Notes on Lean, tactics, and making the theorem prover do more work. https://kim-em.github.io Fri, 24 Jul 2026 00:00:00 +0000 https://kim-em.github.io/blog/2026-7-24-why-lean-is-faster-than-rust/ https://kim-em.github.io/blog/2026-7-24-why-lean-is-faster-than-rust/ Fri, 24 Jul 2026 00:00:00 +0000 performance lean I can't possibly be serious, can I, claiming that Lean is faster than Rust? Let me show you something: # silesia.tar: the 212 MB standard corpus. Each tool compresses at level 6 # and prints the resulting size in bytes; `time` reports wall-clock. $ time deflate-rust silesia.tar # miniz_oxide (pure Rust, no 'unsafe') 68112144 real 0m5.77s $ time deflate-lean silesia.tar # lean-zip 67944712 real 0m5.24s What's going on here? This is the lean-zip implementation of DEFLATE compressing the standard s… https://kim-em.github.io/blog/2026-7-7-lattice-basis-reduction-using-the-hex-lean-library/ https://kim-em.github.io/blog/2026-7-7-lattice-basis-reduction-using-the-hex-lean-library/ Tue, 07 Jul 2026 00:00:00 +0000 computer algebra lean We're starting work on a computational algebra library for Lean, called Hex. We've just released the first collection of packages, providing dense matrices, row reduction, Gram-Schmidt, and lattice basis reduction. These packages have a primarily computational focus (i.e. calculations on concrete inputs, rather than symbolic algebra), and are optimized first for runtime performance, and secondarily for performance during kernel reduction. https://kim-em.github.io/blog/2026-6-14-verified-linear-programming/ https://kim-em.github.io/blog/2026-6-14-verified-linear-programming/ Sun, 14 Jun 2026 00:00:00 +0000 tactics lean I've released leanprover/lp: verified linear programming in Lean 4. It's two things at once — a proof-carrying solver you can call from your own algorithms, and a tactic frontend that behaves a bit like linarith but reaches some goals linarith can't. The examples below are all elaborated by Lean when this page is built, using the actual tactic. Nothing here is a screenshot. https://kim-em.github.io/blog/2026-5-13-a-sum-of-squares-tactic/ https://kim-em.github.io/blog/2026-5-13-a-sum-of-squares-tactic/ Wed, 13 May 2026 00:00:00 +0000 tactics lean I've put together an sos tactic: a sum-of-squares decision procedure for nonlinear real arithmetic, closely following John Harrison's implementation in HOL Light. It closes a range of polynomial-inequality goals over the reals that we don't otherwise have good tactics for. Every example below is elaborated by Lean when this page is built — the tactic really runs, CSDP and all.