SMART  
Strong Modular Proof Assistance

 Cezary Kaliszyk (PI)
 Burak Ekici
 Evan Marzion
 Julian Parsert
 Shawn Wang
Summary
Formal proof technology delivers an unparalleled level of certainty and security. Nevertheless, applying proof assistants to the verification of complex theories and designs is still extremely laborious. High profile certification projects, such as seL4, CompCert, and Flyspeck require tens of personyears. We recently demonstrated that this effort can be significantly reduced by combining reasoning and learning in so called hammer systems: 40% of the Flyspeck, HOL4, Isabelle/HOL, and Mizar toplevel lemmas can be proved automatically.
Today’s early generation of hammers consists of individual systems limited to very few proof assistants. The accessible knowledge repositories are isolated, and there is no reuse of hammer components. It is possible to achieve a breakthrough in proof automation by developing new AI methods that combine reasoning knowledge and techniques into a smart hammer, that works over a very large part of today’s formalized knowledge. The main goal of the project is to develop a strong and uniform learningreasoning system available for multiple logical foundations. To achieve this, we will develop: (a) uniform learning methods, (b) reusable ATP encoding components for different foundational aspects, (c) integration of proof reconstruction, and (d) methods for knowledge extraction, reuse and content merging. The single proof advice system will be made available for multiple proof assistants and their vast heterogeneous libraries.
The ultimate outcome is an advice system able to automatically prove half of Coq, ACL2, and Isabelle/ZF toplevel theorems. Additionally we will significantly improve success rates for HOL provers and Mizar. The combined smart advice method together with the vast accumulated knowledge will result in a novel kind of tool, which allows working mathematicians to automatically find proofs of many simple conjectures, paving the way for the widespread use of formal proof in mathematics and computer science.
Activities
 We coorganize the Conference on Artificial Intelligence and Theorem Proving (AITP)
Publications
 Ł. Czajka and C. Kaliszyk. Hammer for Coq: Automation for Dependent Type Theory. JAR, 2018.
 S. Loos, G. Irving, C. Szegedy, and C. Kaliszyk. Deep Network Guided Proof Search. LPAR 2017.
 M. Färber, C. Kaliszyk, and J. Urban. Monte Carlo Tableau Proof Search. CADE 2017.
 C. Kaliszyk, F. Chollet, and C. Szegedy.
HolStep: A Machine Learning Dataset for Higherorder Logic Theorem Proving.
ICLR 2017.
[ PDF (preprint) ]
 T. Gauthier, C. Kaliszyk, and J. Urban. TacticToe: Learning to reason with HOL4 Tactics. LPAR 2017.
 C. Kaliszyk, J. Urban, and J. Vyskočil. Automating Formalization by Statistical and Semantic Parsing of Mathematics. ITP 2017, volume 10499 of LNCS, pp. 1227. 2017.
 T. Gauthier and C. Kaliszyk.
Aligning Concepts across Proof Assistant Libraries.
J. Symbolic Computation, to appear
[ BibTeX  PDF (preprint) ]
 C. Kaliszyk and K. Pąk. Presentation and Manipulation of Mizar Properties in an Isabelle Object Logic. CICM 2017.
 C. Kaliszyk and K. Pąk. Isabelle Formalization of Set Theoretic Structures and Set Comprehensions. MACIS 2017.
 D. Müller, T. Gauthier, C. Kaliszyk, M. Kohlhase, and F. Rabe. Classification of Alignments between Concepts of Formal Mathematical Systems. CICM 2017.
 J. Parsert and C. Kaliszyk. Formal Microeconomic Foundations and the First Welfare Theorem. CPP 2018.