- Lean is a proof tool that uses a machine to check the correctness of mathematical proofs and programs. According to this article, the lake check command has been added to Lean v4.35.0, so you can export your work and recheck it with the official checker leanchecker. The whole process runs inside a sandbox by default.
- Using the lake check --paranoid option, the same work is rechecked with four additional checkers: nanoda, lean4lean, con-leche, and con-ron. A memory-hardened version of the official checker also runs, so memory errors show up as a check halt instead of a silent wrong answer.
- The article says con-leche is the first kernel written in Lean and proven consistent. The proof relies on a set-theory model, and the approach is described as reducing implementation-mistake type bugs. On the full Mathlib export, the author reports a measurement of 0.69 times the instruction count of the official kernel, using 8 threads in about 100 seconds.
- con-ron is a kernel that the AI ported from con-leche to Rust, then proved to match the original checking algorithm using the Aeneas tool. Aeneas is a tool that verifies Rust code with Lean. The article explains that using both kernels together gives stronger protection against errors in the Lean compiler or runtime.
O: This is useful for researchers who write proofs in Lean and want to run lake check --paranoid on their own project to confirm that the results of the four extra checkers match those of the official checker.
X: The 0.69 instruction count and 100 second figure for con-leche are measurements reported by the authors, and since the measurement conditions have not been fully disclosed, you should verify them in your own environment.