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Autosubst: Reasoning with de Bruijn Terms and Parallel Substitutions

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Interactive Theorem Proving (ITP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9236))

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Abstract

Reasoning about syntax with binders plays an essential role in the formalization of the metatheory of programming languages. While the intricacies of binders can be ignored in paper proofs, formalizations involving binders tend to be heavyweight. We present a discipline for syntax with binders based on de Bruijn terms and parallel substitutions, with a decision procedure covering all assumption-free equational substitution lemmas. The approach is implemented in the Coq library Autosubst, which additionally derives substitution operations and proofs of substitution lemmas for custom term types. We demonstrate the effectiveness of the approach with several case studies, including part A of the POPLmark challenge.

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Notes

  1. 1.

    There are a large number of details which are swept under the carpet in this short overview. The formalization tells the whole story.

  2. 2.

    http://www.seas.upenn.edu/~plclub/poplmark/leroy.html.

  3. 3.

    http://www.chargueraud.org/softs/ln/.

  4. 4.

    http://www.seas.upenn.edu/~plclub/poplmark/vouillon.html.

  5. 5.

    http://www.cis.upenn.edu/~sweirich/papers/lngen/.

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Authors and Affiliations

  1. Saarland University, Saarbrücken, Germany

    Steven Schäfer, Tobias Tebbi & Gert Smolka

Authors
  1. Steven Schäfer
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  2. Tobias Tebbi
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  3. Gert Smolka
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Corresponding author

Correspondence to Steven Schäfer .

Editor information

Editors and Affiliations

  1. Department of Informatics, King's College London, London, United Kingdom

    Christian Urban

  2. PLA University of Science and Technology, Nanjing, China

    Xingyuan Zhang

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Schäfer, S., Tebbi, T., Smolka, G. (2015). Autosubst: Reasoning with de Bruijn Terms and Parallel Substitutions. In: Urban, C., Zhang, X. (eds) Interactive Theorem Proving. ITP 2015. Lecture Notes in Computer Science(), vol 9236. Springer, Cham. https://doi.org/10.1007/978-3-319-22102-1_24

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  • DOI: https://doi.org/10.1007/978-3-319-22102-1_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22101-4

  • Online ISBN: 978-3-319-22102-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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