Unifying Theories in Isabelle/HOL

  • Abderrahmane Feliachi
  • Marie-Claude Gaudel
  • Burkhart Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6445)

Abstract

In this paper, we present various extensions of Isabelle/HOL by theories that are essential for several formal methods. First, we explain how we have developed an Isabelle/HOL theory for a part of the Unifying Theories of Programming (UTP). It contains the theories of alphabetized relations and designs. Then we explain how we have encoded first the theory of reactive processes and then the UTP theory for CSP. Our work takes advantage of the rich existing logical core of HOL.

Our extension contains the proofs for most of the lemmas and theorems presented in the UTP book. Our goal is to propose a framework that will allow us to deal with formal methods that are semantically based, partly or totally, on UTP, for instance CSP and Circus . The theories presented here will allow us to make proofs about such specifications and to apply verified transformations on them, with the objective of assisting refinement and test generation.

Keywords

UTP Theorem Proving Isabelle/HOL CSP Circus 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrews, P.B.: Introduction to Mathematical Logic and Type Theory: To Truth through Proof, 2nd edn. (2002)Google Scholar
  2. 2.
    Arthan, R.: The ProofPower homepage (2009), http://www.lemma-one.com/ProofPower/index/
  3. 3.
    Brucker, A.D., Rittinger, F., Wolff, B.: Hol-z 2.0: A proof environment for z-specifications. Journal of Universal Computer Science 9(2), 152–172 (2003)Google Scholar
  4. 4.
    Brucker, A.D., Wolff, B.: Symbolic test case generation for primitive recursive functions. In: Grabowski, J., Nielsen, B. (eds.) FATES 2004. LNCS, vol. 3395, pp. 16–32. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Brucker, A.D., Wolff, B.: Test-sequence generation with hol-testgen with an application to firewall testing. In: Gurevich, Y., Meyer, B. (eds.) TAP 2007. LNCS, vol. 4454, pp. 149–168. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Brucker, A.D., Wolff, B.: An extensible encoding of object-oriented data models in hol with an application to imp++. Journal of Automated Reasoning (JAR) 41(3-4), 219–249 (2008); Autexier, S., Mantel, H., Merz, S., Nipkow, T. (eds)CrossRefMATHGoogle Scholar
  7. 7.
    Cavalcanti, A.L.C., Woodcock, J.C.P.: 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, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Cavalcanti, A., Gaudel, M.C.: A note on traces refinement and the \({\it conf}\) relation in the Unifying Theories of Programming. In: Butterfield, A. (ed.) UTP 2008. LNCS, vol. 5713, pp. 42–61. Springer, Heidelberg (2008)Google Scholar
  9. 9.
    Church, A.: A formulation of the simple theory of types, vol. 5(2), pp. 56–68 (June 1940)Google Scholar
  10. 10.
    Hoare, C.A.R., Jifeng, H.: Unifying Theories of Programming. Prentice Hall International Series in Computer Science (1998)Google Scholar
  11. 11.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)MATHGoogle Scholar
  12. 12.
    Oliveira, M.V.M., Cavalcanti, A.L.C., Woodcock, J.C.P.: Unifying theories in ProofPower-Z. In: Dunne, S., Stoddart, B. (eds.) UTP 2006. LNCS, vol. 4010, pp. 123–140. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Oliveira, M., Cavalcanti, A., Woodcock, J.: A denotational semantics for Circus. Electron. Notes Theor. Comput. Sci. 187, 107–123 (2007)CrossRefGoogle Scholar
  14. 14.
    Zeyda, F., Cavalcanti, A.: Encoding Circus programs in ProofPowerZ. In: Butterfield, A. (ed.) UTP 2008. LNCS, vol. 5713, pp. 218–237. Springer, Heidelberg (2009), http://www.cs.york.ac.uk/circus/publications/docs/zc09b.pdf Google Scholar
  15. 15.
    Zeyda, F., Cavalcanti, A.: Mechanical reasoning about families of UTP theories. Science of Computer Programming (2010) (in Press) (Corrected Proof, Available online March 17, 2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Abderrahmane Feliachi
    • 1
    • 2
  • Marie-Claude Gaudel
    • 1
    • 2
  • Burkhart Wolff
    • 1
    • 2
  1. 1.Laboratoire LRI, UMR8623Univ Paris-SudOrsayFrance
  2. 2.CNRSOrsayFrance

Personalised recommendations