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.
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References
Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. Texts in Theoretical Computer Science. Springer, Heidelberg (2004)
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)
Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.): ITP 2013. LNCS, vol. 7998. Springer, Heidelberg (2013)
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
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)
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
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
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)
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
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
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
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
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
Leroy, X.: Formal verification of a realistic compiler. Commun. ACM 52(7), 107–115 (2009)
Sternagel, C., Thiemann, R.: The certification problem format. In: Benzmüller, C., Paleo, B. (eds.) UITP, EPTCS, vol. 167, pp. 61–72 (2014)
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
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.
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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
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DOI: https://doi.org/10.1007/978-3-319-66107-0_11
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