Skip to main content
SpringerLink
Log in

Reasoning About Active Objects: A Sound and Complete Assertional Proof Method

  • Chapter
  • First Online:
The Logic of Software. A Tasting Menu of Formal Methods

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13360))

  • 656 Accesses

Abstract

We present a novel assertional proof method for reasoning about global invariant properties of active objects in the context of the Abstract Behavioral Specification (ABS) language. The main result of this paper is a formal justification of the proof method which establishes both its soundness and completeness with respect to a formally defined operational trace semantics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Since we assume that every method body terminates with a return statement, the postcondition of a statement coincides with the precondition of the statement that follows, e.g., the postcondition of the method body itself is the precondition of the return statement.

  2. 2.

    Note that p is also used to denote assertions. From the context however it is clear what is meant.

  3. 3.

    For technical convenience only, we assume that such await statements do not occur in constructor methods.

  4. 4.

    Excluding calls to constructor methods.

  5. 5.

    In the transition for the get operation we assume without loss of generality that the variable x is a local variable.

References

  1. Ahrendt, W., Beckert, B., Bubel, R., Hähnle, R., Schmitt, P.H., Ulbrich, M. (eds.): Deductive Software Verification - The KeY Book - From Theory to Practice. Lecture Notes in Computer Science, vol. 10001. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-49812-6

  2. Ahrendt, W., Dylla, M.: A verification system for distributed objects with asynchronous method calls. In: Breitman, K., Cavalcanti, A. (eds.) ICFEM 2009. LNCS, vol. 5885, pp. 387–406. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10373-5_20

    Chapter  Google Scholar 

  3. Ahrendt, W., Dylla, M.: A system for compositional verification of asynchronous objects. Sci. Comput. Program. 77(12), 1289–1309 (2012). https://doi.org/10.1016/j.scico.2010.08.003

    Article  MATH  Google Scholar 

  4. Apt, K.R.: Formal justification of a proof system for communicating sequential processes. J. ACM 30(1), 197–216 (1983). https://doi.org/10.1145/322358.322372

    Article  MathSciNet  MATH  Google Scholar 

  5. Blom, S., Huisman, M., Mihelcic, M.: Specification and verification of GPGPU programs. Sci. Comput. Program. 95, 376–388 (2014). https://doi.org/10.1016/j.scico.2014.03.013

    Article  Google Scholar 

  6. De Boer, F., et al.: A survey of active object languages. ACM Comput. Surv. 50(5), 76:1–76:39 (2017). http://doi.acm.org/10.1145/3122848, https://doi.org/10.1145/3122848

  7. Cook, S.A.: Soundness and completeness of an axiom system for program verification. SIAM J. Comput. 7(1), 70–90 (1978). https://doi.org/10.1137/0207005

    Article  MathSciNet  MATH  Google Scholar 

  8. de Boer, F.S., Clarke, D., Johnsen, E.B.: A complete guide to the future. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 316–330. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71316-6_22

    Chapter  Google Scholar 

  9. Boer, F.S., Gouw, S.: Compositional semantics for concurrent object groups in ABS. In: Müller, P., Schaefer, I. (eds.) Principled Software Development, pp. 87–98. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98047-8_6

    Chapter  Google Scholar 

  10. de Boer, F.S., et al.: A survey of active object languages. ACM Comput. Surv. 50(5), 76:1–76:39 (2017)

    Google Scholar 

  11. de Gouw, S., de Boer, F., Ahrendt, W., Bubel, R.: Weak arithmetic completeness of object-oriented first-order assertion networks. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds.) SOFSEM 2013. LNCS, vol. 7741, pp. 207–219. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35843-2_19

    Chapter  MATH  Google Scholar 

  12. de Gouw, S., de Boer, F., Ahrendt, W., Bubel, R.: Integrating deductive verification and symbolic execution for abstract object creation in dynamic logic. Softw. Syst. Model. 15(4), 1117–1140 (2014). https://doi.org/10.1007/s10270-014-0446-9

