Abstract
Properties of Term Rewriting Systems are called modular iff they are preserved under disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a limit. Strong Convergence requires in addition that no redex position in a reduction sequence is used infinitely often.
In this paper it is shown that Strong Convergence is a modular property, lifting a restriction from a known result by Simonsen, and that Convergence is modular for non-collapsing Infinitary Term Rewriting Systems.
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
Arnold, A., Nivat, M.: Metric interpretations of infinite trees and semantics of nondeterministic recursive programs. Theoretical Computer Science 11(2), 181–205 (1980)
Dershowitz, N., Kaplan, S.: Rewrite, Rewrite, Rewrite, Rewrite, Rewrite,.. In: Principles of Programming Languages, pp. 250–259. ACM, New York (1989)
Hajnal, A., Hamburger, P.: Set Theory. London Mathematical Society (1999)
Kahrs, S.: Infinitary rewriting: Meta-theory and convergence. Acta Informatica 44(2), 91–121 (2007)
Kennaway, R.: On transfinite abstract reduction systems. Technical Report CS-R9205, Centrum voor Wiskunde en Informatica, Amsterdam (1992)
Kennaway, R., de Vries, F.-J.: Infinitary Rewriting. In: Term Rewriting Systems, pp. 668–711. Cambridge University Press, Cambridge (2003)
Ketema, J.: Böhm-Like Trees for Rewriting. PhD thesis, Vrije Universiteit Amsterdam (2006)
Potter, M.D.: Sets: An Introduction. Oxford University Press, Oxford (1990)
Sierpiński, W.: Cardinal and Ordinal Numbers. Polish Scientific Publishers (1965)
Simonsen, J.G.: On modularity in infinitary term rewriting. Information and Computation 204(6), 957–988 (2006)
Terese (ed.): Term Rewriting Systems. Cambridge University Press, Cambridge (2003)
Toyama, Y.: On the Chuch-Rosser property for the direct sum of term rewriting systems. Journal of the ACM 34(1), 128–143 (1987)
Zantema, H.: Normalisation of infinite terms. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 441–455. Springer, Heidelberg (2008)
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
Kahrs, S. (2009). Modularity of Convergence in Infinitary Rewriting. 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_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-02348-4_13
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)