From: Andrew Polonsky <andrew....@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Cc: shu...@sandiego.edu, vlad...@ias.edu
Subject: Re: [HoTT] FOMUS slides
Date: Tue, 19 Jul 2016 23:07:44 -0700 (PDT) [thread overview]
Message-ID: <6b38173e-7baf-44ba-8d18-b4dc06a5c300@googlegroups.com> (raw)
In-Reply-To: <EB3CE28E-4C7A-465E-A701-8FFE13824531@ias.edu>
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A couple of years ago, I have experimented with a system based on a similar
idea. See page 7 here:
https://dl.dropboxusercontent.com/u/7730626/ett3.pdf
The reduction rules for transporting over a type equality e : A ≈ B can
indeed be defined purely by induction on e, as on page 9. (And, if you
want to add univalence, then equivalence will be a constructor for this
type, in which case the transport will reduce to the function given in this
constructor.)
Cheers,
Andrew
On Tuesday, July 19, 2016 at 9:28:14 PM UTC+2, v v wrote:
>
> Thank you for spotting this typo. It is supposed to be P_1. I have
> corrected the slides.
>
>
> > On Jul 19, 2016, at 8:16 PM, Michael Shulman <shu...@sandiego.edu
> <javascript:>> wrote:
> >
> > Can you explain the idea on the last slide a little more? Did you
> > actually mean to say that R and "transportb0 R e" both have type P2,
> > or should one of them have had type P1? If the latter, then how can
> > we tell what type(s) "transportb0 R e" is allowed to have based on
> > knowing the types of R and e?
> >
> > On Tue, Jul 19, 2016 at 2:18 PM, Vladimir Voevodsky <vla...@ias.edu
> <javascript:>> wrote:
> >> Hello,
> >>
> >> the slides of my FOMUS talk that have started the discussion about
> >> equalities are now available at my website
> >> https://www.math.ias.edu/vladimir/lectures .
> >>
> >> Vladimir.
> >>
> >> --
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> >> email to HomotopyTypeThe...@googlegroups.com <javascript:>.
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> > You received this message because you are subscribed to the Google
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prev parent reply other threads:[~2016-07-20 6:07 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-07-19 17:18 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
2016-07-20 6:07 ` Andrew Polonsky [this message]
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