From: "andré hirschowitz" <"a..."@unice.fr>
To: Andrej Bauer <andrej...@andrej.com>
Cc: Michael Shulman <shu...@sandiego.edu>,
Vladimir Voevodsky <vlad...@ias.edu>,
Homotopy Type Theory <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] a new transport rule
Date: Fri, 22 Jul 2016 14:22:40 +0200 [thread overview]
Message-ID: <CAHPPr6yiAtPNFdiyYs-_odQH=CwR3036M6ZHQzqM=YBxe42V8g@mail.gmail.com> (raw)
In-Reply-To: <CAB0nkh2CmqucrGS2+QS0Yq9OYJCgW6-z8fRkn1JmO0kFVNh+Kg@mail.gmail.com>
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I looked for an example without universe/El and found
P(X) ;= forall p: Id X a, Id p (refl a).
It seems that the formula must involve a "type from term constructor"
(here Id, or there El).
andré
2016-07-22 12:00 GMT+02:00 Andrej Bauer <andrej...@andrej.com>:
> On Wed, Jul 20, 2016 at 11:10 AM, Michael Shulman <shu...@sandiego.edu>
> wrote:
> > Can you give an example of such a P which becomes well-formed when A
> > and B are substituted for X but is not well-formed with X as a
> > variable?
>
> Let
>
> T := Universe
>
> nat : Universe
> Nat type
> El nat = Nat
> 42 : Nat
>
> P(X) := Id (El X) 42 42
>
> Then P(nat) is well-formed, but P(X) is not. Or, if you dislike universes:
>
> T := bool
>
> P(X) := Id (match X with true => Nat | false => (Nat -> Nat) end) 42 42
>
> Now P(true) is well formed, but P(X) is not.
>
> With kind regards,
>
> Andrej
>
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next prev parent reply other threads:[~2016-07-22 12:23 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-07-19 17:18 FOMUS slides Vladimir Voevodsky
2016-07-19 18:16 ` [HoTT] " Michael Shulman
2016-07-19 19:28 ` Vladimir Voevodsky
2016-07-19 19:29 ` Michael Shulman
[not found] ` <7DACC421-37E7-43CC-B61F-D6C5F99921DF@ias.edu>
[not found] ` <CAOvivQzSs5=e=EEfP42nmDJUogkx7TjrAtYJqAEOFHetcPSZtA@mail.gmail.com>
[not found] ` <1B8618C8-0499-4D96-BACF-9AA4623061B9@ias.edu>
[not found] ` <CAOvivQzg_saqj7re-OCTFUFJceKab_eBR+X+OckFYe6fmkuVsQ@mail.gmail.com>
2016-07-20 8:44 ` a new transport rule Vladimir Voevodsky
2016-07-20 9:10 ` [HoTT] " Michael Shulman
2016-07-22 10:00 ` Andrej Bauer
2016-07-22 11:08 ` Michael Shulman
2016-07-26 8:07 ` Vladimir Voevodsky
2016-07-22 12:22 ` andré hirschowitz [this message]
2016-07-20 6:07 ` [HoTT] FOMUS slides Andrew Polonsky
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