Skip to main content

How to Get More Out of Your Oracles

  • Conference paper
Interactive Theorem Proving (ITP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10499))

Included in the following conference series:

  • 995 Accesses

Abstract

Formal verification of large computer-generated proofs often relies on certified checkers based on oracles. We propose a methodology for such proofs, advocating a separation of concerns between formalizing the underlying theory and optimizing the algorithm implemented in the checker, based on the observation that such optimizations can benefit significantly from adequately adapting the oracle.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. Texts in Theoretical Computer Science. Springer, Heidelberg (2004)

    Book  Google Scholar 

  2. Blanqui, F., Koprowski, A.: CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates. Math. Struct. Comp. Sci. 21, 827–859 (2011)

    Article  MathSciNet  Google Scholar 

  3. Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.): ITP 2013. LNCS, vol. 7998. Springer, Heidelberg (2013)

    MATH  Google Scholar 

  4. Claret, G., González-Huesca, L., Régis-Gianas, Y., Ziliani, B.: Lightweight proof by reflection using a posteriori simulation of effectful computation. In: Blazy et al. [3], pp. 67–83

    Google Scholar 

  5. Codish, M., Cruz-Filipe, L., Frank, M., Schneider-Kamp, P.: Sorting nine inputs requires twenty-five comparisons. J. Comput. Syst. Sci. 82(3), 551–563 (2016)

    Article  MathSciNet  Google Scholar 

  6. Cruz-Filipe, L., Larsen, K.S., Schneider-Kamp, P.: Formally proving size optimality of sorting networks. J. Autom. Reason. Accepted for publication. doi:10.1007/s10817-017-9405-9

  7. Cruz-Filipe, L., Marques-Silva, J., Schneider-Kamp, P.: Efficient certified resolution proof checking. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 118–135. Springer, Heidelberg (2017). doi:10.1007/978-3-662-54577-5_7

    Chapter  Google Scholar 

  8. Cruz-Filipe, L., Schneider-Kamp, P.: Formally proving the boolean triples conjecture. In: Eiter, T., Sands, D. (eds.) LPAR-21. EPiC Series in Computing, vol. 46, pp. 509–522. EasyChair Publications (2017)

    Google Scholar 

  9. Cruz-Filipe, L., Wiedijk, F.: Hierarchical reflection. In: Slind, K., Bunker, A., Gopalakrishnan, G. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 66–81. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30142-4_5

    Chapter  Google Scholar 

  10. Darbari, A., Fischer, B., Marques-Silva, J.: Industrial-strength certified SAT solving through verified SAT proof checking. In: Cavalcanti, A., Deharbe, D., Gaudel, M.-C., Woodcock, J. (eds.) ICTAC 2010. LNCS, vol. 6255, pp. 260–274. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14808-8_18

    Chapter  Google Scholar 

  11. Fouilhé, A., Monniaux, D., Périn, M.: Efficient generation of correctness certificates for the abstract domain of polyhedra. In: Logozzo, F., Fähndrich, M. (eds.) SAS 2013. LNCS, vol. 7935, pp. 345–365. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38856-9_19

    Chapter  Google Scholar 

  12. Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 228–245. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_15

    Chapter  MATH  Google Scholar 

  13. Konev, B., Lisitsa, A.: A SAT attack on the Erdős discrepancy conjecture. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 219–226. Springer, Cham (2014). doi:10.1007/978-3-319-09284-3_17

    Chapter  MATH  Google Scholar 

  14. Leroy, X.: Formal verification of a realistic compiler. Commun. ACM 52(7), 107–115 (2009)

    Article  Google Scholar 

  15. Sternagel, C., Thiemann, R.: The certification problem format. In: Benzmüller, C., Paleo, B. (eds.) UITP, EPTCS, vol. 167, pp. 61–72 (2014)

    Google Scholar 

  16. Wetzler, N.D., Heule, M.J.H., Hunt Jr., W.A.: Mechanical verification of SAT refutations with extended resolution. In: Blazy et al. [3], pp. 229–244

    Google Scholar 

Download references

Acknowledgments

We would like to thank Pierre Letouzey for his suggestions and help with making our extracted code more efficient.

The authors were supported by the Danish Council for Independent Research, Natural Sciences, grant DFF-1323-00247, and by the Open Data Experimentarium at the University of Southern Denmark. Computational resources were generously provided by the Danish Center for Scientific Computing.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luís Cruz-Filipe .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Cruz-Filipe, L., Larsen, K.S., Schneider-Kamp, P. (2017). How to Get More Out of Your Oracles. In: Ayala-Rincón, M., Muñoz, C.A. (eds) Interactive Theorem Proving. ITP 2017. Lecture Notes in Computer Science(), vol 10499. Springer, Cham. https://doi.org/10.1007/978-3-319-66107-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66107-0_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66106-3

  • Online ISBN: 978-3-319-66107-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics