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Formal verification using proof assistants, such as Coq, enables the creation of high-quality software. However, the verification process requires significant expertise and manual effort to write proofs. Recent work has explored automating proof synthesis using machine learning and large language models (LLMs). This work has shown that identifying relevant premises, such as lemmas and definitions, can aid synthesis. We present Rango, a fully automated proof synthesis tool for Coq that automatically identifies relevant premises and also similar proofs from the current project and uses them during synthesis. Rango uses retrieval augmentation at every step of the proof to automatically determine which proofs and premises to include in the context of its fine-tuned LLM. In this way, Rango adapts to the project and to the evolving state of the proof. We create a new dataset, CoqStoq, of 2,226 open-source Coq projects and 196,929 theorems from GitHub, which includes both training data and a curated evaluation benchmark of well-maintained projects. On this benchmark, Rango synthesizes proofs for 32.0% of the theorems, which is 29% more theorems than the prior state-of-the-art tool Tactician. Our evaluation also shows that Rango adding relevant proofs to its context leads to a 47% increase in the number of theorems proven., Comment: In Proceedings of the 47th International Conference on Software Engineering (ICSE), Ottawa, ON, Canada, April 2025

Formal verification using proof assistants, such as Coq, is an effective way of improving software quality, but it is expensive. Writing proofs manually requires both significant effort and expertise. Recent research has used machine learning to automatically synthesize proofs, reducing verification effort, but these tools are able to prove only a fraction of the desired software properties. We introduce Cobblestone, a new proof-synthesis approach that improves on the state of the art by taking advantage of partial progress in proof synthesis attempts. Unlike prior tools, Cobblestone can produce multiple unsuccessful proofs using a large language model (LLM), identify the working portions of those proofs, and combine them into a single, successful proof, taking advantage of internal partial progress. We evaluate Cobblestone on two benchmarks of open-source Coq projects, controlling for training data leakage in LLM datasets. Fully automatically, Cobblestone can prove 48% of the theorems, while Proverbot9001, the previous state-of-the-art, learning-based, proof-synthesis tool, can prove 17%. Cobblestone establishes a new state of the art for fully automated proof synthesis tools for Coq. We also evaluate Cobblestone in a setting where it is given external partial proof progress from oracles, serving as proxies for a human proof engineer or another tool. When the theorem is broken down into a set of subgoals and Cobblestone is given a set of relevant lemmas already proven in the project, it can prove up to 58% of the theorems. We qualitatively study the theorems Cobblestone is and is not able to prove to outline potential future research directions to further improve proof synthesis, including developing interactive, semi-automated tools. Our research shows that tools can make better use of partial progress made during proof synthesis to more effectively automate formal verification., Comment: 13 pages, 10 figures

Proof assistants enable users to develop machine-checked proofs regarding software-related properties. Unfortunately, the interactive nature of these proof assistants imposes most of the proof burden on the user, making formal verification a complex, and time-consuming endeavor. Recent automation techniques based on neural methods address this issue, but require good programmatic support for collecting data and interacting with proof assistants. This paper presents CoqPyt, a Python tool for interacting with the Coq proof assistant. CoqPyt improves on other Coq-related tools by providing novel features, such as the extraction of rich premise data. We expect our work to aid development of tools and techniques, especially LLM-based, designed for proof synthesis and repair. A video describing and demonstrating CoqPyt is available at: https://youtu.be/fk74o0rePM8., Comment: Accepted to FSE '24 Demonstrations Track

Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful proof paths, faces a discrepancy at the inference stage, as it must sample and try various tactics at each proof state until finding success, unlike its training which does not incorporate learning from failed attempts. Intuitively, a tactic that leads to a failed search path would indicate that similar tactics should receive less attention during the following trials. In this paper, we demonstrate the benefit of training models that additionally learn from failed search paths. Facing the lack of such trial-and-error data in existing open-source theorem-proving datasets, we curate a dataset on intuitionistic propositional logic theorems and formalize it in Lean, such that we can reliably check the correctness of proofs. We compare our model trained on relatively short trial-and-error information (TrialMaster) with models trained only on the correct paths and discover that the former solves more unseen theorems with lower trial searches., Comment: Accepted as a main conference paper at ACL 2024

AI-powered programming assistants are increasingly gaining popularity, with GitHub Copilot alone used by over a million developers worldwide. These tools are far from perfect, however, producing code suggestions that may be incorrect in subtle ways. As a result, developers face a new challenge: validating AI's suggestions. This paper explores whether Live Programming (LP), a continuous display of a program's runtime values, can help address this challenge. To answer this question, we built a Python editor that combines an AI-powered programming assistant with an existing LP environment. Using this environment in a between-subjects study (N=17), we found that by lowering the cost of validation by execution, LP can mitigate over- and under-reliance on AI-generated programs and reduce the cognitive load of validation for certain types of tasks., Comment: 8 pages, 4 figures

Firefox and other major browsers rely on dozens of third-party libraries to render audio, video, images, and other content. These libraries are a frequent source of vulnerabilities. To mitigate this threat, we are migrating Firefox to an architecture that isolates these libraries in lightweight sandboxes, dramatically reducing the impact of a compromise. Retrofitting isolation can be labor-intensive, very prone to security bugs, and requires critical attention to performance. To help, we developed RLBox, a framework that minimizes the burden of converting Firefox to securely and efficiently use untrusted code. To enable this, RLBox employs static information flow enforcement, and lightweight dynamic checks, expressed directly in the C++ type system. RLBox supports efficient sandboxing through either software-based-fault isolation or multi-core process isolation. Performance overheads are modest and transient, and have only minor impact on page latency. We demonstrate this by sandboxing performance-sensitive image decoding libraries ( libjpeg and libpng ), video decoding libraries ( libtheora and libvpx ), the libvorbis audio decoding library, and the zlib decompression library. RLBox, using a WebAssembly sandbox, has been integrated into production Firefox to sandbox the libGraphite font shaping library., Comment: Accepted at Usenix Security 2020

