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Symposium on Implementation and Application of Functional Languages

IFL 2012: Implementation and Application of Functional Languages pp 157–173Cite as

Engineering Proof by Reflection in Agda

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8241))

Abstract

This paper explores the recent addition to Agda enabling reflection, in the style of Lisp and Template Haskell. It gives a brief introduction to using reflection, and details the complexities encountered when automating certain proofs with proof by reflection. It presents a library that can be used for automatically quoting a class of concrete Agda terms to a non-dependent, user-defined inductive data type, alleviating some of the burden a programmer faces when using reflection in a practical setting.

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Notes

  1. 1.

    All supporting code, including this paper in Literate Agda format, is available on GitHub. https://github.com/toothbrush/reflection-proofs

  2. 2.

    using the function \(\mathsf {\_\; {\mathop = \limits ^{?}} \text {-}Name\_}\)

  3. 3.

    Of course, having been implemented during a single Agda Implementors’ Meeting [19], the current implementation is more a proof-of-concept, and is still far from being considered finished, so it would be unfair to judge the current implementation all too harshly. In fact, we hope that this work might motivate the Agda developers to include some more features, to make the system truly useful.

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Acknowledgements

We would like to thank each of the four anonymous reviewers for taking the time to provide detailed and constructive comments that greatly improved the article.

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Authors and Affiliations

  1. Department of Computer Science, Utrecht University, Utrecht, The Netherlands

    Paul van der Walt & Wouter Swierstra

Authors
  1. Paul van der Walt
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  2. Wouter Swierstra
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Corresponding author

Correspondence to Paul van der Walt .

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Editors and Affiliations

  1. University of Oxford, Oxford, United Kingdom

    Ralf Hinze

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van der Walt, P., Swierstra, W. (2013). Engineering Proof by Reflection in Agda. In: Hinze, R. (eds) Implementation and Application of Functional Languages. IFL 2012. Lecture Notes in Computer Science(), vol 8241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41582-1_10

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  • DOI: https://doi.org/10.1007/978-3-642-41582-1_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41581-4

  • Online ISBN: 978-3-642-41582-1

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