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[Josef Urban <josef.urban AT gmail.com>]

Chad Brown's FMM'19 keynote discussing "fake theorems" and combining HOL and set theory may be interesting in the context of this thread: http://grid01.ciirc.cvut.cz/~chad/host.pdf . I am biased but I think people should read him more.

Best,

Josef

On Tue, Mar 3, 2020, 20:44 Jason Gross <jasongross9 AT gmail.com> wrote:

I'm in the process of writing my thesis on proof assistant performance bottlenecks (with a focus on Coq), and there's a large class of performance bottlenecks that come from (mis)using the power of dependent types.  So in writing the introduction, I want to provide some justification for the design decision of using dependent types, rather than, say, set theory or classical logic (as in, e.g., Isabelle/HOL).  And the only reasons I can come up with are "it's fun" and "lots of people do it"

So I'm asking these mailing lists: why do we base proof assistants on dependent type theory?  What are the trade-offs involved?

I'm interested both in explanations and arguments given on list, as well as in references to papers that discuss these sorts of choices.

Thanks,

Jason