Abstract
Two methods for extracting detailed formal dependencies from the Coq and Mizar system are presented and compared. The methods are used for dependency extraction from two large mathematical repositories: the Coq Repository at Nijmegen and the Mizar Mathematical Library. Several applications of the detailed dependency analysis are described and proposed. Motivated by the different applications, we discuss the various kinds of dependencies that we are interested in, and the suitability of various dependency extraction methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adams, M.: Introducing HOL Zero. In: Fukuda, K., Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 142–143. Springer, Heidelberg (2010)
Alama, J., Heskes, T., Kühlwein, D., Tsivtsivadze, E., Urban, J.: Premise selection for mathematics by corpus analysis and kernel methods. CoRR abs/1108.3446 (2012), http://arxiv.org/abs/1108.3446
Alama, J., Kühlwein, D., Urban, J.: Automated and Human Proofs in General Mathematics: An Initial Comparison. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 37–45. Springer, Heidelberg (2012)
Asperti, A., Padovani, L., Coen, C.S., Guidi, F., Schena, I.: Mathematical knowledge management in HELM. Ann. Math. Artif. Intell. 38(1-3), 27–46 (2003)
Bertot, Y., Pons, O., Pottier, L.: Dependency graphs for interactive theorem provers. Tech. rep., INRIA, report RR-4052 (2000)
Garillot, F., Gonthier, G., Mahboubi, A., Rideau, L.: Packaging Mathematical Structures. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 327–342. Springer, Heidelberg (2009)
Grabowski, A., Kornilowicz, A., Naumowicz, A.: mizar in a nutshell. Journal of Formalized Reasoning 3(2), 153–245 (2010)
Haftmann, F., Wenzel, M.: Constructive Type Classes in Isabelle. In: Altenkirch, T., McBride, C. (eds.) TYPES 2006. LNCS, vol. 4502, pp. 160–174. Springer, Heidelberg (2007)
Hoder, K., Voronkov, A.: Sine Qua Non for Large Theory Reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 299–314. Springer, Heidelberg (2011)
Mamane, L., Geuvers, H.: A document-oriented Coq plugin for TeXmacs. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM 2007 - Work in Progress. RISC Report, vol. 07-06, pp. 47–60. University of Linz, Austria (2007)
Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. Mechanized Mathematics and Its Applications 4, 3–24 (2005)
Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Applied Logic 7(1), 41–57 (2009)
Pons, O., Bertot, Y., Rideau, L.: Notions of dependency in proof assistants. In: UITP 1998. Eindhoven University of Technology (1998)
Spitters, B., van der Weegen, E.: Type classes for mathematics in type theory. Mathematical Structures in Computer Science 21(4), 795–825 (2011)
Urban, J.: MoMM—fast interreduction and retrieval in large libraries of formalized mathematics. International Journal on Artificial Intelligence Tools 15(1), 109–130 (2006)
Urban, J., Hoder, K., Voronkov, A.: Evaluation of Automated Theorem Proving on the Mizar Mathematical Library. In: Fukuda, K., van der Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 155–166. Springer, Heidelberg (2010)
Wiedijk, F.: Mizar’s Soft Type System. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 383–399. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alama, J., Mamane, L., Urban, J. (2012). Dependencies in Formal Mathematics: Applications and Extraction for Coq and Mizar. In: Jeuring, J., et al. Intelligent Computer Mathematics. CICM 2012. Lecture Notes in Computer Science(), vol 7362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31374-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-31374-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31373-8
Online ISBN: 978-3-642-31374-5
eBook Packages: Computer ScienceComputer Science (R0)