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Semantics and strong sequentially of priority term rewriting systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1103))

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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References

  1. 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.

    Article  Google Scholar 

  2. H. Comon. Sequentiality, second order monadic logic and tree automata. In Logic in Computer Science, pages 508–517, 1995.

    Google Scholar 

  3. 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.

    Google Scholar 

  4. P. Henderson. Functional Programming. Prentice Hall International, 1980.

    Google Scholar 

  5. G. Huet and J.-J. Lévy. Call by need computations in non-ambiguous linear term rewriting systems. Technical Report 359, INRIA, 1979.

    Google Scholar 

  6. G. Huet. Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems. Journal of Association for Computing Machinery, 27(4):797–21, October 1980.

    Google Scholar 

  7. S. L. P. Jones. The Implementation of Functional Programming Languages. Prentice Hall International, 1987.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. J. W. Klop and A. Middeldorp. Sequentiality in orthogonal term rewritng systems. J. Symbolic Computation, 12:161–195, 1991.

    Google Scholar 

  10. C. K. Mohan. Priority rewriting: Semantics, confluence, and conditionals. In LNCS, volume 355, pages 278–291. Springer-Verlag, 1989.

    Google Scholar 

  11. R. Plasmeijer and M. van Eekelen. Functional Programming and Parallel Graph Rewriting. Addison-wesley, 1993.

    Google Scholar 

  12. M. Rabin. Decidable theories. In J. Barwise, editor, Handbook of Mathematical Logic, pages 595–629. North-Holland, 1977.

    Google Scholar 

  13. W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 134–191. Elsevier, 1990.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. 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.

    Google Scholar 

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Harald Ganzinger

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© 1996 Springer-Verlag Berlin Heidelberg

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61464-7

  • Online ISBN: 978-3-540-68596-8

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