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(Auto)formalization is supposed to be easy: Trellis... | AI Research

Key Takeaways

The paper "(Auto)formalization is supposed to be easy: Trellis process semantics for spelling out rigorous proofs" introduces Trellis, a new system designed...
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.
We link to an end-to-end Lean formalization of a recent Ramsey theory breakthrough produced by the process.
Rather than relying on specialized training for AI models, the system uses a structured, step-by-step workflow to guide general-purpose AI agents in refining natural language proofs until they are formal and rigorous.
The core motivation behind Trellis is the mathematician’s standard for a rigorous proof: the idea that any part of a proof should be routine to elaborate in further detail.

Paper AbstractExpand

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.

The paper "(Auto)formalization is supposed to be easy: Trellis process semantics for spelling out rigorous proofs" introduces Trellis, a new system designed to automate the process of converting mathematical proofs into the Lean programming language. Rather than relying on specialized training for AI models, the system uses a structured, step-by-step workflow to guide general-purpose AI agents in refining natural language proofs until they are formal and rigorous.

The Philosophy of Rigor

The core motivation behind Trellis is the mathematician’s standard for a rigorous proof: the idea that any part of a proof should be routine to elaborate in further detail. The system treats formalization not as a single, massive task, but as an iterative process of breaking down arguments. By enforcing this "meaning-of-rigor" through a specific workflow, the system ensures that the AI makes incremental, verifiable progress toward a complete formal proof.

How Trellis Works

Trellis operates using a deterministically constrained workflow. Instead of asking an AI to write a full formal proof at once, the system uses process semantics to force the AI to refine its natural language proofs in stages. This approach allows the system to function effectively using generalist LLM agents rather than models specifically trained for formalization. By keeping the agents on a strict path of incremental refinement, the system maintains reliability even when operating on a modest computational budget.

Demonstrating Success

To validate the effectiveness of the Trellis system, the author applied it to a recent breakthrough in Ramsey theory. The paper demonstrates that the process successfully produced an end-to-end formalization of this complex mathematical result in Lean. This serves as a practical proof-of-concept that the system can handle sophisticated, modern mathematical research by leveraging its structured workflow rather than relying on task-specific model training.

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