arXiv:2606.09674cs.AIcs.LO2026-06

用可确定流程的LLM代理实现自然语言证明的逐步形式化。

(Auto)formalization is supposed to be easy: Trellis process semantics for spelling out rigorous proofs

  • 通过受控工作流让LLM逐步细化自然语言证明
  • 在不依赖专用训练的情况下完成完整形式化
  • 适合想用通用AI工具做严谨数学证明的人

我们提出Trellis:一种利用LLM代理在确定性约束工作流中进行自动形式化的系统,通过迭代精炼自然语言证明,推动在Lean中的逐步形式化进展。该方法基于数学家对严格证明的普遍理解——即任何部分都应能轻易展开更详细内容。系统旨在以较低成本和通用代理实现可靠的形式化,其专长并非来自特定任务训练,而是源于以‘严谨性’为指导的工作流语义。我们展示了该流程成功完成近期拉姆齐理论突破的端到端Lean形式化。

原文摘要 · Abstract (English)

We present Trellis: an autoformalization system that leverages LLM agents in a deterministically constrained workflow to enforce incremental progress in Lean autoformalization tasks through iterative refinement of natural language proofs. Our approach is motivated by the common mathematician's notion of what it means to have a rigorous proof in the first place: namely, that it would be routine to elaborate any part of the proof in further detail. The result is a system which aims to achieve reliable autoformalization on a modest budget and with generalist agents, with specialization to autoformalization coming not from any task-specific agent training but instead from a meaning-of-rigor inspired workflow enforced by process semantics. We link to an end-to-end Lean formalization of a recent Ramsey theory breakthrough produced by the process.

形式化LLM应用数学证明

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