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1. thanks, I'll try to take a look later at this. Most of my skepticism was rooted in a personal-hell I endured when trying to parallelize SAT-solving with GPUs...which didn't go well because its hard to share across workers effectively. Another thing to note, I'd frown upon using Claude-written works for communication between humans. If the ideas are yours then it should be feasible to write the paper. Many people will take "Claude wrote this paper" as a big sign telling them to ignore it

2. With no offense, but until it is demonstrated that this is useful for larger verified software projects I will be intensely skeptical; and, I'd advise not making claims like this until you have empirical evidence

4. Assuming this all holds air and isn't AI-bs (I'll make no claims in either direction), then yeah I'd say its valid research. To be clear with what you're claiming here, you're giving the impression that you have a GPU-accelerated proof assistant that is 2 orders of magnitude faster than Lean. If true, then that's a big and interesting contribution

Best of luck with everything. I certainly understand the frustration with how slow proof assistants can be, and I hope that we as a community can significantly speed them up

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2 isn't a big claim though, I think anyone developing Lean or Agda would agree these would be much faster with zero inference, unification or search? They'd just complain the language would become unergonomic, and that's true. Bend is very verbose.

Thanks and your feedbacks are reasonable, I appreciate

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After looking through things a little more, I think I may have had some misunderstandings. Would you be willing to answer a few more questions? I will also take a closer look at the papers at some point, so apologies if these are redundant

1. When I see a comparison of a new proof checker to something like Agda/Lean, I initially evaluate them as systems for formalized mathematics, but I don't think you're making claims of that nature. Would you say that you'd expect, say, the new giganto proof of Fermat's Last Theorem to be expressible in Bend and faster than the corresponding Lean proof?

2. If the answer to the last one is no, that's not expressible, then what is the class of propositions/types that you express? My initial reading was that it was the whole of affine dependent type theory

3. Is the GPU used at both runtime and compile time?

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1. I do, but probably not in the current version, since I believe these proofs probably need full closure cloning to be ergonomic.

2. You can express anything actually, because you can clone data, just not functions. So, anything you could implement with datatypes (i.e., without cloned closures), you could probably also prove. But again, people use and abuse closure cloning a lot in Lean. So, how ergonomic would that be? I don't know. It is less about expressivity and more about ergonomics.

3. No, just in the runtime for now. Checking proofs on the GPU will happen when we implement Bend in itself.

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Hey, I get a 404 from that link.
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fixed ty
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