Lean 4

“the "core" of Lean is a somewhat "simple" core that does simple things to check the proof, so it's quite rare to find meaningful bugs”

“Lean is one of the most popular languages that allow for formal verification, and to me is incredibly powerful”

“There is often value in actually reading the Lean proof script (especially with the IDE support like jump to definition).”

“proving that the ownership rules are sound with Lean, something I would maybe never be able to do without AI”

“The drudgery of mechanically applying logical rules is pushed onto the Lean kernel which is trusted, while the Human can concentrate on semantic correctness”

“It's still faster than doing it all by hand but paper in -> lean out in no way ensures a correspondence between the two.”

“A Lean proof has a much higher probability of being correct (in my opinion) than any published (either preprint or peer-reviewed) paper”

“a mathematician friend of mine has been building a game engine with it. very neat stuff, anything is possible!”

“It's a nice programming language, and it lets you really hack on commands, macros, syntax, and elaboration.”

“the main downside with Lean is that libraries for reasoning about program logic are comparatively less developed”

“Lean's just a little bit too focused on talking about results to tidily talk about how those results are computed.”

“Caching only works until you change a deeply nested constant. Then you must wait 2 hours as Lean re-checks every transitive dependency”

“The tools ground the AI in reality and allow them to make progress without going in hallucinated directions.”

“Lean is apparently so slow that for Fermat's Last Theorem proof verification runs only 1 order of magnitude faster”

“The fact that it's being released alongside a Lean proof from Day 1 is super helpful for verifying that it's correct.”

“The surface of bugs in Lean is infinitely smaller than the human error involeved in a committee of peer reviewers.”

“LEAN is a functional programming language with a type system strong enough to express cutting-edge mathematics”

“The core of Lean got a lot less correct when a well-meaning AI system probed Lean for corner cases (bugs) that would "prove" a false conjecture.”

“it's type system is insanely powerful, indexed dependant inductive and quotient types allow the realization of "making invalid states unrepresentable"”

“the Lean kernel has a lot of fancy features that aren't yet perfectly understood from a type-theoretic perspective”

“Being able to confidently do this is why proof assistants like Lean are really not just another programming language.”

“the quick feedback loop between the AI prose and the Lean verification errors and warnings ensures that its logically consistent”

“I use Lean and occasionally some other languages with expressive type systems, and like you I've found it to be a pretty great experience for working with LLMs”

“It does speak to the benefits of using lean in that you don't need to be clever about the different examples you test.”

“The slowness is relatively unpredictable, too: sometimes changing a 'rewrite' to a 'with' can increase memory usage tenfold.”

“Lean feels like it could legitimately become a successor to Haskell as the go to functional programming language for software development.”

“Lean documents how to write the cat utility in its own docs and generally has a much better, more modern tooling experience”

“It's a great language for math, perhaps the best choice right now. But as a general purpose language it's incredibly quirky.”

“The main bug found was actually in the lean runtime, affecting all proofs using scalar arrays where the size of the array is not bounded.”

“best in class functional programming language, but ... its perfectability is kinda hamstrung by baking non-constructive axioms into the standard library”

“One of the things I like about Lean is precisely that it's an ordinary, Haskell-style functional programming language”

“Using LEAN or Coq requires you to basically convert your code to LEAN/Coq before you can start proving anything”

“using Lean to model things humans care about (business logic, user interfaces, physical environments, dynamic regulations) quickly hits a dead end”

“It’s far easier for Lean because the human has to read very little compared to generating whole programs.”

“Lean is line noise. It's like assembly language for math, which is great, but not what humans should be using day to day.”

“Lean 4 is a language supporting verification, and it's also a full programming language, so you can write your proofs/theorems in the same language that you program in.”

“the lean prover community has a joint project to formalize the proof of Fermat’s Last Theorem, which is a lot of work but is progressing”

“Let the LLM solve the nitty gritty details of proof, but use the higher-level theorem formation as the vessel for doing great things.”

“I would think Lean and other formal languages are the real gold standard. But none of them really have enough training data for LLMs to be any good at them.”

“It's dependent-types / theorem-proving-oriented type-system combined with AI assistants makes it the language of the future IMO.”