Iterative Circular Coinduction for CoCasl in Isabelle/HOL

  • Daniel Hausmann
  • Till Mossakowski
  • Lutz Schröder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3442)


Coalgebra has in recent years been recognized as the framework of choice for the treatment of reactive systems at an appropriate level of generality. Proofs about the reactive behavior of a coalgebraic system typically rely on the method of coinduction. In comparison to ‘traditional’ coinduction, which has the disadvantage of requiring the invention of a bisimulation relation, the method of circular coinduction allows a higher degree of automation. As part of an effort to provide proof support for the algebraic-coalgebraic specification language CoCasl, we develop a new coinductive proof strategy which iteratively constructs a bisimulation relation, thus arriving at a new variant of circular coinduction. Based on this result, we design and implement tactics for the theorem prover Isabelle which allow for both automatic and semiautomatic coinductive proofs. The flexibility of this approach is demonstrated by means of examples of (semi-)automatic proofs of consequences of CoCasl specifications, automatically translated into Isabelle theories by means of the Bremen heterogeneous Casl tool set Hets.


Binary Tree Iterative Construction Automatic Proof Left Subtree Coalgebra Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bidoit, M., Mosses, P.D.: CASL User Manual. LNCS, vol. 2900. Springer, Heidelberg (2004)zbMATHCrossRefGoogle Scholar
  2. 2.
    Dennis, L.: Proof planning coinduction, Ph.D. thesis, Edinburgh University (1998)Google Scholar
  3. 3.
    Dennis, L., Bundy, A., Green, I.: Using a generalisation critic to find bisimulations for coinductive proofs. In: McCune, W. (ed.) CADE 1997. LNCS (LNAI), vol. 1249, pp. 276–290. Springer, Heidelberg (1997)Google Scholar
  4. 4.
    Goguen, J., Lin, K., Rosu, G.: Conditional circular coinductive rewriting with case analysis. In: Wirsing, M., Pattinson, D., Hennicker, R. (eds.) WADT 2003. LNCS, vol. 2755, pp. 216–232. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Mossakowski, T.: HetCASL – heterogeneous specification. Language summary (2004)Google Scholar
  6. 6.
    Mossakowski, T.: Heterogeneous specification and the heterogeneous tool set, Habilitation thesis (draft), University of Bremen (2004)Google Scholar
  7. 7.
    Mossakowski, T., Schröder, L., Roggenbach, M., Reichel, H.: Algebraic-co-algebraic specification in CoCASL, J. Logic Algebraic Programming (to appear)Google Scholar
  8. 8.
    Mosses, P.D.: CASL reference manual. LNCS, vol. 2960. Springer, Heidelberg (2004)zbMATHCrossRefGoogle Scholar
  9. 9.
    Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL, vol. 2283. Springer, Heidelberg (2002)zbMATHCrossRefGoogle Scholar
  10. 10.
    Rosu, G.: Hidden logic, Ph.D. thesis, University of California at San Diego (2000)Google Scholar
  11. 11.
    Rutten, J.: Universal coalgebra: A theory of systems. Theoret. Comput. Sci. 249, 3–80 (2000)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Daniel Hausmann
    • 1
  • Till Mossakowski
    • 1
  • Lutz Schröder
    • 1
  1. 1.BISS, Dept. of Computer ScienceUniversity of Bremen 

Personalised recommendations