AxDafny: Agentic Verified Code Generation in Dafny

We study agentic code generation in Dafny, where a model must generate both executable code and the proof artifacts for verification. We present AxDafny, a verifier-guided repair framework that iteratively generates implementations, invariants, assertions, and termination arguments. We also introduce LiveCodeBench-Pro-Dafny (LCB-Pro-Dafny), a benchmark of 250 competition-style programming problems translated into Dafny with formal specifications and a verifier-based evaluation harness. On LCB-Pro-Dafny, AxDafny substantially improves verification success over baseline GPT-5.5 performance. On DafnyBench, AxDafny achieves 92.7\% verification success, outperforming the strongest previously reported proof-hint baseline by 6.5 percentage points. Lastly, we show that verification success and runtime test performance measure different aspects of generated code.

SorryDB: Can AI Provers Complete Real-World Lean Theorems?

We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub. Unlike existing static benchmarks, often composed of competition problems, hillclimbing the SorryDB benchmark will yield tools that are aligned to the community needs, more usable by mathematicians, and more capable of understanding complex dependencies. Moreover, by providing a continuously updated stream of tasks, SorryDB mitigates test-set contamination and offers a robust metric for an agent's ability to contribute to novel formal mathematics projects. We evaluate a collection of approaches, including generalist large language models, agentic approaches, and specialized symbolic provers, over a selected snapshot of 1000 tasks from SorryDB. We show that current approaches are complementary: even though an agentic approach based on Gemini Flash is the most performant, it is not strictly better than other off-the-shelf large-language models, specialized provers, or even a curated list of Lean tactics.

A Minimal Agent for Automated Theorem Proving

We propose a minimal agentic baseline that enables systematic comparison across different AI-based theorem prover architectures. This design implements the core features shared among state-of-the-art systems: iterative proof refinement, library search and context management. We evaluate our baseline using qualitatively different benchmarks and compare various popular models and design choices, and demonstrate competitive performance compared to state-of-the-art approaches, while using a significantly simpler architecture. Our results demonstrate consistent advantages of an iterative approach over multiple single-shot generations, especially in terms of sample efficiency and cost effectiveness. The implementation is released open-source as a candidate reference for future research and as an accessible prover for the community.