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#lean

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On a more positive note re screwing around with #Lean:

I don't like the principle of explosion, but I think I now understand a little better why some mathematicians insist on it. Specifically, suppose you have (a ∨ b) ↔ b. If a is false, this statement becomes tautological. The folks behind Lean have chosen to put this in as a rewrite rule:
((a ∨ b) ↔ b) ⇒ (a →b) and then you prove ¬a and you apply the principle of explosion.

screwing around with #Lean has mainly served to confirm my prior suspicion that LSPs need to be a lot lighter weight before I'll be interested in using them on a day-to-day basis. I do not appreciate it when my editor lags and my computer's fans howl because some kind of compilation process is being repeated for every keystroke *while I'm in the middle of writing a comment*.

I recently set myself the exercise of using modern automated tools - in particular, a combination of the #GithubCopilot large language model and the dependent type matching tactic #canonical - to try to semi-automatically formalize in #Lean a one-page proof provided by a collaborator of the #EquationalTheoriesProject (Bruno Le Floch). With these tools, I was able to more or less blindly do the formalization in 33 minutes, withou any real high level conception of how the proof proceeded. It was a very different style to how I usually formalize results, but was workable for this type of technical, non-conceptual argument where the main issue is to get the details correct rather than the "big picture".

I recorded my attempt at youtube.com/watch?v=cyyR7j2ChC . See also additional discussion at leanprover.zulipchat.com/#narr . The final proof (which is far from optimized, but got the job done) can be found at github.com/teorth/estimate_too

As part of our (@sarantja@mastodon.social and yt) research on the usability of interactive theorem provers, we are conducting a study on the usage and state of tools and languages for type-driven development. We are interested in tools that encourage and facilitate type-driven development, especially in cases when they can help us reason about complex problems.

We are hoping to use your responses to identify the characteristic language features and tool interactions that enable type-driven development, with the eventual goals of enhancing them and bringing their benefits to a wider range of programmers.

Please fill in our anonymous, 10-minute survey here: https://tudelft.fra1.qualtrics.com/jfe/form/SV_bIsMxYTKUJkhVuS

You are welcome to participate if you have experience with any type-driven development tool, including dependently-typed languages (e.g., Coq, Lean, Agda), refinement types (e.g., Liquid Haskell), or even other static type systems (e.g., in Rust or Haskell).

P.S. In case you remember signing up for an interview with us in a previous survey and are now wondering whether that study will still go on, the answer is: yes! We’ve had to revise our schedule, but we are still excited to talk to you and will start inviting people for an interview soon.

tudelft.fra1.qualtrics.comType-Driven Development in PracticeUnderstanding the usage and state of tools and languages for Type-Driven Development
#Agda#Coq#Rocq
Oh hey, Asterisk has an article on theorem provers, LLMs, and autoformalization (i.e. automatically turning math papers into formalized proofs). I still think this task is significantly more difficult than what some people seem to think, but who can really tell anymore at this point.

asteriskmag.com/issues/09/automating-math

#TheoremProvers #Coq #Lean #Isabelle
asteriskmag.comAutomating Math—AsteriskComputers can already help verify proofs. One day soon, AI may be able to come up with new ones.

@Godefroy_B Je suis en train de préparer une liste de praticiens #Lean sur Mastodon : fedidevs.com/s/MzA0/

Et malheureusement je ne pas ajouter le compte de @ilf parce qu'il n'est pas "découvrable". Si tu as envie que je l'ajoute dans la liste, il suffit que tu coches la case "Autoriser des algorithmes de découverte à mettre en avant votre profil et vos messages" dans le profil ;-) Possible ?