    Article  Google Scholar 

  13. de Roever, W.P., et al.: Concurrency Verification: Introduction to Compositional and Noncompositional Methods. Cambridge Tracts in Theoretical Computer Science, vol. 54. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  14. Din, C.C., Hähnle, R., Johnsen, E.B., Pun, K.I., Tapia Tarifa, S.L.: Locally abstract, globally concrete semantics of concurrent programming languages. In: Schmidt, R.A., Nalon, C. (eds.) TABLEAUX 2017. LNCS (LNAI), vol. 10501, pp. 22–43. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66902-1_2

    Chapter  Google Scholar 

  15. Crystal Chang Din and Olaf Owe: A sound and complete reasoning system for asynchronous communication with shared futures. J. Log. Algebr. Meth. Program. 83(5–6), 360–383 (2014)

    MathSciNet  MATH  Google Scholar 

  16. Din, C.C., Owe, O.: Compositional reasoning about active objects with shared futures. Formal Aspects Comput. 27(3), 551–572 (2014). https://doi.org/10.1007/s00165-014-0322-y

    Article  MathSciNet  MATH  Google Scholar 

  17. Haslbeck, M.P.L., Nipkow, T.: Hoare logics for time bounds - a study in meta theory. In: Beyer, D., Huisman, M. (eds.) TACAS 2018, Part I. LNCS, vol. 10805, pp. 155–171. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89960-2_9

    Chapter  MATH  Google Scholar 

  18. Johnsen, E.B., Hähnle, R., Schäfer, J., Schlatte, R., Steffen, M.: ABS: a core language for abstract behavioral specification. In: Aichernig, B.K., de Boer, F.S., Bonsangue, M.M. (eds.) FMCO 2010. LNCS, vol. 6957, pp. 142–164. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25271-6_8

    Chapter  Google Scholar 

  19. Kamburjan, E., Chen, T.-C.: Stateful behavioral types for active objects. In: Furia, C.A., Winter, K. (eds.) IFM 2018. LNCS, vol. 11023, pp. 214–235. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98938-9_13

    Chapter  Google Scholar 

  20. Kamburjan, E., Din, C.C., Hähnle, R., Johnsen, E.B.: Asynchronous cooperative contracts for cooperative scheduling. In: Ölveczky, P.C., Salaün, G. (eds.) SEFM 2019. LNCS, vol. 11724, pp. 48–66. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30446-1_3

    Chapter  Google Scholar 

  21. Kamburjan, E., Hähnle, R., Schön, S.: Formal modeling and analysis of railway operations with active objects. Sci. Comput. Program. 166, 167–193 (2018)

    Article  Google Scholar 

  22. Owicki, S.S., Gries, D.: An axiomatic proof technique for parallel programs I. Acta Inf. 6, 319–340 (1976)

    Article  MathSciNet  Google Scholar 

  23. Zaharieva-Stojanovski, M., Huisman, M.: Verifying class invariants in concurrent programs. In: Gnesi, S., Rensink, A. (eds.) FASE 2014. LNCS, vol. 8411, pp. 230–245. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54804-8_16

    Chapter  Google Scholar 

Download references

Acknowledgement

We thank Olaf Owe for some insightful discussions.

Author information

Authors and Affiliations

  1. Leiden Institute for Advanced Computer Science, Leiden, The Netherlands

    Frank de Boer

  2. Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands

    Frank de Boer & Stijn de Gouw

  3. Open University, Heerlen, The Netherlands

    Stijn de Gouw

Authors
  1. Frank de Boer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stijn de Gouw
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stijn de Gouw .

Editor information

Editors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Wolfgang Ahrendt

  2. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Bernhard Beckert

  3. TU Darmstadt, Darmstadt, Germany

    Richard Bubel

  4. University of Oslo, Oslo, Norway

    Einar Broch Johnsen

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

de Boer, F., de Gouw, S. (2022). Reasoning About Active Objects: A Sound and Complete Assertional Proof Method. In: Ahrendt, W., Beckert, B., Bubel, R., Johnsen, E.B. (eds) The Logic of Software. A Tasting Menu of Formal Methods. Lecture Notes in Computer Science, vol 13360. Springer, Cham. https://doi.org/10.1007/978-3-031-08166-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-08166-8_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08165-1

  • Online ISBN: 978-3-031-08166-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation