Checking Conservativity with Hets

  • Mihai Codescu
  • Till Mossakowski
  • Christian Maeder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8089)


Conservative extension is an important notion in the theory of formal specification [8]. If we can implement a specification SP, we can implement any conservative extension of SP as well. Hence, a specification can be shown consistent by starting with a consistent specification and extending it using a number of conservative extension steps. This is important, because during a formal development, it is desirable to guarantee consistency of specifications as soon as possible. Checks for conservative extensions also arise in calculi for proofs in structured specifications [12,9]. Furthermore, consistency is a special case of conservativity: it is just conservativity over the empty specification. Moreover, using consistency, also non-consequence can be checked: an axiom does not follow from a specification if the specification augmented by the negation of the axiom is consistent. Finally, [3] puts forward the idea of simplifying the task of checking consistency of large theories by decomposing them with the help of an architectural specification [2]. In order to show that an architectural specification is consistent, it is necessary to show that a number of extensions are conservative (more precisely, the specifications of its generic units need to be conservative extensions of their argument specifications, and those of the non-generic units need to be consistent).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beckert, B., Hoare, T., Hähnle, R., Smith, D.R., Green, C., Ranise, S., Tinelli, C., Ball, T., Rajamani, S.K.: Intelligent systems and formal methods in software engineering. IEEE Intelligent Systems 21(6), 71–81 (2006)CrossRefGoogle Scholar
  2. 2.
    Bidoit, M., Sannella, D., Tarlecki, A.: Architectural specifications in Casl. Formal Aspects of Computing 13, 252–273 (2002)zbMATHCrossRefGoogle Scholar
  3. 3.
    Codescu, M., Mossakowski, T.: Refinement Trees: Calculi, Tools, and Applications. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 145–160. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Mosses, P.D. (ed.): CASL Reference Manual. LNCS, vol. 2960. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  5. 5.
    Kutz, O., Mossakowski, T.: A modular consistency proof for Dolce. In: Burgard, W., Roth, D. (eds.) Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence and the Twenty-Third Innovative Applications of Artificial Intelligence Conference, pp. 227–234. AAAI Press, Menlo Park (2011)Google Scholar
  6. 6.
    Liu, M.: Konsistenz-Check von Casl-Spezifikationen. Master’s thesis, University of Bremen (2008)Google Scholar
  7. 7.
    Lüth, C., Roggenbach, M., Schröder, L.: CCC – the casl consistency checker. In: Fiadeiro, J.L., Mosses, P.D., Orejas, F. (eds.) WADT 2004. LNCS, vol. 3423, pp. 94–105. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Maibaum, T.S.E.: Conservative extensions, interpretations between theories and all that? In: Bidoit, M., Dauchet, M. (eds.) TAPSOFT 1997. LNCS, vol. 1214, pp. 40–66. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Mossakowski, T., Autexier, S., Hutter, D.: Development graphs – proof management for structured specifications. Journal of Logic and Algebraic Programming 67(1-2), 114–145 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Mossakowski, T., Maeder, C., Lüttich, K.: The Heterogeneous Tool Set, hets. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 519–522. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Mossakowski, T., Hoffman, P., Autexier, S., Hutter, D., Mossakowski, E.: Part V. CASL Libraries. In: Mosses, P.D. (ed.) CASL Reference Manual. LNCS, vol. 2960, pp. 273–359. Springer, Heidelberg (2004), CrossRefGoogle Scholar
  12. 12.
    Sannella, D., Tarlecki, A.: Foundations of Algebraic Specification and Formal Software Development. EATCS Monographs on theoretical computer science. Springer (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mihai Codescu
    • 1
  • Till Mossakowski
    • 2
    • 3
  • Christian Maeder
    • 2
  1. 1.University of Erlangen-NürnbergGermany
  2. 2.DFKI GmbH BremenGermany
  3. 3.SFB/TR 8 “Spatial Cognition”University of BremenGermany

Personalised recommendations