Abstract
We relate Kamin and Lévy’s original presentation of lexicographic path orders (LPO), using an inductive definition, to a presentation, which we will refer to as iterative lexicographic path orders (ILPO), based on Bergstra and Klop’s definition of recursive path orders by way of an auxiliary term rewriting sytem.
This is a preview of subscription content, log in via an institution to check access.
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
Dershowitz, N.: Orderings for term rewriting systems. TCS 17(3), 279–301 (1982)
Marcone, A.: Fine analysis of the quasi-orderings on the power set. Order 18, 339–347 (2001)
Bergstra, J., Klop, J.: Algebra of communicating processes. TCS 37(1), 171–199 (1985)
Bergstra, J., Klop, J., Middeldorp, A.: Termherschrijfsystemen. In: Programmatuurkunde, Kluwer Academic Publishers, Dordrecht (1989)
Buchholz, W.: Proof-theoretic analysis of termination proofs. APAL 75(1-2), 57–65 (1995)
Kamin, S., Lévy, J.J.: Two generalizations of the recursive path ordering. University of Illinois (1980)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Geser, A.: Relative Termination. PhD thesis, Universität Passau, Germany (1990)
Klop, J.: Term rewriting systems. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science. Background: Computational Structures, vol. 2, pp. 1–116. Oxford University Press, Oxford (1992)
Terese: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55, Cambridge University Press, Cambridge (2003)
Dedekind, R.: Was sind und was sollen die Zahlen?, Brunswick (1888)
Dershowitz, N., Jouannaud, J.P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 243–320. Elsevier, Amsterdam (1990)
Jouannaud, J.P., Rubio, A.: The higher-order recursive path ordering. In: 14th Annual IEEE Symposium on Logic in Computer Science, pp. 402–411. IEEE Computer Society, Los Alamitos (1999)
Bundy, A., Basin, D., Hutter, D., Ireland, A.: Rippling: Meta-Level Guidance for Mathematical Reasoning. Cambridge Tracts in Theoretical Computer Science, vol. 56. Cambridge University Press, Cambridge (2005)
Persson, H.: Type Theory and the Integrated Logic of Programs. PhD thesis, Chalmers, Sweden (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Klop, J.W., van Oostrom, V., de Vrijer, R. (2006). Iterative Lexicographic Path Orders. In: Futatsugi, K., Jouannaud, JP., Meseguer, J. (eds) Algebra, Meaning, and Computation. Lecture Notes in Computer Science, vol 4060. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780274_28
Download citation
DOI: https://doi.org/10.1007/11780274_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35462-8
Online ISBN: 978-3-540-35464-2
eBook Packages: Computer ScienceComputer Science (R0)