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ModuRes: A Coq Library for Modular Reasoning About Concurrent Higher-Order Imperative Programming Languages

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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

It is well-known that it is challenging to build semantic models of type systems or logics for reasoning about concurrent higher-order imperative programming languages. One of the key challenges is that such semantic models often involve constructing solutions to certain kinds of recursive domain equations, which in practice has been a barrier to formalization efforts. Here we present the ModuRes Coq library, which provides an easy way to solve such equations. We show how the library can be used to construct models of type systems and logics for reasoning about concurrent higher-order imperative programming languages.

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Notes

  1. 1.

    Available at http://cs.au.dk/~birke/modures/tutorial.

  2. 2.

    Although in the case of subset types an extra condition is required to make sure the subset is complete.

  3. 3.

    Since the category of COFEs itself is cartesian closed it is indeed enriched over itself, and hence it is a special case of the general approach provided by the library.

  4. 4.

    For the actual application to modeling ML-style reference types, the functions should not only be non-expansive, but also monotone wrt. a suitable extension ordering on the worlds. The ModuRes library includes support for such, but we omit that here.

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Acknowledgements

The formalization of the general solution of the recursive domain equation is inspired by an earlier, unpublished development by Varming and Birkedal. While both the proof engineering methods used and the scope of the ModuRes library differ significantly from this earlier effort, some of the setup is borrowed from that. Yannick Zakowski was the first user of the library, providing important feedback, as well as a formalization of the example used in Sect. 3. We thank the anonymous reviewers for their comments.

This research was supported in part by the ModuRes Sapere Aude Advanced Grant from The Danish Council for Independent Research for the Natural Sciences (FNU).

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Authors and Affiliations

  1. Department of Computer Science, Aarhus University, Aarhus, Denmark

    Filip Sieczkowski, Aleš Bizjak & Lars Birkedal

Authors
  1. Filip Sieczkowski
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  2. Aleš Bizjak
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  3. Lars Birkedal
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Corresponding author

Correspondence to Filip Sieczkowski .

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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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Sieczkowski, F., Bizjak, A., Birkedal, L. (2015). ModuRes: A Coq Library for Modular Reasoning About Concurrent Higher-Order Imperative Programming Languages. 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_25

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  • DOI: https://doi.org/10.1007/978-3-319-22102-1_25

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