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Infinite terms and infinite rewritings

  • Chapter 2 Infinite Terms, Non-Terminating Systems, And Termination
  • Conference paper
  • First Online:
Conditional and Typed Rewriting Systems (CTRS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 516))

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Abstract

We discuss here the properties of term rewriting systems that allow infinite derivations leading to infinite normal forms. We extend work of Dershowitz and Kaplan to preserve more information about infinite derivations in the resulting normal forms, and to give finite representations of cyclic infinite terms. We develop algebraic semantics of the new system that are very similar to those of the old.

The research of these authors was supported in part by NSF grant CMPS 8805503.

Yiyun Chen is supported by a grant from the People's Republic of China.

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References

  1. Yiyun Chen, Michael J. O'Donnell. Testing Confluence of Nonterminating Rewriting Systems. In this Proceedings.

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  2. Yiyun Chen, Michael J. O'Donnell. Nonterminating Rewritings with Head Boundedness. Technical Report, The University of Chicago, 1990.

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  3. Nachum Dershowitz and Stéphane Kaplan. Rewrite, rewrite, rewrite, rewrite, rewrite ... In 16th Annual Symposium on Principles of Programming Languages, pp. 250–259, SIGPLAN and SIGACT, 1989.

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  4. Nachum Dershowitz, Stéphane Kaplan and David A. Plaisted. Infinite Normal Forms. Volume 372 of Lecture Notes in Computer Science, Springer-Verlag, pp. 249–262, 1989.

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  5. G. Huet. Confluent reductions:Abstract properties and applications to term rewriting systems. J. of the Association for Computing Machinery 27(4), pp. 797–821, 1980.

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  6. M. J. O'Donnell. Computing in systems described by equations. Volume 58 of Lecture Notes in Computer Science, Springer-Verlag, 1977.

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Authors and Affiliations

  1. The University of Chicago, USA

    Yiyun Chen & Michael J. O'Donnell

Authors
  1. Yiyun Chen
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  2. Michael J. O'Donnell
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Editor information

S. Kaplan M. Okada

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© 1991 Springer-Verlag Berlin Heidelberg

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Chen, Y., O'Donnell, M.J. (1991). Infinite terms and infinite rewritings. 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_84

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  • DOI: https://doi.org/10.1007/3-540-54317-1_84

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54317-6

  • Online ISBN: 978-3-540-47558-3

  • eBook Packages: Springer Book Archive

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