Abstract
In this paper we introduce a notion of recurrence-terms for finitely representing infinite sequences of terms. A recurrence-term utilizes the structural similarities among terms and expresses them explicitly using recurrence relations. Its formalism is natural and simple, and based on which algebraic operations such as unification, matching, and reductions can be defined. Recurrence-rewrite rules, defined respectively, also yield finite representation of certain divergent term rewriting systems.
Recurrence-rules do not only play a passive role in detecting divergence, they can also be incorporated as part of the completion process. In addition to giving the formalism, we present methods of inferring recurrence-terms from finite sets of regular terms, and a matching algorithm between a recurrence-term and a regular term. Recurrence-term rewriting systems are also defined, and we prove the equivalence between a recurrence-system and the (infinite) term rewriting system it schematizes, as well as the preservation of desirable properties such as termination and confluence.
This work was partially supported by NSF grants INT-8715231, CCR-8805734, and CCR-8901322
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References
H. Chen, J. Hsiang, Logic Programming with Recurrence Domains, in preparation.
H. Comon, Inductive Proofs by Specifications Transformation, RTA 89, LNCS 355, Page 76–91, Springer-Berlag, April 1989.
N. Dershowitz, Ordering for Term Rewriting Systems, Theoretical Computer Science, 17, 1982, Page 279–301
M. Hermann, H. Hirchner, Meta-rule Synthesis from Crossed Rewrite Systems, CTRS 90, June 11–14, 1990, Montreal, Canada.
M. Hermann, Chain Properties of Rule Closures, Lecture Notes in CS, Stacs 89, 349, Page 339–347.
M. Hermann, I. Privara, On Nontermination of Knuth-Bendix Algorithm, Automata, Languages and Programming, 13th International Colloquium, Rennes, France, July 1986, Ed G.Goos and J. Hartmanis, Page 146–156.
H. Kirchner, Schematization of Infinite Sets of Rewrite Rules, Application to the Divergence of Completion Processes, Lecture Notes in CS, Rewriting Techniques and Applications, Bordequs, France, May 1987, Page 180–191.
H. Kirchner, Schematization of Infinite Sets of Rewrite Rules, Application to the Divergence of Completion Processes, Theoretical Computer Science 67 (1989) 303–332.
H. C. Kong, The Embedding Property and Its Application to Divergent Term Rewriting Systems, M.S. thesis, Dept of Computer Science, National Taiwan University, June 1989.
J.B. Kruskal, The Theory of Well-quasi-ordering: A Frequently Discovered Concept, J. Combinatorial Theory Ser.A 13(3), pp. 297–305, November 1972.
S. Lange, K. Jantke, Towards A Learning Calculus for Solving Divergence in Knuth-Bendix Completion, Communications of the Algorithm Learning Group, Nov. 1989
P. Mishra, U. Reddy, Declaration-free Type Checking, POPL 1985, Page 7–21.
R. Mong, P. Purdom, Divergence in the Completion of Rewriting Systems, Memo.
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© 1991 Springer-Verlag Berlin Heidelberg
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Chen, H., Hsiang, J., Kong, HC. (1991). On finite representations of infinite sequences of terms. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_83
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DOI: https://doi.org/10.1007/3-540-54317-1_83
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