SEPIA: Search for Proofs Using Inferred Automata

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9195)

Abstract

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.

Keywords

Interactive theorem proving Model inference Proof automation 

References

  1. 1.
    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) CrossRefGoogle Scholar
  2. 2.
    Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development - Coq’Art: The Calculus of Inductive Constructions. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  3. 3.
    Duncan, H.: The Use of Data Mining for the Automatic Formation of Tactics. Ph.d. thesis, University of Edinburgh (2007)Google Scholar
  4. 4.
    Gransden, T., Walkinshaw, N., Raman, R.: Mining state-based models from proof corpora. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS, vol. 8543, pp. 282–297. Springer, Heidelberg (2014) Google Scholar
  5. 5.
    Grov, G., Komendantskata, E., Bundy, A.: A Statistical Relational Learning Challenge Extracting Proof Strategies from Exemplar Proofs. In: ICML-12 Workshop on Statistical Relational Learning (2012)Google Scholar
  6. 6.
    Jamnik, M., Kerber, M., Pollet, M., Benzmüller, C.: Automatic learning of proof methods in proof planning. Logic J. IGPL 11(6), 647–673 (2003)CrossRefMATHGoogle Scholar
  7. 7.
    Kohavi, R.: A Study of Cross-validation and Bootstrap for Accuracy Estimation and Model Selection. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence, pp. 1137–1143. Morgan Kaufmann (1995)Google Scholar
  8. 8.
    Komendantskaya, E., Heras, J., Grov, G.: Machine learning in proof general: interfacing interfaces. In: User Interfaces for Theorem Provers, EPTCS, vol. 118, pp. 15–41 (2013)Google Scholar
  9. 9.
    Lang, K.J., Pearlmutter, B.A., Price, R.A.: Results of the abbadingo one DFA learning competition and a new evidence-driven state merging algorithm. In: Honavar, V.G., Slutzki, G. (eds.) ICGI 1998. LNCS (LNAI), vol. 1433, pp. 1–12. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  10. 10.
    The Coq Development Team: The Coq Proof Assistant Reference Manual, Version 8.4. LogiCal Project. http://coq.inria.fr/refman
  11. 11.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL – A Proof Assistant for Higher-Order Logic, LNCS, vol. 2283. Springer, Heidelberg (2002)Google Scholar
  12. 12.
    Walkinshaw, N., Lambeau, B., Damas, C., Bogdanov, K., Dupont, P.: STAMINA: a competition to encourage the development and assessment of software model inference techniques. Empir. Softw. Eng. 18(4), 791–824 (2013)CrossRefGoogle Scholar
  13. 13.
    Walkinshaw, N., Taylor, R., Derrick, J.: Inferring Extended Finite State Machine Models from Software Executions. Empir. Softw. Eng. 1–43 (2015)Google Scholar
  14. 14.
    Wiedijk, F.: Formal proof - getting started. Not. AMS 55(11), 1408–1414 (2008)MathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thomas Gransden
    • 1
  • Neil Walkinshaw
    • 1
  • Rajeev Raman
    • 1
  1. 1.Department of Computer ScienceUniversity of LeicesterLeicesterUK

Personalised recommendations