OASIcs.WPTE.2014.39.pdf
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On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings
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First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2014)
Series: Open Access Series in Informatics (OASIcs) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2014-07-13
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Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner. On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings. In First International Workshop on Rewriting Techniques for Program Transformations and Evaluation. Open Access Series in Informatics (OASIcs), Volume 40, pp. 39-50, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/OASIcs.WPTE.2014.39
https://doi.org/10.4230/OASIcs.WPTE.2014.39
Abstract
In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is sound for weakly left-linear normal conditional term rewriting systems (CTRS). Here, soundness for a CTRS means that reduction of the transformed unconditional term rewriting system (TRS) creates no undesired reduction for the CTRS. We first show that every reduction sequence of the transformed TRS starting with a term corresponding to the one considered on the CTRS is simulated by the reduction of the TRS obtained by the simultaneous unraveling. Then, we use the fact that the unraveling is sound for weakly left-linear normal CTRSs.
Keywords
- conditional term rewriting
- unraveling
- condition elimination
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