Abstract
This paper gives an operational semantics of priority term rewriting systems (PRS) by using conditional systems, whose reduction is decidable and stable under substitution. We also define the class of strong sequential PRSs and show that this class is decidable. Moreover, we show that the index rewriting of strong sequential PRSs gives a normalizing strategy.
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J. C. M. Baeten, J. A. Bergstra, J. W. Klop, and W. P. Weijland. Term rewriting systems with rule priorities. Theoretical Computer Science, 67:283–301, 1989.
H. Comon. Sequentiality, second order monadic logic and tree automata. In Logic in Computer Science, pages 508–517, 1995.
N. Dershouwitz and J.-P. Jouannaud. Rewrite Systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, pages 243–320. North-Holland, 1990.
P. Henderson. Functional Programming. Prentice Hall International, 1980.
G. Huet and J.-J. Lévy. Call by need computations in non-ambiguous linear term rewriting systems. Technical Report 359, INRIA, 1979.
G. Huet. Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems. Journal of Association for Computing Machinery, 27(4):797–21, October 1980.
S. L. P. Jones. The Implementation of Functional Programming Languages. Prentice Hall International, 1987.
J. W. Klop. Term rewriting systems. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science, volume I. Oxford University Press, 1992.
J. W. Klop and A. Middeldorp. Sequentiality in orthogonal term rewritng systems. J. Symbolic Computation, 12:161–195, 1991.
C. K. Mohan. Priority rewriting: Semantics, confluence, and conditionals. In LNCS, volume 355, pages 278–291. Springer-Verlag, 1989.
R. Plasmeijer and M. van Eekelen. Functional Programming and Parallel Graph Rewriting. Addison-wesley, 1993.
M. Rabin. Decidable theories. In J. Barwise, editor, Handbook of Mathematical Logic, pages 595–629. North-Holland, 1977.
W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 134–191. Elsevier, 1990.
Y. Toyama. Strong sequentiality of left-linear overlapping term rewriting systems. In Proc. of the 7'th annual IEEE Symposium on Login in Computer Science, pages 274–284, 1992.
Y. Toyama, S. Smetsers, M. van Eekelen, and R. Plasmeijer. The Functional Strategy and Transitive Term Rewriting Systems. In Ronan Sleep, Rinus Plasmeijer, and Marko van Eelkelen, editors, Term Graph Rewriting: Theory and Practice, pages 61–75. John Wiley & Sons Ltd, 1993.
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Sakai, M., Toyama, Y. (1996). Semantics and strong sequentially of priority term rewriting systems. In: Ganzinger, H. (eds) Rewriting Techniques and Applications. RTA 1996. Lecture Notes in Computer Science, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61464-8_66
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DOI: https://doi.org/10.1007/3-540-61464-8_66
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