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We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics.
The mathematical language AUTOMATH, its usage, and some of its extensions
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E - A Brainiac Theorem Prover
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G. Gonthier · 2007
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Theorem Proving in Higher Order Logics, 21st International Conference, TPHOLs 2008, Montreal, Canada, August 18-21, 2008. Proceedings
O. A. Mohamed, C. A. Muñoz, and S. Tahar, editors · 2008
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Formal verification of a realistic compiler
X. Leroy · 2009
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Understanding the difficulty of training deep feedforward neural networks
X. Glorot and Y. Bengio · 2010
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Mizar in a nutshell
A. Grabowski, A. Korniłowicz, and A. Naumowicz · 2010
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seL4: formal verification of an operating-system kernel
G. Klein, J. Andronick, K. Elphinstone, G. Heiser, D. Cock, P. Derrin, D. Elkaduwe, K. Engelhardt, R. Kolanski, M. Norrish, T. Sewell, H. Tuch, and S. Winwood · 2010
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Recurrent neural network based language model
T. Mikolov, M. Karafiát, L. Burget, J. Cernockỳ, and S. Khudanpur · 2010
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A machine-checked proof of the Odd Order Theorem
G. Gonthier, A. Asperti, J. Avigad, Y. Bertot, C. Cohen, F. Garillot, S. L. Roux, A. Mahboubi, R. O’Connor, S. O. Biha, I. Pasca, L. Rideau, A. Solovyev, E. Tassi, and L. Théry · 2013
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Stronger automation for Flyspeck by feature weighting and strategy evolution
C. Kaliszyk and J. Urban · 2013
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Learning from multiple proofs: First experiments
D. Kuehlwein and J. Urban · 2013
TensorFlow: Large-scale machine learning on heterogeneous systems, 2015
M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng · 2015
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Gated feedback recurrent neural networks
J. Chung, C. Gulcehre, K. Cho, and Y. Bengio · 2015
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Semi-supervised sequence learning
A. M. Dai and Q. V. Le · 2015
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A formal proof of the Kepler conjecture
T. C. Hales, M. Adams, G. Bauer, D. T. Dang, J. Harrison, T. L. Hoang, C. Kaliszyk, V. Magron, S. McLaughlin, T. T. Nguyen, T. Q. Nguyen, T. Nipkow, S. Obua, J. Pleso, J. Rute, A. Solovyev, A. H. T. Ta, T. N. Tran, D. T. Trieu, J. Urban, K. K. Vu, and R. Zumkeller · 2015
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Theorem proving in large formal mathematics as an emerging AI field
J. Urban and J. Vyskočil · 2013
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History of interactive theorem proving
J. Harrison, J. Urban, and F. Wiedijk · 2014
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Learning-assisted automated reasoning with Flyspeck
C. Kaliszyk and J. Urban · 2014
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Adam: A method for stochastic optimization
D. Kingma and J. Ba · 2014
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W. Zaremba and I. Sutskever · 2014
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http://coq.inria.fr
The Coq Proof Assistant
Cited in the paper.
Ł. Kaiser and I. Sutskever · 2015
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MizAR 40 for Mizar 40
C. Kaliszyk and J. Urban · 2015
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Efficient semantic features for automated reasoning over large theories
C. Kaliszyk, J. Urban, and J. Vyskocil · 2015
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End-to-end memory networks
S. Sukhbaatar, J. Weston, R. Fergus, et al · 2015
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O. Vinyals and Q. Le · 2015
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Sentence pair scoring: Towards unified framework for text comprehension
P. Baudiš, J. Pichl, T. Vyskočil, and J. Šedivý · 2016
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Hammering towards QED
J. C. Blanchette, C. Kaliszyk, L. C. Paulson, and J. Urban · 2016
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