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Formal verification is a promising method for producing reliable software, but the difficulty of manually writing verification proofs severely limits its utility in practice. Recent methods have automated some proof synthesis by guiding a search through the proof space using a theorem prover. Unfortunately, the theorem prover provides only the crudest estimate of progress, resulting in effectively undirected search. To address this problem, we create QEDCartographer, an automated proof-synthesis tool that combines supervised and reinforcement learning to more effectively explore the proof space. QEDCartographer incorporates the proofs' branching structure, enabling reward-free search and overcoming the sparse reward problem inherent to formal verification. We evaluate QEDCartographer using the CoqGym benchmark of 68.5K theorems from 124 open-source Coq projects. QEDCartographer fully automatically proves 21.4% of the test-set theorems. Previous search-based proof-synthesis tools Tok, Tac, ASTactic, Passport, and Proverbot9001, which rely only on supervised learning, prove 9.6%, 9.8%, 10.9%, 12.5%, and 19.8%, respectively. Diva, which combines 62 tools, proves 19.2%. Comparing to the most effective prior tool, Proverbot9001, QEDCartographer produces 26% shorter proofs 27% faster, on average over the theorems both tools prove. Together, QEDCartographer and non-learning-based CoqHammer prove 31.8% of the theorems, while CoqHammer alone proves 26.6%. Our work demonstrates that reinforcement learning is a fruitful research direction for improving proof-synthesis tools' search mechanisms. 

Industrial deployments of automated program repair (APR), e.g., at Facebook and Bloomberg, signal a new milestone for this exciting and potentially impactful technology. In these deployments, developers use APR-generated patch suggestions as part of a human-driven debugging process. Unfortunately, little is known about how using patch suggestions affects developers during debugging. This paper conducts a controlled user study with 40 developers with a median of 6 years of experience. The developers engage in debugging tasks on nine naturally-occurring defects in real-world, open-source, Java projects, using Recoder, SimFix, and TBar, three state-of-the-art APR tools. For each debugging task, the developers either have access to the project's tests, or, also, to code suggestions that make all the tests pass. These suggestions are either developer-written or APR-generated, which can be correct or deceptive. Deceptive suggestions, which are a common APR occurrence, make all the available tests pass but fail to generalize to the intended specification. Through a total of 160 debugging sessions, we find that access to a code suggestion significantly increases the odds of submitting a patch. Correct APR suggestions increase the odds of debugging success by 14,000%, but deceptive suggestions decrease the odds of success by 65%. Correct suggestions also speed up debugging. Surprisingly, we observe no significant difference in how novice and experienced developers are affected by APR, suggesting that APR may find uses across the experience spectrum. Overall, developers come away with a strong positive impression of APR, suggesting promise for APR-mediated, human-driven debugging, despite existing challenges in APR-generated repair quality. 

Formally verifying system properties is one of the most effective ways of improving system quality, but its high manual effort requirements often render it prohibitively expensive. Tools that automate formal verification by learning from proof corpora to synthesize proofs have just begun to show their promise. These tools are effective because of the richness of the data the proof corpora contain. This richness comes from the stylistic conventions followed by communities of proof developers, together with the powerful logical systems beneath proof assistants. However, this richness remains underexploited, with most work thus far focusing on architecture rather than on how to make the most of the proof data. This article systematically explores how to most effectively exploit one aspect of that proof data: identifiers. We develop the Passport approach, a method for enriching the predictive Coq model used by an existing proof-synthesis tool with three new encoding mechanisms for identifiers: category vocabulary indexing, subword sequence modeling, and path elaboration. We evaluate our approach’s enrichment effect on three existing base tools: ASTactic, Tac, and Tok. In head-to-head comparisons, Passport automatically proves 29% more theorems than the best-performing of these base tools. Combining the three tools enhanced by the Passport approach automatically proves 38% more theorems than combining the three base tools. Finally, together, these base tools and their enhanced versions prove 45% more theorems than the combined base tools. Overall, our findings suggest that modeling identifiers can play a significant role in improving proof synthesis, leading to higher-quality software.