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Mining the Archive of Formal Proofs

Published: 13 July 2015 Publication History

Abstract

The Archive of Formal Proofs is a vast collection of computer-checked proofs developed using the proof assistant Isabelle. We perform an in-depth analysis of the archive, looking at various properties of the proof developments, including size, dependencies, and proof style. This gives some insights into the nature of formal proofs.

References

[1]
The Mizar mathematical library. http://mizar.org
[2]
An, Y., Janssen, J., Milios, E.: Characterizing and mining citation graphs of the computer science literature. Knowl. Inf. Syst. 6, 664---678 2004
[3]
Blanchette, J.C., Böhme, S., Fleury, M., Smolka, S.J., Steckermeier, A.: Semi-intelligible Isar proofs from machine-generated proofs. Accepted in J. Autom. Reason. http://www21.in.tum.de/~blanchet/isar2.pdf
[4]
Blanchette, J.C., Böhme, S., Paulson, L.C.: Extending Sledgehammer with SMT solvers. J. Autom. Reason. 511, 109---128 2013
[5]
Blanchette, J.C., Greenaway, D., Kaliszyk, C., Kühlwein, D., Urban, J.: A learning-based relevance filter for Isabelle/HOL 2015 Submitted. http://www21.in.tum.de/~blanchet/mash2.pdf
[6]
Böhme, S., Nipkow, T.: Sledgehammer: judgement day. In: Giesl, J., Hähnle, R. eds. IJCAR 2010. LNCS, vol. 6173, pp. 107---121. Springer, Heidelberg 2010
[7]
Chaudhuri, K., Doligez, D., Lamport, L., Merz, S.: The TLA$$^ \text{+ } $$+ proof system: building a heterogeneous verification platform. In: Cavalcanti, A., Deharbe, D., Gaudel, M.-C., Woodcock, J. eds. ICTAC 2010. LNCS, vol. 6255, p. 44. Springer, Heidelberg 2010
[8]
Church, A.: A formulation of the simple theory of types. J. Symb. Logic 52, 56---68 1940
[9]
Crovella, M.E., Bestavros, A.: Self-similarity in world wide web traffic: evidence and possible causes. IEEE/ACM Trans. Network. 56, 835---846 1997
[10]
de Moura, L., BjØrner, N.S.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. eds. TACAS 2008. LNCS, vol. 4963, pp. 337---340. Springer, Heidelberg 2008
[11]
Gonthier, G., et al.: A machine-checked proof of the odd order theorem. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. eds. ITP 2013. LNCS, vol. 7998, pp. 163---179. Springer, Heidelberg 2013
[12]
Hölzl, J., Immler, F., Huffman, B.: Type classes and filters for mathematical analysis in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. eds. ITP 2013. LNCS, vol. 7998, pp. 279---294. Springer, Heidelberg 2013
[13]
Kaliszyk, C., Urban, J.: HOLyHammer: online ATP service for HOL light. Math. Comput. Sci. 91, 5---22 2015
[14]
Lammich, P., Lochbihler, A.: The Isabelle collections framework. In: Kaufmann, M., Paulson, L.C. eds. ITP 2010. LNCS, vol. 6172, pp. 339---354. Springer, Heidelberg 2010
[15]
Leroy, X.: A formally verified compiler back-end. J. Autom. Reason. 43, 363---446 2009
[16]
Lochbihler, A.: Java and the Java memory model -- a unified, machine-checked formalisation. In: Seidl, H. ed. ESOP 2012. LNCS, vol. 7211, pp. 497---517. Springer, Heidelberg 2012
[17]
Matichuk, D., Murray, T., Andronick, J., Jeffery, R., Klein, G., Staples, M.: Empirical study towards a leading indicator for cost of formal software verification. In: Canfora, G., Elbaum, S. eds. International Conference on Software Engineering ICSE 2015. ACM 2015
[18]
Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. Mech. Math. Appl. 41, 3---24 2005
[19]
Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Appl. Logic 71, 41---57 2009
[20]
Nipkow, T., Klein, G.: Concrete Semantics with Isabelle/HOL. Springer, Heidelberg 2014. http://concrete-semantics.org
[21]
Nipkow, T., Paulson, L.C., Wenzel, M. eds.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg 2002
[22]
Paulson, L.C., Blanchette, J.C.: Three years of experience with Sledgehammer, a practical link between automatic and interactive theorem provers. In: Sutcliffe, G., Schulz, S., Ternovska, E. eds. International Workshop on the Implementation of Logics IWIL 2010. EPiC Series, vol. 2, pp. 1---11. EasyChair 2012
[23]
Riazanov, A., Voronkov, A.: The design and implementation of Vampire. AI Commun. 152---3, 91---110 2002
[24]
Schulz, S.: System description: E 1.8. In: McMillan, K., Middeldorp, A., Voronkov, A. eds. LPAR-19 2013. LNCS, vol. 8312, pp. 735---743. Springer, Heidelberg 2013
[25]
Staples, M., Jeffery, R., Andronick, J., Murray, T., Klein, G., Kolanski, R.: Productivity for proof engineering. In: Morisio, M., Dybå, T., Torchiano, M. eds. Empirical Software Engineering and Measurement ESEM 2014, pp. 15:1---15:4. ACM, New York 2014
[26]
Urban, J.: MPTP 0.2: design, implementation, and initial experiments. J. Autom. Reason. 371---2, 21---43 2006
[27]
Urban, J., Rudnicki, P., Sutcliffe, G.: ATP and presentation service for Mizar formalizations. J. Autom. Reason. 502, 229---241 2013
[28]
Weidenbach, C., Dimova, D., Fietzke, A., Kumar, R., Suda, M., Wischnewski, P.: SPASS version 3.5. In: Schmidt, R.A. ed. CADE-22. LNCS, vol. 5663, pp. 140---145. Springer, Heidelberg 2009
[29]
Wenzel, M.: Isabelle/Isar--a versatile environment for human-readable formal proof documents. Ph.D. thesis, Institut für Informatik, Technische Universität München 2002. http://tumb1.biblio.tu-muenchen.de/publ/diss/in/2002/wenzel.html
[30]
Wiedijk, F.: Statistics on digital libraries of mathematics. Stud. Logic, Gramm. Rhetor. 1831, 137---151 2009

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cover image Guide Proceedings
Proceedings of the International Conference on Intelligent Computer Mathematics - Volume 9150
July 2015
344 pages
ISBN:9783319206141

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 13 July 2015

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