Skip to main content
SpringerLink
Log in

Implementing and Reasoning About Hash-consed Data Structures in Coq

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

We report on four different approaches to implementing hash-consing in Coq programs. The use cases include execution inside Coq, or execution of the extracted OCaml code. We explore the different trade-offs between faithful use of pristine extracted code, and code that is fine-tuned to make use of OCaml programming constructs not available in Coq. We discuss the possible consequences in terms of performances and guarantees.We use the running example of binary decision diagrams and then demonstrate the generality of our solutions by applying them to other examples of hash-consed data structures.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Melquiond, G.: Inf. Comput. 216 (14) (2012). doi:10.1016/j.ic.2011.09.005

  2. Vafeiadis, V.: In: ITP, Lecture Notes in Computer Science, vol. 7998, pp. 328–337. Springer (2013)

  3. Knuth, D. E.: The Art of Computer Programming, vol. 4A, chap. 7.1.4. Addison-Wesley (2011), Binary decision diagrams

  4. Verma, K. N., Goubault-Larrecq, J.: Reflecting BDDs in Coq. In: Proc. ASIAN, vol. 1961, pp. 162–181. Springer (2000), LNCS. doi:10.1007/3-540-44464-5_13

  5. Verma, K.N., Goubault-Larrecq, J.: Reflecting BDDs in Coq. Rapport de recherche RR-3859. INRIA (2000)

  6. Braibant, T., Jourdan, J.H., Monniaux, D.: Supplementary Material. https://github.com/braibant/hash-consing-coq

  7. Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: In: The Essence of Computation: Complexity, Analysis, Transformation, pp. 85–108. LNCS 2566. Springer (2002)

  8. Conchon, S., Filliâtre, J. C.: Type-safe modular hash-consing. In: ACM SIGPLAN Workshop on ML. Portland, Oregon (2006), http://www.lri.fr/filliatr/ftp/publis/hash-consing2.pdf

  9. The Why3 platform 0.80. http://why3.lri.fr

  10. Huet, G.: Constructive Computation Theory. Course notes, available at http://yquem.inria.fr/huet/PUBLIC/CCT.pdf

  11. Charguéraud, A.: In: Chakravarty, M.M.T., Hu, Z., Danvy, O. (eds.), pp. 418–430. Proceeding of the 16th ACM SIGPLAN International Conference on Functional programming (ICFP). ACM (2011)

  12. Sozeau, M.: Subset coercions in Coq. In: TYPES, vol. 4502., pp. 237–252, Lecture Notes in Computer Science. Springer (2007)

  13. Jeremy Bradley, N. D.: Compositional BDD construction: A lazy algorithm. Tech. Rep. CSTR-98-005, Department of Computer Science, University of Bristol (1998), http://www.cs.bris.ac.uk/Publications/Papers/1000250.pdf

  14. Christiansen, J., Huch, F.: A purely functional implementation of ROBDDs in Haskell. In: Nilsson, H. (ed.) Trends in Functional Programming, vol. 7, pp. 55–71. Intellect (2006), Trends in Functional Programming

  15. Beckert, B., Hähnle, R.: Verification of Object-Oriented Software: The KeY Approach, vol. 4334. LNCS, Springer (2007), doi:10.1007/978-3-540-69061-0 Schmitt, P. H. (ed.)

  16. Bulwahn, L., Krauss, A., Haftmann, F., Erkök, L., Matthews, J.: Imperative functional programming with Isabelle/HOL. In: Theorem Proving in Higher Order Logics (TPHOL), LNCS, vol. 5170, pp. 134–149. Springer (2008), doi:10.1007/978-3-540-71067-7_14

  17. Giorgino, M., Strecker, M.: Correctness of pointer manipulating algorithms illustrated by a verified BDD construction. In: Giannakopoulou, D., Méry, D. (eds.) Formal Methods (FM), LNCS, vol. 7436, pp. 202–216. Springer (2012), doi:10.1007/978-3-642-32759-9_18

  18. Armand, M., Grégoire, B., Spiwack, A., Théry, L.: Extending Coq with Imperative Features and Its Application to SAT Verification. In: Proc. ITP, LNCS, vol. 6172, pp. 83–98. Springer (2010), doi:10.1007/978-3-642-14052-5_8

  19. Ortner, V., Schirmer, N.: Verification of BDD Normalization. In: TPHOLs, vol. 3603, pp. 261–277. Springer (2005), Lecture Notes in Computer Science

  20. Boyer, R. S., Hunt Jr., W. A.: Function memoization and unique object representation for ACL2 functions In: ACL2, pp. 81–89. ACM (2006)

  21. Goubault, J.: HimML: Standard ML with Fast Sets and Maps. In: 5th ACM SIGPLAN Workshop on ML and its Applications (1994), http://citeseerx.ist.psu.edu/viewdoc/summary?, doi:10.1.1.40.4967

  22. Goubault-Larrecq, J. HimML: HimML is a map-oriented ML (2008), http://www.lsv.ens-cachan.fr/goubault/himml-dwnld.html

  23. Goubault, J.: Implementing functional languages with fast equality, sets and maps: an exercise in Hash Consing. Tech. rep. Bull S.A. Research Center (1994), http://citeseerx.ist.psu.edu/viewdoc/summary? doi:10.1.1.41.1757

Download references

Author information

Authors and Affiliations

  1. Inria Paris-Rocquencourt, Domaine de Voluceau, BP 105, 78153, Le Chesnay, France

    Thomas Braibant & Jacques-Henri Jourdan

  2. VERIMAG, CNRS & Université de Grenoble, Centre Équation, 2 avenue de Vignate, 38610, Gières, France

    David Monniaux

Authors
  1. Thomas Braibant
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacques-Henri Jourdan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David Monniaux
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacques-Henri Jourdan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Braibant, T., Jourdan, JH. & Monniaux, D. Implementing and Reasoning About Hash-consed Data Structures in Coq. J Autom Reasoning 53, 271–304 (2014). https://doi.org/10.1007/s10817-014-9306-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10817-014-9306-0

Keywords

Search

Navigation