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Innermost Termination of Context-Sensitive Rewriting

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Developments in Language Theory (DLT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

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Abstract

Context-sensitive rewriting is a restriction of term rewriting used to model evaluation strategies in functional programming and in programming languages like OBJ. For example, under certain conditions termination of an OBJ program is equivalent to innermost termination of the corresponding context-sensitive rewrite system [18]. To prove termination of context-sensitive rewriting, several methods have been proposed in the literature which transform context-sensitive rewrite systems into ordinary rewrite systems such that termination of the transformed ordinary system implies termination of the original context-sensitive system. Most of these transformations are not very satisfactory when it comes to proving innermost termination. We investigate the relationship between termination and innermost termination of context-sensitive rewriting and we examine the applicability of the different transformations for innermost termination proofs. Finally, we present a simple transformation which is both sound and complete for innermost termination.

Partially supported by the Grant-in-Aid for Scientific Research (C)(2) 13224006 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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Author information

Authors and Affiliations

  1. LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074, Aachen, Germany

    Jürgen Giesl

  2. Institute of Information Sciences and Electronics, University of Tsukuba, 305-8573, Tsukuba, Japan

    Aart Middeldorp

Authors
  1. Jürgen Giesl
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  2. Aart Middeldorp
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Editor information

Editors and Affiliations

  1. Faculty of Science and Faculty of Engineering, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Masami Ito  & Masafumi Toyama  & 

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Giesl, J., Middeldorp, A. (2003). Innermost Termination of Context-Sensitive Rewriting. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_20

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  • DOI: https://doi.org/10.1007/3-540-45005-X_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40431-6

  • Online ISBN: 978-3-540-45005-4

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