Software based fault isolation (SFI) is a powerful approach to reduce the impact of security vulnerabilities in large C/C++ applications like Firefox and Apache. Unfortunately, practical SFI tools have not been broadly available. Developing SFI toolchains are a significant engineering challenge. Only in recent years have browser vendors invested in building production quality SFI tools like Native Client (NaCl) to sandbox code. Further, without committed support, these tools are not viable, e.g. NaCl has been discontinued, orphaning projects that relied on it. WebAssembly (Wasm) offers a promising solution---it can support high performance sandboxing and has been embraced by all major browser vendors---thus seems to have a viable future. However, Wasm presently only offers a solution for sandboxing mobile code. Providing SFI for native application, such as C/C++ libraries requires additional steps. To reconcile the different worlds of Wasm on the browser and native platforms, we present Gobi. Gobi is a system of compiler changes and runtime support that can sandbox normal C/C++ libraries with Wasm---allowing them to be compiled and linked into native applications. Gobi has been tested on libjpeg, libpng, and zlib. Based on our experience developing Gobi, we conclude with a call to arms to the Wasm community and SFI research community to make Wasm based module sandboxing a first class use case and describe how this can significantly benefit both communities. Addendum: This short paper was originally written in January of 2019. Since then, the implementation and design of Gobi has evolved substantially as some of the issues raised in this paper have been addressed by the Wasm community. Nevertheless, several challenges still remain. We have thus left the paper largely intact and only provide a brief update on the state of Wasm tooling as of November 2019 in the last section.

Foundational verification allows programmers to build software which has been empirically shown to have high levels of assurance in a variety of important domains. However, the cost of producing foundationally verified software remains prohibitively high for most projects,as it requires significant manual effort by highly trained experts. In this paper we present Proverbot9001,a proof search system using machine learning techniques to produce proofs of software correctness in interactive theorem provers. We demonstrate Proverbot9001 on the proof obligations from a large practical proof project,the CompCert verified C compiler,and show that it can effectively automate what were previously manual proofs,automatically producing proofs for 27.5% of theorem statements in our test dataset, when combined with solver-based tooling. Without any additional solvers,we exhibit a proof completion rate that is a 4X improvement over prior state-of-the-art machine learning models for generating proofs in Coq., Comment: Condensed version to be published at MAPL 2020

Programmers frequently maintain implicit data invariants, which are relations between different data structures in a program. Traditionally, such invariants are manually enforced and checked by programmers. This ad-hoc practice is difficult because the programmer must manually account for all the locations and configurations that break an invariant. Moreover, implicit invariants are brittle under code-evolution: when the invariants and data structures change, the programmer must repeat the process of manually repairing all of the code locations where invariants are violated. A much better approach is to introduce data invariants as a language feature and rely on language support to maintain invariants. To handle this challenge, we introduce Targeted Synthesis, a technique for integrating data invariants with invariant-agnostic imperative code at compile-time. This technique is nontrivial due to the complex structure of both invariant specifications, as well as general imperative code. The key insight is to take a language co-design approach involving both the language of data invariants, as well as the imperative language. We leverage this insight to produce two high-level results: first, we support a language with iterators without requiring general quantified reasoning, and second, we infer complicated invariant-preserving patches. We evaluate these claims through a language termed Spyder, a core calculus of data invariants over imperative iterator programs. We evaluate the expressiveness and performance of Spyder on a variety of programs inspired by web applications, and we find that Spyder efficiently compiles and maintains data invariants.

Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root causes, which is difficult because floating-point errors are generally non-local, non-compositional, and non-uniform. This paper presents Herbgrind, a tool to help developers identify and address root causes in numerical code written in low-level C/C++ and Fortran. Herbgrind dynamically tracks dependencies between operations and program outputs to avoid false positives and abstracts erroneous computations to a simplified program fragment whose improvement can reduce output error. We perform several case studies applying Herbgrind to large, expert-crafted numerical programs and show that it scales to applications spanning hundreds of thousands of lines, correctly handling the low-level details of modern floating point hardware and mathematical libraries, and tracking error across function boundaries and through the heap., Comment: 15 pages published at PLDI 18

Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for structuring the optimization phase of a compiler. In our approach, optimizations take the form of equality analyses that add equality information to a common intermediate representation. The optimizer works by repeatedly applying these analyses to infer equivalences between program fragments, thus saturating the intermediate representation with equalities. Once saturated, the intermediate representation encodes multiple optimized versions of the input program. At this point, a profitability heuristic picks the final optimized program from the various programs represented in the saturated representation. Our proposed way of structuring optimizers has a variety of benefits over previous approaches: our approach obviates the need to worry about optimization ordering, enables the use of a global optimization heuristic that selects among fully optimized programs, and can be used to perform translation validation, even on compilers other than our own. We present our approach, formalize it, and describe our choice of intermediate representation. We also present experimental results showing that our approach is practical in terms of time and space overhead, is effective at discovering intricate optimization opportunities, and is effective at performing translation validation for a realistic optimizer., Comment: 80 pages, 39 figures