MechGeo: Autoformalizing and Proving Euclidean Geometry in Lean 4
We present MechGeo, a Mathlib native agentic framework that jointly addresses faithful autoformalization and certified proof construction for Euclidean geometry. In this framework, GeoFormalizer represents informal problems in GeoIR, deterministically translates them into Lean 4, and iteratively repairs candidate statements using structural diagnostics and semantic evaluation. GeoProver constructs geometric proof plans, derives intermediate lemmas, and selectively algebraizes suitable subgoals through a library verified in Lean. Singular or SymPy may generate algebraic certificates, but all resulting proofs and counterexamples are checked by Lean's kernel. Experiments across seven LLM bac...
| Authors | Hao Shen, Junyu Guo, Tian Cui et al. |
|---|---|
| Primary category | cs.AI |
| Published | 3 August 2026 |
| Last updated at source | 3 August 2026 |
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