[Agda] [Coq-Club] Why dependent type theory?

[Josef Urban]

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
>
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