Skip to main content

On the Strong Co–induction in Coq

  • Conference paper
Computer Aided Systems Theory - EUROCAST 2003 (EUROCAST 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2809))

Included in the following conference series:

  • 655 Accesses

Abstract

In this paper, we provide a library in Coq containing intuitionistic proofs of some facts that are on the basis of formal verification tools such as Model Checking or Theorem Proving: the Reduction Lemma [8] [17] and the correspondent on minimum fixed points [1].

In order to improve usability, most of the proofs are given in a general frame of partial order relations and not only in the specific complete lattice of a power-set.

Supported by projects: Xunta Galicia: PGIDIT02TIC00101CT and Spanish Gov. MCyT:TIC 2002-02859.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersen, H.R.: On Model Checking Infinite-State Systems. In: Matiyasevich, Y.V., Nerode, A. (eds.) LFCS 1994. LNCS, vol. 813. Springer, Heidelberg (1995)

    Google Scholar 

  2. Collins, G.: A Proof Tool for Reasoning about Functional Programs. In: Proc. of TPHOL 1996, Turku, Finland (1996)

    Google Scholar 

  3. Constable, R.L., et al.: Implementing Mathematics with the NuPRL Proof Development System. Prentice-Hall, Englewood Cliffs (1986)

    Google Scholar 

  4. Dowek, G., Felty, A., Herbelin, H., Huet, G., Murty, C., Parent, C., Paulin- Mohring, C., Werner, B.: The Coq proof assistant user’s guide. INRIA Technical Report 134 (1993)

    Google Scholar 

  5. Freire, J.L., Freire, J.E., Blanco-Ferro, A., Sánchez, J.J.: Fusion in Coq. In: Moreno-Díaz Jr., R., Buchberger, B., Freire, J.-L. (eds.) EUROCAST 2001. LNCS, vol. 2178, p. 583. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Gordon, A.D.: Bisimilarity as a Theory of Functional Programming. Technical Report NS-95-3, Basic Research in Computer Science, University of Aarhus (1995)

    Google Scholar 

  7. Gordon, M.J.C., Melham, T.F.: Introduction to Hol: A Theorem-proving Environment for Higher-Order Logic. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  8. Kozen, D.: Results on the propositional mu-calculus. Theoretical Computer Science 27, 333–354 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gordon, M.J.C., Milner, R., Wadsworth, C.P.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)

    Google Scholar 

  10. Luo, Z., Pollack, R.: LEGO Proof Development System: User’s Manual. LFCS Report ECS-LFCS-92-211, Departament of Computer Science, University of Edinburgh (1992)

    Google Scholar 

  11. Miculan, M.: On the formalization of the modal mu-calculus in the Calculus of Inductive Constructions. Information and Computation 164(1), 199–231 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Owre, S., Rushby, J.M., Shankar, N.: PVS: A prototype verification system. In: Kapur, D. (ed.) 11th International Conference on Automated Deduction (CADE). LNCS, vol. 607. Springer, Heidelberg (1981)

    Google Scholar 

  13. Sprenger, C.: A Verified Model Checker for the modal μ-calculus in Coq. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 167–183. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Tarski, A.: A Lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5, 285–309 (1955)

    MATH  MathSciNet  Google Scholar 

  15. Verma, K.N.: Reflecting Symbolic Model Checking in Coq. INRIA (2000)

    Google Scholar 

  16. Walukiewicz, I.: Notes on the Propositional μ-calculus: Completeness and Related Results. BRICS Notes Series NS-95-1 (1995) ISSN 0909-3206

    Google Scholar 

  17. Winskel, G.: A note on model checking the modal ν-calculus. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  18. Yu, S.-W.: Formal Verification of Concurrent Programs Based on Type Theory. Ph.D. Thesis, Departament of Computer Science. University of Durham (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nistal, J.L.F., Ferro, A.B., Gulías, V.M., Brañas, E.F. (2003). On the Strong Co–induction in Coq . In: Moreno-Díaz, R., Pichler, F. (eds) Computer Aided Systems Theory - EUROCAST 2003. EUROCAST 2003. Lecture Notes in Computer Science, vol 2809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45210-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45210-2_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20221-9

  • Online ISBN: 978-3-540-45210-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics