Formal verification has the potential to drastically reduce software bugs, but its high additional cost has hindered large-scale adoption. While Dafny presents a promise to significantly reduce the effort to write verified programs, users are often required to provide logical annotations to aid the verifier. Here, we explore using a combination of Large Language Models and search to build dafny-annotator: a tool that adds logical annotations to a Dafny method until the verifier can prove it correct. On a test set from the DafnyBench collection of programs, greedy search guided by LLaMa 3.1 8B successfully annotates only 15.7% of the methods. Since this data-driven approach is hindered by the lack of large-scale training data, we propose a method for open-ended synthesis of new Dafny programs in a flexible pipeline where LLMs formulate high-level ideas, implement them, and incrementally propose changes to existing programs, which Dafny validates. This gives us a synthetic dataset, DafnySynth, which we use to augment DafnyBench for training. Fine-tuning on both datasets boosts LLaMa 8B's success rate to 50.6% -- significantly better than the base model, or training on either dataset alone. Our results suggest a path towards capable AI assistants for languages that don't yet have large-scale human-generated examples. In turn, such assistants might reduce friction for users and ultimately drive adoption.

We introduce DafnyBench, the largest benchmark of its kind for training and evaluating machine learning systems for formal software verification. We test the ability of LLMs such as GPT-4 and Claude 3 to auto-generate enough hints for the Dafny formal verification engine to successfully verify over 750 programs with about 53,000 lines of code. The best model and prompting scheme achieved 68% success rate, and we quantify how this rate improves when retrying with error message feedback and how it deteriorates with the amount of required code and hints. We hope that DafnyBench will enable rapid improvements from this baseline as LLMs and verification techniques grow in quality.