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System F in Agda, for Fun and Profit

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Mathematics of Program Construction (MPC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11825))

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Abstract

System F, also known as the polymorphic \(\lambda \)-calculus, is a typed \(\lambda \)-calculus independently discovered by the logician Jean-Yves Girard and the computer scientist John Reynolds. We consider \(F_{\omega \mu }\), which adds higher-order kinds and iso-recursive types. We present the first complete, intrinsically typed, executable, formalisation of System \(F_{\omega \mu }\) that we are aware of. The work is motivated by verifying the core language of a smart contract system based on System \(F_{\omega \mu }\). The paper is a literate Agda script [14].

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Notes

  1. 1.

    The code in this paper is typeset in .

  2. 2.

    We thank an anonymous reviewer for bringing this to our attention.

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Acknowledgements

We thank the anonymous reviewers for their helpful comments and insightful constructive criticism. We thank IOHK for their support of this work. We thank our colleagues Marko Dimjaević, Kenneth MacKenzie, and Michael Peyton Jones for helpful comments on an multiple drafts. The first author would like to James McKinna for spending an afternoon explaining pure type systems and Guillaume Allais, Apostolis Xekoukoulotakis and Ulf Norell for help with diagnosing and fixing bugs that we encountered in Agda’s GHC backend in the course of writing this paper.

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  1. IOHK, Hong Kong, Hong Kong

    James Chapman & Roman Kireev

  2. University of Edinburgh, Edinburgh, UK

    Chad Nester & Philip Wadler

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  1. James Chapman
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Correspondence to James Chapman .

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  1. University of Nottingham, Nottingham, UK

    Graham Hutton

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Chapman, J., Kireev, R., Nester, C., Wadler, P. (2019). System F in Agda, for Fun and Profit. In: Hutton, G. (eds) Mathematics of Program Construction. MPC 2019. Lecture Notes in Computer Science(), vol 11825. Springer, Cham. https://doi.org/10.1007/978-3-030-33636-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-33636-3_10

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