Re:Mathematicians welcome computer-assisted proof in ‘grand ...
by kevinbuzzard on Sunday June 20, 2021 @07:57PM
(#27574910)
The fact remains though that Lean 3 worked well enough to do Scholze level mathematics. I never quite know what to make of people saying "if the designers had done it in some other way, it would have been better". Of course if someone comes along doing it another way, and then they go on to also achieve Scholze level mathematics, then I will be all ears.
Re:Mathematicians welcome computer-assisted proof in ‘grand ...
by Jweb_Guru on Monday June 21, 2021 @01:08PM
(#27581144)
That's a very strange line of argument. Many great programs have been written in C. That doesn't mean that there is no way to improve on C. Perhaps to even the playing field, this hypothetical competitor should be given the resources of Microsoft Research as well :)
Re:Mathematicians welcome computer-assisted proof in ‘grand ...
by foooobar on Monday June 21, 2021 @01:52PM
(#27581684)
I think Kevin is asserting that to make strong comparative claims about the quality of either system, it's good to have a large and functionally similar body of work to compare the systems with, not that there is no way to improve on Lean's core :)
MSR funds a single developer. The Lean community consists of at least 30 or so active contributors right now, with many more having contributed in the past. Most folks work in academia. Much of Lean's success is absolutely due to the work of that single developer, but I don't think that the playing field is uneven due to MSR's funding.
In terms of stuff that do go more or less directly through the kernel, some followup papers to the one I linked discuss how to translate inductive definitions etc. automatically into a form accepted by the simpler kernel, so I am even more confident that this would not present a problem.