From: Michael Shulman <shulman@sandiego.edu> To: Valery Isaev <valery.isaev@gmail.com> Cc: Jon Sterling <jon@jonmsterling.com>, "HomotopyTypeTheory@googlegroups.com" <homotopytypetheory@googlegroups.com> Subject: Re: [HoTT] New theorem prover Arend is released Date: Sat, 10 Aug 2019 16:37:07 -0700 Message-ID: <CAOvivQxKMPvpm9Vwkt4ARR7R5qLmzJMUkFCrf=rFUL5sd4nXLQ@mail.gmail.com> (raw) In-Reply-To: <CAA520ftTacC4iegu2UM887nbyJWQTByMKhrcsftKPXCadH06kQ@mail.gmail.com> On Sat, Aug 10, 2019 at 5:25 AM Valery Isaev <valery.isaev@gmail.com> wrote: > The document is slightly outdated. We do not have the rule iso A B (λx ⇒ x) (λx ⇒ x) idp idp i ⇒β A in the actual implementation since univalence is true even without it. This rule has another problem. It seems that the theory as presented in the document introduces a quasi-equivalence between A = B and Equiv A B, which means that there are some true statements which are not provable in it. I don't understand. By "quasi-equivalence" do you mean an incoherent equivalence (what the book calls a map with a quasi-inverse)? If so, then every quasi-equivalence can of course be promoted to a strong equivalence. However, as I said, I'm more worried about the fourth rule coe_{λ k ⇒ iso A B f g p q k} a right ⇒β f a. That's the one that I have trouble seeing how to interpret in a model category. Can you say anything about that? > If you can prove that some \data or \record satisfies isSet (or, more generally, that it is an n-type), then you can put this proof in \use \level function corresponding to this definition and it will be put in the corresponding universe. What does it mean for it to be "put in" the corresponding universe? The documentation for \use \level makes it sound as though the definition *itself*, rather than something equivalent to it, ends up in the corresponding universe. How is the equivalence between A and F(A,p) accessed inside the proof assistant? -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAOvivQxKMPvpm9Vwkt4ARR7R5qLmzJMUkFCrf%3DrFUL5sd4nXLQ%40mail.gmail.com.

next prev parent reply indexThread overview:20+ messages / expand[flat|nested] mbox.gz Atom feed top 2019-08-06 22:16 Валерий Исаев 2019-08-07 15:01 ` Andrej Bauer 2019-08-07 22:13 ` Nicolai Kraus 2019-08-08 9:55 ` Valery Isaev 2019-08-10 9:47 ` Michael Shulman 2019-08-10 12:30 ` Valery Isaev 2019-08-10 12:37 ` Valery Isaev 2019-08-08 12:20 ` Jon Sterling 2019-08-08 12:29 ` Bas Spitters 2019-08-08 14:44 ` Valery Isaev 2019-08-08 15:11 ` Jon Sterling 2019-08-08 15:22 ` Valery Isaev 2019-08-10 9:42 ` Michael Shulman 2019-08-10 12:24 ` Valery Isaev2019-08-10 23:37 ` Michael Shulman [this message]2019-08-11 10:46 ` Valery Isaev 2019-08-11 12:39 ` Michael Shulman 2019-08-11 16:55 ` Michael Shulman 2019-08-12 14:44 ` Daniel R. Grayson 2019-08-12 17:32 ` Michael Shulman

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