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[Viktor Kunčak <vkuncak AT gmail.com>]

I would be also curious to hear answers to this questions!

("Lots of people do it" seems like a very compelling answer.)

Which bottlenecks are you referring to? Are they intrinsically tied to dependent types, or they are related to the treatment of propositions and equality in systems such as Coq?

There are type systems overlayed on top of initially untyped languages (e.g. the language of Alloy Analyzer) and there are gradual types and designs like TypeScript for to initially untyped programming languages. ACL2 theorem prover for pure LISP, SPASS theorem prover for first-order logic, and "TLA+ model checking made symbolic" model checker for TLA+ all include techniques to recover types from an initially untyped language.

Best regards,

  Viktor

On Tue, Mar 3, 2020 at 8:44 PM 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