.
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69–116, 1987.
N. Dershowitz and C. Hoot. Topics in termination. In C. Kirchner, editor, 5th RTA, pages 198–212. Springer Verlag LNCS 690, 1983.
G. Dowek and B. Werner. Proof normalization modulo. Research Report RR-3542, INRIA, Nov. 1998.
M. Fernández and J.-P. Jouannaud. Modular termination of term rewriting systems revisited. In E. Astesiano, G. Reggio, and A. Tarlecki, editors, Recent Trends in Data Type Specification. Springer-Verlag LNCS 906, 906.
M. C. F. Ferreira and H. Zantema. Well-foundedness of term orderings. In N. Dershowitz, editor, 4th International Workshop on Conditional Term Rewriting Systems (CTRS’94), pages 106–123. Springer Verlag LNCS 968, 1995.
F. Gécseg and M. Steinby. Tree languages. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 3, chapter 1, pages 1–68. Springer-Verlag, 1997. Beyond Words.
J.-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types, volume 7 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1989.
J. Goubault-Larrecq. A method for automatic cryptographic protocol verification (extended abstract). In FMPPTA’2000, pages 977–984. Springer Verlag LNCS 1800, 2000.
H. Herbelin, Dec. 1996. Private communication.
J.-P. Jouannaud and A. Rubio. The higher-order recursive path ordering. In G. Longo, editor, 14th LICS, pages 402–411, Trento, Italy, July 1999.
J.-P. Jouannaud and A. Rubio. Higher-order recursive path orderings á la carte. Draft available at ftp://ftp.lri.fr/LRI/articles/jouannaud/horpo-full.ps.gz, 2001.
S. Kamin and J.-J. Lévy. Two generalizations of the recursive path ordering. Technical report, University of Illinois, 1980.
P.-A. Melliès. On a duality between Kruskal and Dershowitz theorems. In 25th ICALP, pages 518–529. Springer Verlag LNCS 1443, 1998.
D. Monniaux. Abstracting cryptographic protocols with tree automata. In 6th International Static Analysis Symposium (SAS’99). Springer-Verlag LNCS 1694, 1999.
C. Thomassen. Embeddings and minors. In R. Graham, M. Grötschel, and L. Lovász, editors, Handbook of Combinatorics, chapter 5. Elsevier Science B.V., 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goubault-Larrecq, J. (2001). Well-Founded Recursive Relations. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_34
Download citation
DOI: https://doi.org/10.1007/3-540-44802-0_34
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42554-0
Online ISBN: 978-3-540-44802-0
eBook Packages: Springer Book Archive