Abstract
Proofs by induction are often incompatible with functions in tail-recursive form as the accumulator changes in the course of unfolding the definitions. Context-moving and context-splitting (Giesl, 2000) for functional programs transform tail-recursive programs into non tail-recursive ones which are more suitable for proofs by induction and thus for verification. In this paper, we formulate context-moving and context-splitting transformations in the framework of term rewriting systems, and prove their correctness with respect to both eager evaluation semantics and initial algebra semantics under some conditions on the programs to be transformed. The conditions for the correctness with respect to initial algebra semantics can be checked by automated methods for inductive theorem proving developed in the field of term rewriting systems.
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- 1.
In the case of many-sorted TRSs, we assume sufficient completeness only for the sort of return values of the target f of the context-moving transformation, meaning that any ground term of that sort can be rewritten to a constructor term. Cf. Example 6.
- 2.
For terms of sort \( NatStream \), we do not seek the correctness of the context-moving transformation in the style of Theorem 2.
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Acknowledgements
We are grateful to the anonymous referees for valuable comments. This research was supported by JSPS KAKENHI Grant Numbers 25330004, 25280025 and 15K00003.
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Sato, K., Kikuchi, K., Aoto, T., Toyama, Y. (2015). Correctness of Context-Moving Transformations for Term Rewriting Systems. In: Falaschi, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2015. Lecture Notes in Computer Science(), vol 9527. Springer, Cham. https://doi.org/10.1007/978-3-319-27436-2_20
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DOI: https://doi.org/10.1007/978-3-319-27436-2_20
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