At the Lean FRO, Kim Morrison, a Senior Research Software Engineer, recently ran an experiment that went well beyond our expectations. An AI agent converted zlib, a widely used C compression library embedded in countless systems, to Lean, with minimal human guidance. No special tooling was built. It was Claude, a general-purpose AI, with no special training for theorem proving, out of the box. The workflow had four steps. First, the AI produced a clean, readable Lean implementation of the zlib compression format, including the DEFLATE algorithm at its core. Second, the Lean version passed the library’s existing test suite, confirming behavioral equivalence. Third, key properties were stated and proved, not as tests, but as mathematical theorems. The capstone theorem:
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One challenge is having enough training data. Another is that the training data needs to be free of contamination. For a model trained up till 1900, there needs to be no information from after 1900 that leaks into the data. Some metadata might have that kind of leakage. While it’s not possible to have zero leakage - there’s a shadow of the future on past data because what we store is a function of what we care about - it’s possible to have a very low level of leakage, sufficient for this to be interesting.
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