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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. 

Machine learning technology has become ubiquitous, but, unfortunately, often exhibits bias. As a consequence, disparate stakeholders need to interact with and make informed decisions about using machine learning models in everyday systems. Visualization technology can support stakeholders in understanding and evaluating trade-offs between, for example, accuracy and fairness of models. This paper aims to empirically answer “Can visualization design choices affect a stakeholder's perception of model bias, trust in a model, and willingness to adopt a model?” Through a series of controlled, crowd-sourced experiments with more than 1,500 participants, we identify a set of strategies people follow in deciding which models to trust. Our results show that men and women prioritize fairness and performance differently and that visual design choices significantly affect that prioritization. For example, women trust fairer models more often than men do, participants value fairness more when it is explained using text than as a bar chart, and being explicitly told a model is biased has a bigger impact than showing past biased performance. We test the generalizability of our results by comparing the effect of multiple textual and visual design choices and offer potential explanations of the cognitive mechanisms behind the difference in fairness perception and trust. Our research guides design considerations to support future work developing visualization systems for machine learning. 

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.