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Type Inference for ZFH

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Intelligent Computer Mathematics (CICM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9150))

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Abstract

ZFH stands for Zermelo-Fraenkel set theory implemented in higher-order logic. It is a descendant of Agerholm’s and Gordon’s HOL-ST but does not allow the use of type variables nor the definition of new types. We first motivate why we are using ZFH for ProofPeer, the collaborative theorem proving system we are building. We then focus on the type inference algorithm we have developed for ZFH. In ZFH’s syntax, function application, written as juxtaposition, is overloaded to be either set-theoretic or higher-order. Our algorithm extends Hindley-Milner type inference to cope with this particular overloading of function application. We describe the algorithm, prove its correctness, and discuss why prior general approaches to type inference in the presence of coercions or overloading do not cover our particular case.

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References

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Author information

Authors and Affiliations

  1. School of Informatics, Edinburgh University, 10 Crichton Street, EH8 9AB, Edinburgh, Scotland, UK

    Steven Obua, Jacques Fleuriot, Phil Scott & David Aspinall

Authors
  1. Steven Obua
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  2. Jacques Fleuriot
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  3. Phil Scott
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  4. David Aspinall
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Corresponding author

Correspondence to Steven Obua .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham, United Kingdom

    Manfred Kerber

  2. McMaster University, Hamilton, Ontario, Canada

    Jacques Carette

  3. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. University of Birmingham, Birmingham, United Kingdom

    Volker Sorge

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Obua, S., Fleuriot, J., Scott, P., Aspinall, D. (2015). Type Inference for ZFH. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds) Intelligent Computer Mathematics. CICM 2015. Lecture Notes in Computer Science(), vol 9150. Springer, Cham. https://doi.org/10.1007/978-3-319-20615-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-20615-8_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20614-1

  • Online ISBN: 978-3-319-20615-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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