A Stepwise Approach to Linking Theories

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10134)

Abstract

Formal modelling of complex systems requires catering for a variety of aspects. The Unifying Theories of Programming (UTP) distinguishes itself as a semantic framework that promotes unification of results across different modelling paradigms via linking functions. The naive composition of theories, however, may yield unexpected or undesirable semantic models. Here, we propose a stepwise approach to linking theories where we deal separately with the definition of the relation between the variables in the different theories and the identification of healthiness conditions. We explore this approach by deriving healthiness conditions for Open image in new window via calculation, based on the healthiness conditions of CSP and a small set of principles underlying the timed model.

Keywords

Theory engineering Open image in new window CSP UTP 

References

  1. 1.
    Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall International Series in Computer Science. Prentice Hall, Upper Saddle River (1998)MATHGoogle Scholar
  2. 2.
    Roscoe, A.W.: Understanding Concurrent Systems. Springer, London (2010)CrossRefMATHGoogle Scholar
  3. 3.
    Oliveira, M., Cavalcanti, A., Woodcock, J.: A UTP semantics for Circus. Formal Aspects Comput. 21(1), 3–32 (2007)MATHGoogle Scholar
  4. 4.
    Sherif, A., Cavalcanti, A.L.C., He, J., Sampaio, A.C.A.: A process algebraic framework for specification and validation of real-time systems. Formal Aspects Comput. 22(2), 153–191 (2010)CrossRefMATHGoogle Scholar
  5. 5.
    Wei, K., Woodcock, J., Cavalcanti, A.: Circus Time with reactive designs. In: Wolff, B., Gaudel, M.-C., Feliachi, A. (eds.) UTP 2012. LNCS, vol. 7681, pp. 68–87. Springer, Berlin (2013). doi:10.1007/978-3-642-35705-3_3 CrossRefGoogle Scholar
  6. 6.
    Cavalcanti, A., Sampaio, A., Woodcock, J.: A Refinement Strategy for Circus. Formal Aspects Comput. 15, 146–181 (2003)CrossRefMATHGoogle Scholar
  7. 7.
    Harwood, W., Cavalcanti, A., Woodcock, J.: A theory of pointers for the UTP. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds.) ICTAC 2008. LNCS, vol. 5160, pp. 141–155. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85762-4_10 CrossRefGoogle Scholar
  8. 8.
    Woodcock, J., Davies, J.: Using Z: Specification, Refinement, and Proof. Prentice Hall, Upper Saddle River (1996)MATHGoogle Scholar
  9. 9.
    Schneider, S.: Concurrent and Real-Time Systems: the CSP Approach. Worldwide Series in Computer Science. Wiley, New York (2000)Google Scholar
  10. 10.
    Wei, K., Woodcock, J., Cavalcanti, A.: New Circus Time. Technical report, University of York (2012). https://www.cs.york.ac.uk/circus/publications/techreports/reports/Circus%20Time.pdf
  11. 11.
    Butterfield, A., Gancarski, P., Woodcock, J.: State visibility and communication in unifying theories of programming. In: Third IEEE International Symposium on Theoretical Aspects of Software Engineering, TASE 2009, pp. 47–54, July 2009Google Scholar
  12. 12.
    Canham, S., Woodcock, J.: Three approaches to timed external choice in UTP. In: Naumann, D. (ed.) UTP 2014. LNCS, vol. 8963, pp. 1–20. Springer, Heidelberg (2015). doi:10.1007/978-3-319-14806-9_1 Google Scholar
  13. 13.
    Morgan, C.: Programming from Specifications. Prentice Hall, Upper Saddle River (1994)MATHGoogle Scholar
  14. 14.
    Woodcock, J., Cavalcanti, A.: A tutorial introduction to designs in unifying theories of programming. In: Boiten, E.A., Derrick, J., Smith, G. (eds.) IFM 2004. LNCS, vol. 2999, pp. 40–66. Springer, Berlin (2004). doi:10.1007/978-3-540-24756-2_4 CrossRefGoogle Scholar
  15. 15.
    Cavalcanti, A., Woodcock, J.: A tutorial introduction to CSP in unifying theories of programming. In: Cavalcanti, A., Sampaio, A., Woodcock, J. (eds.) PSSE 2004. LNCS, vol. 3167, pp. 220–268. Springer, Berlin (2006). doi:10.1007/11889229_6 CrossRefGoogle Scholar
  16. 16.
    Spivey, J.M.: The Z Notation: A Reference Manual. Prentice Hall, Upper Saddle River (1989)MATHGoogle Scholar
  17. 17.
    Ribeiro, P.: Super-Theories. Technical report, University of York (2016). https://www-users.cs.york.ac.uk/pfr/reports/super-theories.pdf
  18. 18.
    Foster, S., Zeyda, F., Woodcock, J.: Isabelle/UTP: A Mechanised Theory Engineering Framework. In: Naumann, D. (ed.) UTP 2014. LNCS, vol. 8963, pp. 21–41. Springer, Heidelberg (2015). doi:10.1007/978-3-319-14806-9_2 Google Scholar
  19. 19.
    Banks, M.J., Jacob, J.L.: On integrating confidentiality and functionality in a formal method. Formal Aspects Comput. 26(5), 963–992 (2013)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of YorkYorkUK

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