Abstract
We investigate combinatorial commutation properties for reordering a sequence of two kinds of steps, and for separating well-foundedness of unions of relations. To that end, we develop the notion of a constricting sequence. These results can be applied, for example, to generic path orderings used in termination proofs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science, vol. 236, pp. 133–178 (2000)
Bachmair, L., Dershowitz, N.: Commutation, transformation, and termination. In: Siekmann, J.H. (ed.) CADE 1986. LNCS, vol. 230, pp. 5–20. Springer, Heidelberg (1986), http://www.cs.tau.ac.il/~nachum/papers/CommutationTermination.pdf
Blanqui, F., Jouannaud, J.-P., Rubio, A.: HORPO with computability closure: A reconstruction. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS, vol. 4790, pp. 138–150. Springer, Heidelberg (2007)
Blass, A., Gurevich, Y.: Program termination and well partial orderings. ACM Transactions on Computational Logic (TOCL) 9(3), Article No. 18 (June 2008), http://research.microsoft.com/en-us/um/people/gurevich/opera/178.pdf
Di Cosmo, R., Piperno, A.: Expanding extensional polymorphism. In: Dezani-Ciancaglini, M., Plotkin, G.D. (eds.) TLCA 1995. LNCS, vol. 902, pp. 139–153. Springer, Heidelberg (1995)
Dawson, J.E., Gore, R.: Termination of abstract reduction systems. In: Proceedings of Computing: The Australasian Theory Symposium (CATS 2007), Ballarat, Australia, pp. 35–43 (2007)
Dershowitz, N.: Termination of linear rewriting systems (Preliminary version). In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 448–458. Springer, Heidelberg (1981), http://www.cs.tau.ac.il/~nachum/papers/Linear.pdf
Dershowitz, N.: Orderings for term-rewriting systems. Theoretical Computer Science 17(3), 279–301 (1982)
Dershowitz, N.: Termination of rewriting. J. of Symbolic Computation 3, 69–116 (1987)
Dershowitz, N.: Termination by abstraction. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 1–18. Springer, Heidelberg (2004), http://www.cs.tau.ac.il/~nachum/papers/TerminationByAbstraction.pdf
Dershowitz, N., Hoot, C.: Natural termination. Theoretical Computer Science 142(2), 179–207 (1995)
Dershowitz, N., Manna, Z.: Proving termination with multiset orderings. Communications of the ACM 22(8), 465–476 (1979)
Doornbos, H., Backhouse, R., van der Woude, J.: A calculational approach to mathematical induction. Theoretical Computer Science 179, 103–135 (1997)
Doornbos, H., von Karger, B.: On the union of well-founded relations. Logic Journal of the IGPL 6(2), 195–201 (1998)
Fernández, M., Jouannaud, J.-P.: Modular termination of term rewriting systems revisited. In: Astesiano, E., Reggio, G., Tarlecki, A. (eds.) Recent Trends in Data Type Specification. LNCS, vol. 906, pp. 255–272. Springer, Heidelberg (1995)
Ferreira, M.C.F., Zantema, H.: Well-foundedness of term orderings. In: Dershowitz, N. (ed.) CTRS 1994. LNCS, vol. 968, pp. 106–123. Springer, Heidelberg (1995)
Geser, A.: Relative Termination, Ph.D. dissertation, Fakultät für Mathematik und Informatik, Universität Passau, Germany (1990); also available as: Report 91-03, Ulmer Informatik-Berichte, Universität Ulm (1991), http://ginevras.pil.fbeit.htwk-leipzig.de/pil-website/public_html/geser/diss_geser.ps.gz .
Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems. J. of the Association for Computing Machinery 27(4), 797–821 (1980)
Goubault-Larrecq, J.: Well-founded recursive relations. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 484–497. Springer, Heidelberg (2001)
Hindley, J.R.: The Church-Rosser Property and a Result in Combinatory Logic, Ph.D. thesis, University of Newcastle upon Tyne (1964)
Jouannaud, J.-P., Rubio, A.: Higher-order recursive path orderings. In: Proceedings 14th Annual IEEE Symposium on Logic in Computer Science (LICS), Trento, Italy, pp. 402–411 (1999)
Kamin, S., Lévy, J.-J.: Attempts for generalising the recursive path orderings, unpublished note, Department of Computer Science, University of Illinois, Urbana, IL (February 1980), http://pauillac.inria.fr/~levy/pubs/80kamin.pdf
Klop, J.W.: Combinatory Reduction Systems, Mathematical Centre Tracts 127, CWI, Amsterdam, The Netherlands (1980)
Lescanne, P.: On the recursive decomposition ordering with lexicographical status and other related orderings. J. Automated Reasoning 6(1), 39–49 (1990)
Melliès, P.-A.: On a duality between Kruskal and Dershowitz theorems. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 518–529. Springer, Heidelberg (1998)
Nash-Williams, C.St.J.A.: On well-quasi-ordering finite trees. Proceedings Cambridge Phil. Soc. 59, 833–835 (1963)
Newman, M.H.A.: On theories with a combinatorial definition of “equivalence”. Annals of Mathematics 43(2), 223–243 (1942)
Plaisted, D.A.: Semantic confluence tests and completion methods. Information and Control 65(2/3), 182–215 (1985)
Porat, S., Francez, N.: Full-commutation and fair-termination in equational (and combined) term-rewriting systems. In: Siekmann, J.H. (ed.) CADE 1986. LNCS, vol. 230, pp. 21–41. Springer, Heidelberg (1986)
Staples, J.: Church-Rosser theorems for replacement systems. In: Crosley, J. (ed.) Algebra and Logic. Lecture Notes in Mathematics, vol. 450, pp. 291–307. Springer, Heidelberg (1975)
Struth, G.: Reasoning automatically about termination and refinement (Abstract). In: International Workshop on First-Order Theorem Proving (FTP 2007), Liverpool, UK (September 2007). Full Version at: http://www.dcs.shef.ac.uk/intranet/research/resmes/CS0710.pdf
Struth, G.: Personal communication (November 2007)
“Terese” (Bezem, M., Klop, J.W., de Vrijer, R., eds.): Term Rewriting Systems. Cambridge University Press, Cambridge (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dershowitz, N. (2009). On Lazy Commutation. In: Grumberg, O., Kaminski, M., Katz, S., Wintner, S. (eds) Languages: From Formal to Natural. Lecture Notes in Computer Science, vol 5533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01748-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-01748-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01747-6
Online ISBN: 978-3-642-01748-3
eBook Packages: Computer ScienceComputer Science (R0)