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A Sound and Complete Hoare Logic for Dynamically-Typed, Object-Oriented Programs

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Theory and Practice of Formal Methods

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9660))

Abstract

A simple dynamically-typed, (purely) object-oriented language is defined. A structural operational semantics as well as a Hoare-style program logic for reasoning about programs in the language in multiple notions of correctness are given. The Hoare logic is proved to be both sound and (relative) complete and is – to the best of our knowledge – the first such logic presented for a dynamically-typed language.

This work is supported by the German Research Foundation through the Research Training Group (DFG GRK 1765) SCARE (www.scare.uni-oldenburg.de).

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Notes

  1. 1.

    One may ask whether it is at all possible to obtain a sound and relatively complete Hoare logic for dyn in light of Clarke’s incompleteness result [5]. However, Clarke’s argument is not applicable to dyn for various reasons elaborated in [7, Appendix C].

  2. 2.

    Assuming an infinite sequence of already existing, but deactivated objects, object creation boils down to picking the next one and marking it as “activated”.

  3. 3.

    Other methods to distinguish the values true and false are conceivable.

  4. 4.

    The predicate \(\mathbb {N}(o,n)\) is recursive. However, the technique used for proving the case for primitive recursion in [7, Lemma 5], allows expressing it in AL.

  5. 5.

    \(@\mathrm {pred}\) and \(@\mathrm {to\_ref}\) are instance variables of the classes num and bool, respectively.

  6. 6.

    We use the polymorphic version for the sake of readability although the type system of AL does not allow polymorphism. However, polymorphic functions can be emulated using one version for each element type.

References

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Acknowledgements

We thank Dennis Kregel for noticing that restricting \(\mathbf {r}\) causes incompleteness and him, Nils-Erik Flick and the anonymous referees for many useful comments on prior versions of this paper.

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Authors and Affiliations

  1. Department of Computing Science, University of Oldenburg, Oldenburg, Germany

    Björn Engelmann & Ernst-Rüdiger Olderog

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  1. Björn Engelmann
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  2. Ernst-Rüdiger Olderog
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Correspondence to Björn Engelmann .

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  1. Informatik 2, RWTH Aachen University Informatik 2, Aachen, Germany

    Erika Ábrahám

  2. Leiden University , Leiden, The Netherlands

    Marcello Bonsangue

  3. University of Oslo , Oslo, Norway

    Einar Broch Johnsen

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Engelmann, B., Olderog, ER. (2016). A Sound and Complete Hoare Logic for Dynamically-Typed, Object-Oriented Programs. In: Ábrahám, E., Bonsangue, M., Johnsen, E. (eds) Theory and Practice of Formal Methods. Lecture Notes in Computer Science(), vol 9660. Springer, Cham. https://doi.org/10.1007/978-3-319-30734-3_13

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