Advertisement

Embedding a Proof System in Haskell

Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6299)

Abstract

This article reports about a work-in-progress project that aims at embedding a proof system [4] in the Haskell programming language. The goal of the system is to create formally verified software using the correctness by construction principle. Using Haskell as the host language provides a powerful and flexible environment so that programming language tools can be used to build proofs.

The main contribution of this paper is the systematic analysis of different techniques for language embedding. We present design decisions by pointing out which techniques are applicable and which ones are inappropriate or inconvenient to use when embedding a proof system like the our one. We also point out the advantages of the embedding compared to a previous implementation of the same system.

Keywords

Proof System Safety Property Proof Obligation Imperative Program Proof Checker 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
  3. 3.
    Home of HackageDB, http://hackage.haskell.org
  4. 4.
  5. 5.
    Abrial, J.-R.: The B-book: assigning programs to meanings. Cambridge University Press, New York (1996)CrossRefzbMATHGoogle Scholar
  6. 6.
    Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334. Springer, Heidelberg (2007)Google Scholar
  7. 7.
    Claessen, K., Sands, D.: Observable sharing for functional circuit description. In: Thiagarajan, P.S., Yap, R.H.C. (eds.) ASIAN 1999. LNCS, vol. 1742, pp. 62–73. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Cok, D.R., Kiniry, J.R.: ESC/Java2: Uniting ESC/Java and JML. In: Barthe, G., Burdy, L., Huisman, M., Lanet, J.-L., Muntean, T. (eds.) CASSIS 2004. LNCS, vol. 3362, pp. 108–128. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    de Mol, M., van Eekelen, M., Plasmeijer, R.: Theorem proving for functional programmers, Sparkle: A functional theorem prover. In: Arts, T., Mohnen, M. (eds.) IFL 2002. LNCS, vol. 2312, pp. 55–72. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Dévai, G.: Programming language elements for proof construction. In: Volume of abstracts of the 6th Joint Conference on Mathematics and Computer Science (2006)Google Scholar
  11. 11.
    Dévai, G.: Programming language elements for correctness proofs. Acta Cybernetica (accepted for publication 2007)Google Scholar
  12. 12.
    Dévai, G.: Meta programming on the proof level. Acta Universitatis Sapientiae, Informatica 1(1), 15–34 (2009)zbMATHGoogle Scholar
  13. 13.
    Dévai, G., Csörnyei, Z.: Separation logic style reasoning in a refinement based language. In: Proceedings of the 7th International Conference on Applied Informatics (2007) (to appeare)Google Scholar
  14. 14.
    Dévai, G., Pataki, N.: A tool for formally specifying the C++ standard template library. Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae, Sectio Computatorica 31, 147–166 (2009)zbMATHGoogle Scholar
  15. 15.
    Horváth, Z., Kozsik, T., Tejfel, M.: Extending the Sparkle core language with object abstraction. Acta Cybernetica 17, 419–445 (2005)zbMATHGoogle Scholar
  16. 16.
    Peyton Jones, S., Vytiniotis, D., Weirich, S., Washburn, G.: Simple unification-based type inference for GADTs. In: ICFP 2006: Proceedings of the eleventh ACM SIGPLAN International Conference on Functional Programming, pp. 50–61. ACM Press, New York (2006)CrossRefGoogle Scholar
  17. 17.
    Kozsik, T.: Proving Program Properties Specified with Subtype Marks. In: Horváth, Z., Zsók, V., Butterfield, A. (eds.) IFL 2006. LNCS, vol. 4449, pp. 163–180. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    McBride, C.: Faking it: Simulating dependent types in Haskell. Journal of Functional Programming 12(5), 375–392 (2002)MathSciNetzbMATHGoogle Scholar
  19. 19.
    McBride, C.: Epigram: Practical programming with dependent types. In: Advanced Functional Programming, pp. 130–170 (2004)Google Scholar
  20. 20.
    Morgan, C.: Programming from specifications, 2nd edn. Prentice Hall International (UK) Ltd. Englewood Cliffs (1994)zbMATHGoogle Scholar
  21. 21.
    Norell, U.: Towards a practical programming language based on dependent type theory. PhD thesis, Chalmers University of Technology (2007)Google Scholar
  22. 22.
    Schreiner, W.: The RISC ProofNavigator: A proving assistant for program verification in the classroom. Formal Aspects of Computing 21(3) (2009)Google Scholar
  23. 23.
    Winkler, J.: The frege program prover FPP. Internationales Wissenschaftliches Kolloquium 42, 116–121 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Faculty of Informatics, Dept. of Programming Languages and CompilersEötvös Loránd UniversityBudapestHungary

Personalised recommendations