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Chris Henson

@_chenson__

CS PhD student @DrexelCCI working on formalization in Lean. Maintainer of cslib.io. Student Researcher @GoogleDeepMind
Philadelphia, PA chrishenson.net Joined December 2014
2.7K Following 1.1K Followers 4.9K Posts

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Chris Henson @_chenson__
I figured my math followers would especially appreciate this! Just got these, they are originals from 1740 and 1751. Include the original publication of Euler's solution to the Basel problem, among other very cool things. So crazy to have these pieces of history on my bookshelf.
Chris Henson @_chenson__
Autoformalization is now mature and widespread enough that we need to think closer about the different reasons we formalize and the different degrees of informal/formal proofs being aligned. (Short thread)
Ricardo Pérez-Marco Verified account @rperezmarco 1d
Reminder. Formalization is void if you cannot prove that the lean certificate matches exactly the proof.

I suspect some people with bugs in their papers are going to produce lean certificates of the main result that avoids the holes that have been filled bu the clankers.
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Chris Henson @_chenson__
And what will they do when they get to the nLab page about 1Lab? Formalize all the metatheory of cubical type theory? Port it all? (I'm half joking here, but my point is that nLab pages are notoriously widely varied in scope and specificity)

ncatlab.org/nlab/show/1lab
Другая планета Verified account @nihilunbounded 4d
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Chris Henson @_chenson__
Is there a coherent, non-slop paper about Bend's type theory/kernel yet? The last paper version I saw was unreadable and so concerning from the perspective being amenable to a lean4lean style formalization. I think this will be table stakes for the next gen proof assistants.
Taelin Verified account @VictorTaelin 4d
when bend2 launched, some complained about AI usage. in my view, this is only a problem if bugs can occur. the current typescript compiler, for example, has many. I hate it. with well-designed laws, though, that ceases to be a problem. so, for the better or for the worse, bend3 will be 100% AI-written. there is no going back

while I was raising, I left a fleet of agents working on bend3, a small scale version of this vision. this was a huge success, beyond my own expectations. opus 5.5 successfully rewrote all of bend in itself, including its compiler, which is now certified, with zero bugs, and already 2x faster (!!). we now have a model of Bend, C, CUDA and the compiler, all written in Bend itself, and properly formalized. with this, we'll soon start the largest proof-driven compiler self-improvement loop in history

news on Bend have been slow because I was busy raising, but as soon as this is over, expect updates at a breath-taking place. this is the most exciting thing I've ever done and I can't wait for the big run to start
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Chris Henson @_chenson__
FWIW if you look at the Lean Zulip discussion, you'll see a much more measured conversation about what "gaps" were already known, unpublished work, etc. leanprover.zulipchat.com/#narrow/channe…
Daniel Litt Verified account @littmath 5d
I don’t find this to be true. While the correctness of results will be less in doubt, formalization has now given strong evidence that major results were already very reliable. On the other hand, the influx of capital into the profession has been accompanied by a huge number of claims about significance, applicability etc. that I find much less reliable than most mathematical claims previously.
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