Towards a UTP Semantics for Modelica

  • Simon Foster
  • Bernhard Thiele
  • Ana Cavalcanti
  • Jim Woodcock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10134)

Abstract

We describe our work on a UTP semantics for the dynamic systems modelling language Modelica. This is a language for modelling a system’s continuous behaviour using a combination of differential-algebraic equations and an event-handling system. We develop a novel UTP theory of hybrid relations, inspired by Hybrid CSP and Duration Calculus, that is purely relational and provides uniform handling of continuous and discrete variables. This theory is mechanised in our Isabelle implementation of the UTP, Isabelle/UTP, with which we verify some algebraic properties. Finally, we show how a subset of Modelica models can be given semantics using our theory. When combined with the wealth of existing UTP theories for discrete system modelling, our work enables a sound approach to heterogeneous semantics for Cyber-Physical systems by leveraging the theory linking facilities of the UTP.

References

  1. 1.
    Åkesson, J., Ekman, T., Hedin, G.: Implementation of a Modelica compiler using JastAdd attribute grammars. Sci. Comput. Program. 75(1–2), 21–38 (2010). Special Issue on ETAPS 2006 and 2007 Workshops on Language Descriptions, Tools, and Applications (LDTA 2006 and 2007)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bachmann, B., Aronsson, P., Fritzson, P.: Robust initialization of differential algebraic equation. In: 5th International Modelica Conference, Austria, September 2006Google Scholar
  3. 3.
    Blanchette, J.C., Bulwahn, L., Nipkow, T.: Automatic proof and disproof in Isabelle/HOL. In: Tinelli, C., Sofronie-Stokkermans, V. (eds.) FroCoS 2011. LNCS (LNAI), vol. 6989, pp. 12–27. Springer, Berlin (2011). doi:10.1007/978-3-642-24364-6_2 CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    Feliachi, A., Gaudel, M.-C., Wolff, B.: Isabelle/Circus: a process specification and verification environment. In: Joshi, R., Müller, P., Podelski, A. (eds.) VSTTE 2012. LNCS, vol. 7152, pp. 243–260. Springer, Berlin (2012). doi:10.1007/978-3-642-27705-4_20 CrossRefGoogle Scholar
  6. 6.
    Fidge, C.J.: Modelling discrete behaviour in a continuous-time formalism. In: Araki, K., Galloway, A., Taguchi, K. (eds.) Proceedings of the 1st International Conference on Integrated on Integrated Formal Methods, pp. 170–188. Springer, Heidelberg (1999)Google Scholar
  7. 7.
    Fleuriot, J.D.: On the mechanization of real analysis in Isabelle/HOL. In: Aagaard, M., Harrison, J. (eds.) TPHOLs 2000. LNCS, vol. 1869, pp. 145–161. Springer, Berlin (2000). doi:10.1007/3-540-44659-1_10 CrossRefGoogle Scholar
  8. 8.
    FMI development group. Functional mock-up interface for model exchange and co-simulation, 2.0 (2014). https://www.fmi-standard.org
  9. 9.
    Foster, S., Miyazawa, A., Woodcock, J., Cavalcanti, A., Fitzgerald, J., Larsen, P.: An approach for managing semantic heterogeneity in systems of systems engineering. In: Proceedings of the 9th International Conference on Systems of Systems Engineering. IEEE (2014)Google Scholar
  10. 10.
    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, Cham (2015). doi:10.1007/978-3-319-14806-9_2 Google Scholar
  11. 11.
    Harrison, J.: A HOL theory of euclidean space. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 114–129. Springer, Berlin (2005). doi:10.1007/11541868_8 CrossRefGoogle Scholar
  12. 12.
    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, Berlin (2008). doi:10.1007/978-3-540-85762-4_10 CrossRefGoogle Scholar
  13. 13.
    Hayes, I.J., Dunne, S.E., Meinicke, L.: Unifying theories of programming that distinguish nontermination and abort. In: Bolduc, C., Desharnais, J., Ktari, B. (eds.) MPC 2010. LNCS, vol. 6120, pp. 178–194. Springer, Berlin (2010). doi:10.1007/978-3-642-13321-3_12 CrossRefGoogle Scholar
  14. 14.
    He, J.: From CSP to hybrid systems. In: Roscoe, A.W. (ed.) A Classical Mind: Essays in Honour of C.A.R. Hoare, pp. 171–189. Prentice Hall (1994)Google Scholar
  15. 15.
    He, J.: HRML: a hybrid relational modelling language. In: IEEE International Conference on Software Quality, Reliability and Security, QRS 2015, August 2015Google Scholar
  16. 16.
    Henzinger, T.A.: The theory of hybrid automata, pp. 278–292. IEEE (1996)Google Scholar
