Node-Based Connection Semantics for Equation-Based Object-Oriented Modeling Languages

  • David Broman
  • Henrik Nilsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7149)


Declarative, Equation-Based Object-Oriented (EOO) modeling languages, like Modelica, support modeling of physical systems by composition of reusable component models. An important application area is modeling of cyber-physical systems. EOO languages typically feature a connection construct allowing component models to be assembled into systems much like physical components are. Different designs are possible. This paper introduces, formalizes, and validates an approach based on explicit nodes that expressly is designed to work for functional EOO languages supporting higher-order modeling. The paper also considers Modelica-style connections and explains why that design does not work for functional EOO languages, thus mapping out the design space.


Declarative Languages Modeling Simulation 


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  1. 1.
    Accellera Organization. Verilog-AMS Language Reference Manual - Analog & Mixed-Signal Extensions to Verilog HDL Version 2.3.1 (2009)Google Scholar
  2. 2.
    Ashenden, P.J., Peterson, G.D., Teegarden, D.A.: The System Designer’s Guide to VHDL-AMS: Analog, Mixed-Signal, and Mixed-Technology Modeling. Morgan Kaufmann Publishers, USA (2002)Google Scholar
  3. 3.
    Axelsson, E., Claessen, K., Sheeran, M.: Wired: Wire-Aware Circuit Design. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 5–19. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Bjesse, P., Claessen, K., Sheeran, M., Singh, S.: Lava: hardware design in Haskell. In: Proceedings of the Third ACM SIGPLAN International Conference on Functional Programming, pp. 174–184. ACM Press, New York (1998)CrossRefGoogle Scholar
  5. 5.
    Broman, D.: Flow Lambda Calculus for Declarative Physical Connection Semantics. Technical Reports in Computer and Information Science No. 1. LiU Electronic Press (2007)Google Scholar
  6. 6.
    Broman, D.: Meta-Languages and Semantics for Equation-Based Modeling and Simulation. PhD thesis, Department of Computer and Information Science, Linköping University, Sweden (2010)Google Scholar
  7. 7.
    Broman, D., Fritzson, P.: Higher-Order Acausal Models. Simulation News Europe 19(1), 5–16 (2009)Google Scholar
  8. 8.
    Cellier, F.E.: Continuous System Modeling. Springer, New York (1991)CrossRefzbMATHGoogle Scholar
  9. 9.
    Dassault Systems. Multi-Engineering Modeling and Simulation - Dymola - CATIA - Dassault Systemes, (last accessed: September 16, 2011)
  10. 10.
    Elmqvist, H., Mattsson, S.E., Otter, M.: Modelica - A Language for Physical System Modeling, Visualization and Interaction. In: Proceedings of the IEEE International Symposium on Computer Aided Control System Design (1999)Google Scholar
  11. 11.
    Fritzson, P.: Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley-IEEE Press, New York (2004)Google Scholar
  12. 12.
    Furic, S.: Enforcing model composability in Modelica. In: Proceedings of the 7th International Modelica Conference, Como, Italy, pp. 868–879 (2009)Google Scholar
  13. 13.
    Giorgidze, G., Nilsson, H.: Embedding a Functional Hybrid Modelling Language in Haskell. In: Scholz, S.-B., Chitil, O. (eds.) IFL 2008. LNCS, vol. 5836, pp. 138–155. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Giorgidze, G., Nilsson, H.: Higher-Order Non-Causal Modelling and Simulation of Structurally Dynamic Systems. In: Proceedings of the 7th International Modelica Conference, Como, Italy, pp. 208–218. LiU Electronic Press (September 2009)Google Scholar
  15. 15.
    IEEE Std 1076.1-2007. IEEE Standard VHDL Analog and Mixed-Signal Extensions. IEEE Press (2007)Google Scholar
  16. 16.
    Kunkel, P., Mehrmann, V.: Differential-Algebraic Equations Analysis and Numerical Solution. European Mathematical Society (2006)Google Scholar
  17. 17.
    Lee, E.A.: CPS foundations. In: Proceedings of the 47th Design Automation Conference, DAC 2010, pp. 737–742. ACM Press, New York (2010)Google Scholar
  18. 18.
    Mattsson, S.E., Söderlind, G.: Index reduction in differential-algebraic equations using dummy derivatives. SIAM Journal on Scientific Computing 14(3), 677–692 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Modelica Association. Modelica - A Unified Object-Oriented Language for Physical Systems Modeling - Language Specification Version 3.2 (2010),
  20. 20.
    Nilsson, H., Peterson, J., Hudak, P.: Functional Hybrid Modeling. In: Dahl, V. (ed.) PADL 2003. LNCS, vol. 2562, pp. 376–390. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Pantelides, C.C.: The Consistent Initialization of Differential-Algebraic Systems. SIAM Journal on Scientific and Statistical Computing 9(2), 213–231 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Petzold, L.R.: A Description of DASSL: A Differential/Algebraic System Solver. In: IMACS Trans. on Scientific Comp., 10th IMACS World Congress on Systems Simulation and Scientific Comp., Montreal, Canada (1982)Google Scholar
  23. 23.
    Quarles, T.L., Newton, A.R., Pedersen, D.O., Sangiovanni-Vincentelli, A.: SPICE3 Version 3f3 User’s Manual. Technical report, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley (1993)Google Scholar
  24. 24.
    Jones, S.P.: Haskell 98 Language and Libraries – The Revised Report. Cambridge University Press (2003)Google Scholar
  25. 25.
    Wan, Z., Hudak, P.: Functional reactive programming from first principles. In: PLDI 2000: Proceedings of the ACM SIGPLAN 2000 Conference on Programming Language Design and Implementation, pp. 242–252. ACM Press, New York (2000)CrossRefGoogle Scholar
  26. 26.
    Zimmer, D.: Enhancing Modelica towards variable structure systems. In: Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools, Berlin, Germany, pp. 61–70. LiU Electronic Press (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • David Broman
    • 1
  • Henrik Nilsson
    • 2
  1. 1.Department of Computer and Information ScienceLinköping UniversitySweden
  2. 2.School of Computer ScienceUniversity of NottinghamUnited Kingdom

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