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

2026-06-08

AI Summary

This work addresses the challenge of achieving reliable, low-cost automatic formalization of mathematical proofs under limited computational resources. It introduces Trellis, a novel system that translates mathematicians’ intuitive notion of “rigor” into executable process semantics by constructing a deterministic, constraint-guided workflow based on general-purpose large language model agents. Without requiring domain-specific training, Trellis employs an iterative refinement mechanism to progressively transform informal natural language proofs into formal Lean proofs. The system demonstrates its efficacy and practicality by successfully formalizing, in an end-to-end manner, a recent breakthrough result in Ramsey theory, thereby validating its capacity to bridge informal mathematical reasoning and machine-checkable formalization.

Abstract

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.

Problem

• autoformalization
• rigorous proof
• LLM agents
• process semantics
• Lean

Innovation

• autoformalization
• process semantics
• iterative refinement
• rigorous proof
• Lean