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

Researchers present Trellis, an autoformalization system that uses LLM agents within constrained workflows to convert natural language mathematical proofs into Lean formal code. The system achieves reliable formalization on modest computational budgets by enforcing incremental progress through iterative refinement, demonstrated by formalizing a recent Ramsey theory breakthrough.

Trellis addresses a fundamental challenge in mathematical verification: the gap between how mathematicians naturally express proofs and how formal proof assistants like Lean require them to be written. Rather than relying on task-specific training or specialized models, the system employs process semantics grounded in mathematical rigor itself—the principle that any rigorous proof should allow detailed elaboration of its components. This philosophy-driven approach enables generalist LLM agents to produce correct formalizations through deterministic workflows that enforce meaningful progress rather than trial-and-error exploration.

The autoformalization challenge has grown increasingly important as mathematicians seek to verify complex proofs and integrate computational verification into research. Previous approaches required either expensive specialized models or labor-intensive human intervention. Trellis demonstrates that constraint-based workflows can achieve comparable results with modest resources, making formalization more accessible to the broader mathematical community.

The practical demonstration through the Ramsey theory formalization validates the approach's applicability to cutting-edge mathematics. This suggests autoformalization systems could accelerate verification of novel results and reduce proof-checking bottlenecks in research. For the AI community, Trellis exemplifies how domain-specific problem constraints can substitute for model specialization, offering efficiency gains relevant to other structured reasoning tasks.

Future development will likely focus on expanding the system's capability across mathematical domains and reducing the engineering overhead required to apply process semantics to different proof types. The work signals growing maturity in LLM-assisted formal verification, with implications for both mathematical practice and AI's role in knowledge validation.

• →Trellis uses constraint-based LLM workflows rather than specialized model training to achieve reliable mathematical proof formalization
• →The system operates on modest computational budgets by enforcing deterministic progress through iterative natural language refinement
• →Successful formalization of a recent Ramsey theory breakthrough demonstrates practical applicability to contemporary mathematics
• →Process semantics grounded in mathematical rigor principles enables generalist agents to produce correct formal code
• →The approach reduces barriers to autoformalization adoption across the mathematical research community