  17. 17.
    Hoare, T.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)MATHGoogle Scholar
  18. 18.
    Hoare, T., He, J.: Unifying Theories of Programming. Prentice-Hall, Englewood Cliffs (1998)MATHGoogle Scholar
  19. 19.
    Huffman, B., Kunčar, O.: Lifting and transfer: a modular design for quotients in Isabelle/HOL. In: Gonthier, G., Norrish, M. (eds.) CPP 2013. LNCS, vol. 8307, pp. 131–146. Springer, Cham (2013). doi:10.1007/978-3-319-03545-1_9 CrossRefGoogle Scholar
  20. 20.
    Kågedal, D., Fritzson, P.: Generating a Modelica compiler from natural semantics specifications. In: Proceedings of 1998 Summer Computer Simulation Conference, SCSC 1998 (1998)Google Scholar
  21. 21.
    Liu, J., Lv, J., Quan, Z., Zhan, N., Zhao, H., Zhou, C., Zou, L.: A calculus for hybrid CSP. In: Ueda, K. (ed.) APLAS 2010. LNCS, vol. 6461, pp. 1–15. Springer, Berlin (2010). doi:10.1007/978-3-642-17164-2_1 CrossRefGoogle Scholar
  22. 22.
    Modelica Association. Modelica - A Unified Object-Oriented Language for Systems Modeling - Version 3.3 Revision 1. Standard Specification, July 2014Google Scholar
  23. 23.
    Nipkow, T., Wenzel, M., Paulson, L.C. (eds.): Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Berlin (2002)MATHGoogle Scholar
  24. 24.
    Ochel, L.A., Bachmann, B.: Initialization of equation-based hybrid models within OpenModelica. In: 5th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools, Nottingham, UK, pp. 97–103, April 2013Google Scholar
  25. 25.
    Pantelides, C.: The consistent initialization of differential-algebraic systems. SIAM J. Sci. Stat. Comput. 9(2), 213–231 (1988)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Perna, J.I., Woodcock, J.: UTP semantics for handel-C. In: Butterfield, A. (ed.) UTP 2008. LNCS, vol. 5713, pp. 142–160. Springer, Berlin (2010). doi:10.1007/978-3-642-14521-6_9 CrossRefGoogle Scholar
  27. 27.
    Platzer, A.: Logical Analysis of Hybrid Systems. Springer, Heidelberg (2010)CrossRefMATHGoogle Scholar
  28. 28.
    Satabin, L., Colao, J., Andrieu, O., Pagano, B.: Towards a formalized Modelica subset. In: 11th International Modelica Conference, September 2015Google Scholar
  29. 29.
    Thiele, B., Knoll, A., Fritzson, P.: Towards qualifiable code generation from a clocked synchronous subset of modelica. Model. Identif. Control 36(1), 23–52 (2015)CrossRefGoogle Scholar
  30. 30.
    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
  31. 31.
    Zhao, H., Yang, M., Zhan, N., Gu, B., Zou, L., Chen, Y.: Formal verification of a descent guidance control program of a lunar lander. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 733–748. Springer, Cham (2014). doi:10.1007/978-3-319-06410-9_49 CrossRefGoogle Scholar
  32. 32.
    Zhou, C., Hansen, M.R.: Chopping a point. In: Proceedings of 7th BCS-FACS Refinement Workshop. Springer, Heidelberg (1996)Google Scholar
  33. 33.
    Zhou, C., Hoare, C.A.R., Ravn, A.P.: A calculus of durations. Inf. Process. Lett. 40(5), 269–276 (1991)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Chaochen, Z., Ji, W., Ravn, A.P.: A formal description of hybrid systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 511–530. Springer, Berlin (1996). doi:10.1007/BFb0020972 CrossRefGoogle Scholar
  35. 35.
    Chaochen, Z., Ravn, A.P., Hansen, M.R.: An extended duration calculus for hybrid real-time systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.) HS 1991–1992. LNCS, vol. 736, pp. 36–59. Springer, Berlin (1993). doi:10.1007/3-540-57318-6_23 CrossRefGoogle Scholar
  36. 36.
    Zhu, H., Yang, F., He, J.: Generating denotational semantics from algebraic semantics for event-driven system-level language. In: Qin, S. (ed.) UTP 2010. LNCS, vol. 6445, pp. 286–308. Springer, Berlin (2010). doi:10.1007/978-3-642-16690-7_15 CrossRefGoogle Scholar
  37. 37.
    Zou, L., Zhan, N., Wang, S., Fränzle, M.: Formal verification of simulink/stateflow diagrams. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 464–481. Springer, Cham (2015). doi:10.1007/978-3-319-24953-7_33 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Simon Foster
    • 1
  • Bernhard Thiele
    • 2
  • Ana Cavalcanti
    • 1
  • Jim Woodcock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkYorkUK
  2. 2.PELABLinköping UniversityLinköpingSweden

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