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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What’s more, the “best” sleeping position can change throughout a lifetime and will balance your body’s needs. For example, shoulder pain sometimes becomes a problem during side sleeping as people get older, which can conflict with the common advice that people with sleep apnea should avoid sleeping on their backs, according to Dr. David McCarty, MD, FAASM, chief medical officer of Rebis, a sleep medicine clinic. And while stomach sleeping is often considered the position that causes the most neck and back strain, its many people’s go-to position that gets them to fall sleep fast.