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Into the Infinite - Theory Exploration for Coinduction

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Artificial Intelligence and Symbolic Computation (AISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11110))

Abstract

Theory exploration is a technique for automating the discovery of lemmas in formalizations of mathematical theories, using testing and automated proof techniques. Automated theory exploration has previously been successfully applied to discover lemmas for inductive theories, about recursive datatypes and functions. We present an extension of theory exploration to coinductive theories, allowing us to explore the dual notions of corecursive datatypes and functions. This required development of new methods for testing infinite values, and for proof automation. Our work has been implemented in the Hipster system, a theory exploration tool for the proof assistant Isabelle/HOL.

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Notes

  1. 1.

    https://github.com/moajohansson/IsaHipster.

  2. 2.

    https://github.com/moajohansson/IsaHipster/tree/master/benchmark/AISC18.

  3. 3.

    https://www.isa-afp.org/.

  4. 4.

    http://isabelle.in.tum.de/library/HOL/HOL-Library/Extended_Nat.html.

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Acknowledgements

The authors would like to thank Nicholas Smallbone for technical assistance with QuickSpec. The first author was partially supported by the GRACeFUL project, grant agreement No. 640954, which has received funding from the European Union’s Horizon 2020 research and innovation program.

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Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Sólrún Halla Einarsdóttir & Moa Johansson

  2. Data61/CSIRO, Sydney, Australia

    Johannes Åman Pohjola

Authors
  1. Sólrún Halla Einarsdóttir
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  2. Moa Johansson
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  3. Johannes Åman Pohjola
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Corresponding authors

Correspondence to Sólrún Halla Einarsdóttir , Moa Johansson or Johannes Åman Pohjola .

Editor information

Editors and Affiliations

  1. University of Edinburgh, Edinburgh, United Kingdom

    Jacques Fleuriot

  2. Beihang University, Beijing, China

    Dongming Wang

  3. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Jacques Calmet

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Einarsdóttir, S.H., Johansson, M., Åman Pohjola, J. (2018). Into the Infinite - Theory Exploration for Coinduction. In: Fleuriot, J., Wang, D., Calmet, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2018. Lecture Notes in Computer Science(), vol 11110. Springer, Cham. https://doi.org/10.1007/978-3-319-99957-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-99957-9_5

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