Abstract
Huet and Lévy defined the (orthogonal) strongly sequential term rewriting systems, for which index reduction, i.e., reduction of redexes placed at special positions called (strong) indices, is optimal and normalizing. Despite the fact that Huet and Lévy give an algorithm to compute indices for the general case, there are many proposals to define subclasses of strongly sequential rewrite systems for which this can be done more efficiently. In this paper, we show that sometimes it is possible to enlarge such classes by only introducing fixed replacement restrictions, without forcing any sensible modification of the corresponding index reduction strategy.
Work partially supported by Bancaixa (Bancaxa-Europa grant) and CICYT (under grant TIC 95-0433-C03-03).
Preview
Unable to display preview. Download preview PDF.
References
S. Antoy and A. Middeldorp. A Sequential Reduction Strategy. Theoretical Computer Science 165:75–95, 1996.
G. Huet and J.J. Lévy. Computations in orthogonal term rewriting systems. In Computational logic: essays in honour of J. Alan Robinson, MIT Press, 1991.
J.W. Klop. Term Rewriting Systems. In Handbook of Logic in Computer Science, volume 3, pages 1–116. Oxford University Press, 1992.
J.W. Klop and A. Middeldorp. Sequentiality in Orthogonal Term Rewriting Systems. Journal of Symbolic Computation 12:161–195, 1991.
S. Lucas. Context-sensitive computations in functional and functional logic programs. Journal of Functional and Logic Programming, 1997, to appear.
S. Lucas. Needed Reductions with Context-Sensitive Rewriting. In Proc. of ALP'97, LNCS to appear.
S. Lucas. Termination of Context-Sensitive Rewriting by Rewriting. In Proc. of ICALP'96, LNCS 1099:122–133, Springer-Verlag, 1996.
M.J. O'Donnell. Equational Logic as a Programming Language. The MIT Press, 1985.
R.C. Sekar, S. Pawagi and I.V. Ramakrishnan. Transforming Strongly Sequential Rewrite Systems with Constructors for Efficient Parallel Execution. In Proc. of RTA'89, LNCS 355:404–418, 1989.
Y. Toyama, S. Smetsers, M.C.J.D. van Eekelen and R. Plasmeijer. The Functional Strategy and Transitive Term Rewriting Systems. Term Graph Rewriting — Theory and Practice, pages 117–129, John Wiley & sons, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lucas, S. (1997). Efficient strong sequentiality using replacement restrictions. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_130
Download citation
DOI: https://doi.org/10.1007/3-540-63774-5_130
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63774-5
Online ISBN: 978-3-540-69645-2
eBook Packages: Springer Book Archive