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Uncurrying for Innermost Termination and Derivational Complexity

Harald Zankl, Nao Hirokawa, and Aart Middeldorp

Proceedings of the 5th International Workshop on Higher-Order Rewriting (HOR 2010), Electronic Proceedings in Theoretical Computer Science 49, pp. 46 – 57, 2011.

Abstract

First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we
introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we investigate how this transformation behaves for innermost termination and (innermost) derivational complexity. We prove that it reflects innermost termination and innermost derivational complexity and that it preserves and reflects polynomial derivational complexity. For the preservation of innermost termination and innermost derivational complexity we give counterexamples. Hence uncurrying may be used as a preprocessing transformation for innermost termination proofs and establishing polynomial upper and lower bounds on the derivational complexity. Additionally it may be used to establish upper bounds on the innermost derivational complexity while it neither is sound for proving innermost non-termination nor for obtaining lower bounds on the innermost
derivational complexity.

 

  PDF |    doi:10.4204/EPTCS.49.4  |  © Creative Commons

BibTeX 

@inproceedings{HZNHAM-HOR10,
author = "Harald Zankl and Nao Hirokawa and Aart Middeldorp",
title = "Uncurrying for Innermost Termination and Derivational Complexity",
booktitle = "Proceedings of the 5th International Workshop on Higher-Order Rewriting",
series = "Electronic Proceedings in Theoretical Computer Science",
volume = 49,
pages = "46--57",
year = 2011,
}
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