Mario Carneiro (at 12:29):Īs long as you can make a big enough type you can do most of the same things in HOL Kevin Buzzard (at 12:29): Set theory doesn't really have types at all, but you can reconstruct it all Kevin Buzzard (at 12:29):Īn example of a dependent type is a function which Johan will have seen, which takes a topological space and presheaf on it, and defines a function from the space sending a point to an element of the stalk of the presheaf at that point. You can, that's kind of the point Johannes Hölzl (at 12:29):
Wait - you can basically make dependent types in set theory, right? Mario Carneiro (at 12:28):īeing a de facto foundation for pen-and-paper maths? Mario Carneiro (at 12:29): Set theory probably doesn't have schemes either :rolling_eyes: Kevin Buzzard (at 12:28): Set theory doesn't have dependent types either. Or, at least, skeptical that you could do it whilst remaining sane. When he'd left I told the post-doc that I'd met people who were skeptical. I gave a talk in Cambridge two weeks ago and at the end of it Larry Paulson told one of his post-docs to go away and define a scheme in Isabelle, to prove it could be done. Kevin Buzzard (at 12:26):Įveryone knows that mathematicians can't use Isabelle because it doesn't have dependent types? Kevin Buzzard (at 12:27): Now I'm disappointed they didn't ask about Isabelle. My partner was out at an aerials (circus stuff) class this evening, talking to someone, who at some point in the conversation asked "Coq or Lean"? (Context: they worked in CS at a research institute here in Canberra, my partner mentioned to them I was interested in automated theorem proving.) Johannes Hölzl (at 12:25): Scott Morrison (at 10:41):Ī slightly unusual "Lean in the wild" story: This guy obviously has no idea about how mathematics works in practice. "When describing a proof of a theorem, one must be cautious to ensure said proofĭoes not contain errors or inconsistencies.". Mario Carneiro (at 11:14):Īctually I think you're right Kevin Buzzard (at 11:37): I thought it was a Prop-valued variable, but I'm not sure. Is premise still a keyword? Looks like it means axiom from context Rob Lewis (at 11:06): More Lean in the wild, if you're willing to read some Portuguese: someone was working on cryptography last summer. Here's a cool writeup of the thesis that includes the esverify project mentioned up above by Hölzl Rob Lewis (at 10:55):
is a bad thing in my opinion Bryan Gin-ge Chen (at 22:02): Johan Commelin (at Buzzard Did you just confess on Reddit that you don't know much about Reddit? Johan Commelin (at 10:42):Īnyway, congrats with the visibility! Kenny Lau (at 10:54): rar.txt."Our choice of Lean as the language for the formalisation of this paper has been a consequence of a failed attempt at embedding two-level type theory in the Agda proof assistant."Īdventures in Formalisation p.124 - Scott Fleischman Kevin Buzzard (at 07:17):
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