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Reasoning about Separation Using Abstraction and Reification

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Software Engineering and Formal Methods (SEFM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9276))

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Abstract

Showing that concurrent threads operate on separate portions of their shared state is a way of establishing non-interference. Furthermore, in many useful programs, ownership of parts of the state are exchanged dynamically. Reasoning about separation and ownership of heap-based variables is often conducted using some form of separation logic. This paper examines the issue of separation and investigates the use of abstraction to specify and to reason about separation in program design. Two case studies demonstrate that using separation as an abstraction is a potentially useful approach.

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Notes

  1. 1.

    VDM notation is used throughout the current paper; see [Jon90] for details.

  2. 2.

    VDM aficionados would normally employ a ‘record’ construct here but using a pair and selecting by index reduces the potentially unfamiliar notation in this paper.

  3. 3.

    Of course, Srep and start are mutually recursive but it is clearer to separate their descriptions.

  4. 4.

    So far, separation is a convenience that ensures transferring cells from one sequence to the other provides unused pointers; the restriction plays a bigger role in Sect. 2.4.

  5. 5.

    The conference version of this paper omits all detailed proofs which are, anyway, mostly routine — they can be found in the Technical Report [JY15, Appendix].

  6. 6.

    The fact that ‘cells’ contain both data and pointer (rather than them being in locations n and \(n+1\) as in Fig. 1) is incidental — think of car/cdr in Lisp. Furthermore, the decision to use Ptr rather than \({\mathbb {N}}\) is deliberate.

  7. 7.

    A suitable formal proof rule is given in Sect. 4.

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Acknowledgements

The research reported here is supported by (UK) EPSRC ‘Taming Concurrency’ and ‘TrAmS-2’ research grants. The authors would like to thank Andrius Velykis and our colleagues Ian Hayes, Larissa Meinicke and Kim Solin from the (Australian) ARC-funded project ‘Understanding concurrent programs using rely-guarantee thinking’ for their invaluable feedback.

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Authors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Cliff B. Jones & Nisansala Yatapanage

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  1. Cliff B. Jones
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  2. Nisansala Yatapanage
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Correspondence to Cliff B. Jones .

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Editors and Affiliations

  1. Department of Computer Science, University of York, York, United Kingdom

    Radu Calinescu

  2. Software Engineering, Department of Computer Science, RWTH Aachen University, Aachen, Germany

    Bernhard Rumpe

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Jones, C.B., Yatapanage, N. (2015). Reasoning about Separation Using Abstraction and Reification. In: Calinescu, R., Rumpe, B. (eds) Software Engineering and Formal Methods. SEFM 2015. Lecture Notes in Computer Science(), vol 9276. Springer, Cham. https://doi.org/10.1007/978-3-319-22969-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-22969-0_1

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