Abstract
Modern theorem provers can discharge a significant proportion of Proof Obligation (POs) that arise in the use of Formal Method (FMs). Unfortunately, the residual POs require tedious manual guidance. On the positive side, these “difficult” POs tend to fall into families each of which requires only a few key ideas to unlock. This paper outlines a system that can lessen the burden of FM proofs by identifying and characterising ways of discharging POs of a family by tracking an interactive proof of one member of the family. This opens the possibility of capturing ideas — represented as proof strategies — from an expert and/or maximising reuse of ideas after changes to definitions. The proposed system has to store a wealth of meta-information about conjectures, which can be matched against previously learned strategies, or can be used to construct new strategies based on expert guidance.
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Notes
- 1.
It is assumed that ATP is always used before strategic intervention is required.
- 2.
ProofProcess framework, http://github.com/andriusvelykis/proofprocess.
References
Butterfield, A., Freitas, L., Woodcock, J.: Mechanising a formal model of flash memory. Sci. Comp. Prog. 74(4), 219–237 (2009)
Freitas, L., Jones, C.B., Velykis, A.: Can a system learn from interactive proofs?. In: Voronkov, A., Korovina, M. (eds.) HOWARD-60. A Festschrift on the Occasion of Howard Barringer’s 60th Birthday, pp. 124–139. EasyChair (2014)
Freitas, L., Jones, C.B., Velykis, A., Whiteside, I.: How to say why. Technical report CS-TR-1398, Newcastle University, November 2013. www.ai4fm.org/tr
Freitas, L., Woodcock, J.: Mechanising mondex with Z/Eves. Formal Aspects Comput. 20(1), 117–139 (2008)
Freitas, L., Woodcock, J.: A chain datatype in Z. Int. J. Softw. Inform. 3(2–3), 357–374 (2009)
Freitas, L., Whiteside, I.: Proof Patterns for Formal Methods. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 279–295. Springer, Heidelberg (2014)
Grov, G., Kissinger, A., Lin, Y.: A graphical language for proof strategies. In: McMillan et al. [MMV13], pp. 324–339
Heras, J., Komendantskaya, E.: ML4PG in computer algebra verification. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS, vol. 7961, pp. 354–358. Springer, Heidelberg (2013)
Heras, J., Komendantskaya, E., Johansson, M., Maclean, E.: Proof-pattern recognition and lemma discovery in acl2. In: McMillan et al. [MMV13], pp. 389–406
Johansson, M., Dixon, L., Bundy, A.: Conjecture synthesis for inductive theories. J. Autom. Reason. 47(3), 251–289 (2011)
Jones, C.B., Freitas, L., Velykis, A.: Ours Is to reason why. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 227–243. Springer, Heidelberg (2013)
Jones, C.B., Jones, K.D., Lindsay, P.A., Moore, R.: mural: A Formal Development Support System. Springer, London (1991)
Jones, C.B., Shaw, R.C.F. (eds.): Case Studies in Systematic Software Development. Prentice Hall International, Englewood (1990)
Kaliszyk, C., Urban, J.: Learning-assisted theorem proving with millions of lemmas. CoRR, abs/1402.3578 (2014)
McMillan, K., Middeldorp, A., Voronkov, A. (eds.): LPAR-19 2013. LNCS, vol. 8312. Springer, Heidelberg (2013)
Paulson, L.C. (ed.): Isabelle: A Generic Theorem Prover. LNCS, vol. 828. Springer, Heidelberg (1994)
Saaltink, M.: The Z/EVES system. In: Till, D., Bowen, J.P., Hinchey, M.G. (eds.) ZUM 1997. LNCS, vol. 1212, pp. 72–85. Springer, Heidelberg (1997)
Velykis, A.: Inferring the proof process. In: Choppy, C., et al. (eds.) FM2012 Doctoral Symposium, Paris, France, August 2012
Acknowledgements
Other AI4FM members helped us understand important problems in automated reasoning. We are grateful for discussions with Moa Johansson on lemma generation. EPSRC grants EP/H024204/1 and EP/J008133/1 support our research.
Several interesting questions were raised after the presentation at VSTTE in Vienna. Shankar emphasised the virtue of recording information about proof strategies that fail — this was recognised early in AI4FM [JFV13] but the reminder is timely and a way of handling this will be made more explicit in the model. Christoph Gladisch questioned the extent to which “machine learning” could help improve an AI4FM system: currently mechanised learning is focussed on setting of the \(Weight\) field — we agreed to pursue a dialogue on the topic. Mike Whalen urged others to make source material available to the AI4FM project — we would obviously welcome this but emphasise that we need (instrumented) proof processes rather than just finished proofs — our proof material is available via http://www.ai4fm.org
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Freitas, L., Jones, C.B., Velykis, A., Whiteside, I. (2014). A Model for Capturing and Replaying Proof Strategies. In: Giannakopoulou, D., Kroening, D. (eds) Verified Software: Theories, Tools and Experiments. VSTTE 2014. Lecture Notes in Computer Science(), vol 8471. Springer, Cham. https://doi.org/10.1007/978-3-319-12154-3_12
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