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Formalizing Soundness and Completeness of Unravelings

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Frontiers of Combining Systems (FroCoS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9322))

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Abstract

Unravelings constitute a class of program transformations to model conditional rewrite systems as standard term rewrite systems. Key properties of unravelings are soundness and completeness with respect to reductions, in the sense that rewrite sequences in the unraveled system correspond to rewrite sequences in the conditional system and vice versa. While the latter is easily satisfied, the former holds only under certain conditions and is notoriously difficult to prove. This paper describes an Isabelle formalization of both properties. The soundness proof is based on the approach by Nishida, Sakai, and Sakabe (2012) but we also contribute to the theory by showing it applicable to a larger class of unravelings.

Based on our formalization we developed the first certifier to check output of conditional rewrite tools. In particular, quasi-decreasingness proofs by AProVE and conditional confluence proofs by ConCon can be certified.

This research was supported by the Austrian Science Fund (FWF) projects I963 and Y757.

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Authors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, 6020, Innsbruck, Austria

    Sarah Winkler & René Thiemann

Authors
  1. Sarah Winkler
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  2. René Thiemann
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Corresponding author

Correspondence to Sarah Winkler .

Editor information

Editors and Affiliations

  1. Universität Bremen, Bremen, Germany

    Carsten Lutz

  2. Fondazione Bruno Kessler, Trento, Italy

    Silvio Ranise

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Winkler, S., Thiemann, R. (2015). Formalizing Soundness and Completeness of Unravelings. In: Lutz, C., Ranise, S. (eds) Frontiers of Combining Systems. FroCoS 2015. Lecture Notes in Computer Science(), vol 9322. Springer, Cham. https://doi.org/10.1007/978-3-319-24246-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-24246-0_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24245-3

  • Online ISBN: 978-3-319-24246-0

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