Confluence of Conditional Term Rewrite Systems via Transformations

Karl Gmeiner
(UAS Technikum Wien)

Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term rewrite systems.

Recent results provide confluence criteria for conditional term rewrite systems via transformations, yet they are restricted to CTRSs with certain syntactic properties like weak left-linearity. These syntactic properties imply that the transformations are sound for the given CTRS.

This paper shows how to use transformations to prove confluence of operationally terminating, right-stable deterministic conditional term rewrite systems without the necessity of soundness restrictions. For this purpose, it is shown that certain rewrite strategies, in particular almost U-eagerness and innermost rewriting, always imply soundness.

In Horatiu Cirstea and Santiago Escobar: Proceedings Third International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2016), Porto, Portugal, 23rd June 2016, Electronic Proceedings in Theoretical Computer Science 235, pp. 32–45.
Published: 1st January 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.235.3 bibtex PDF
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