Skip to main content

Developing A New Language to Construct Algebraic Hierarchies for Event-B

  • Conference paper
  • First Online:
Dependable Software Engineering. Theories, Tools, and Applications (SETTA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10998))

  • 823 Accesses

Abstract

This paper proposes a new extension to the Event-B modelling method to facilitate the building of hierarchical mathematical libraries to ease the formal modelling of many systems. The challenges are to facilitate building mathematical theories, be compatible with the current method and tools, and to be extensible by users within the Rodin Platform supporting Event-B.

Our contribution is a new language, called B\(^\sharp \), which includes the additional features of type classes and sub-typing. The B\(^\sharp \) language compiles to the current language used by the Rodin’s Theory Plug-in, which ensures consistency, and also gives compatibility with the current Rodin tools. We demonstrate the advantages of the new language by comparative examples with the existing Theory Plug-in language.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Abrial, J.-R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  2. Abrial, J.R., Butler, M., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: an open toolset for modelling and reasoning in Event-B. STTT 12(6), 447–466 (2010)

    Article  Google Scholar 

  3. Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development - Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-662-07964-5

    Book  MATH  Google Scholar 

  4. Bogdiukiewicz, C., et al.: Formal development of policing functions for intelligent systems. In: 28th IEEE International Symposium on Software Reliability Engineering, ISSRE 2017, Toulouse, France, 23–26 October 2017, pp. 194–204. IEEE Computer Society (2017)

    Google Scholar 

  5. Butler, M., Maamria, I.: Practical theory extension in Event-B. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 67–81. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39698-4_5

    Chapter  Google Scholar 

  6. Cruz-Filipe, L., Geuvers, H., Wiedijk, F.: C-CoRN, the constructive Coq repository at Nijmegen. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 88–103. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27818-4_7

    Chapter  Google Scholar 

  7. Goguen, J.A., Winkler, T., Meseguer, J., Futatsugi, K., Jouannaud, J.P.: Introducing OBJ. In: Goguen, J., Malcolm, G. (eds.) Software Engineering with OBJ. Advances in Formal Methods, pp. 3–167. Springer, Boston (2000). https://doi.org/10.1007/978-1-4757-6541-0_1

    Chapter  Google Scholar 

  8. Guttag, J.V., Horning, J.J.: The algebraic specification of abstract data types. Acta Inform. 10(1), 27–52 (1978)

    Article  MathSciNet  Google Scholar 

  9. Kammüller, F., Wenzel, M., Paulson, L.C.: Locales a sectioning concept for isabelle. In: Bertot, Y., Dowek, G., Théry, L., Hirschowitz, A., Paulin, C. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 149–165. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48256-3_11

    Chapter  Google Scholar 

  10. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL - A Proof Assistant for Higher-Order Logic, vol. 2283. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45949-9

    Book  MATH  Google Scholar 

  11. Wadler, P., Blott, S.: How to make ad-hoc polymorphism less ad hoc. In: Proceedings of the 16th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 60–76. ACM (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to James Snook .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Snook, J., Butler, M., Hoang, T.S. (2018). Developing A New Language to Construct Algebraic Hierarchies for Event-B. In: Feng, X., MĂĽller-Olm, M., Yang, Z. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2018. Lecture Notes in Computer Science(), vol 10998. Springer, Cham. https://doi.org/10.1007/978-3-319-99933-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99933-3_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99932-6

  • Online ISBN: 978-3-319-99933-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics