From: Jasper Hugunin <jas...@cs.washington.edu>
To: HomotopyTypeTheory@googlegroups.com
Subject: Re: [HoTT] Re: Where is the problem with initiality?
Date: Fri, 1 Jun 2018 14:52:09 -0700 [thread overview]
Message-ID: <CAGTS-a8gXmo4=JuHAFLhqVSvfZjYemgtbpC+79EVY=L2UmTgEw@mail.gmail.com> (raw)
In-Reply-To: <CAA3CDBagp=z5f-h3gBamc-dV7eUSb07s7eZUwf0qau-efNEZXg@mail.gmail.com>
[-- Attachment #1: Type: text/plain, Size: 1428 bytes --]
On Friday, 1 June 2018 18:45:42 UTC+1, Eric Finster wrote:
> But, then, this seems to be a statement about *extrinsic* syntax. If,
> as Thorsten advocates, we somehow manage to produce a highly
> structured, internal description of the syntax of type theory,
> then typechecking for this syntax is, by definition, unnecessary!
On Fri, Jun 1, 2018 at 1:59 PM András Kovács <putta...@gmail.com> wrote:
> Type checking must be performed in any case, at some level. If we use
> intrinsic embedded syntaxes, then the implementation of the metalanguage
> (in a meta-metalanguage) does the type checking. Hence, if we intend to
> formalize a syntax of type theory which is intended as a metatheoretical
> setting for mathematics, then I think decidability is quite important.
>
If we don't intend our type theory to be used as a metatheoretical setting
for mathematics, it seems interesting to consider for example a type theory
with a family of base types indexed by the circle, the syntax of which I
think would not form a set.
That is, if we have a way to represent dependent type theory in Coq, what
happens if we add a constructor `a_circle_of_types : circle -> type` to our
syntax (for a postulated circle, or HIT)? This should be consistent, to add
a family of uninterpreted types, but I believe equality is no longer
decidable (since equality of circle is not decidable).
- Jasper Hugunin
[-- Attachment #2: Type: text/html, Size: 2669 bytes --]
next prev parent reply other threads:[~2018-06-01 21:52 UTC|newest]
Thread overview: 57+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-05-22 5:46 Michael Shulman
2018-05-22 16:47 ` Ambrus Kaposi
2018-05-23 16:26 ` [HoTT] " Thorsten Altenkirch
2018-05-24 5:52 ` Michael Shulman
2018-05-24 8:11 ` Thorsten Altenkirch
2018-05-24 9:53 ` Ambrus Kaposi
2018-05-24 17:26 ` Michael Shulman
2018-05-26 9:21 ` Thomas Streicher
2018-05-26 11:47 ` Michael Shulman
2018-05-26 16:47 ` stre...
2018-05-27 5:14 ` Bas Spitters
2018-05-28 22:39 ` Michael Shulman
2018-05-29 9:15 ` [HoTT] " Thorsten Altenkirch
2018-05-29 15:15 ` Michael Shulman
2018-05-30 9:33 ` Thomas Streicher
2018-05-30 9:37 ` Thorsten Altenkirch
2018-05-30 10:10 ` Thomas Streicher
2018-05-30 12:08 ` Thorsten Altenkirch
2018-05-30 13:40 ` Thomas Streicher
2018-05-30 14:38 ` Thorsten Altenkirch
2018-05-30 10:53 ` Alexander Kurz
2018-05-30 12:05 ` Thorsten Altenkirch
2018-05-30 19:07 ` Michael Shulman
2018-05-31 10:06 ` Thorsten Altenkirch
2018-05-31 11:05 ` Michael Shulman
2018-05-31 19:02 ` Alexander Kurz
2018-06-01 9:55 ` Martin Escardo
2018-06-01 17:07 ` Martín Hötzel Escardó
2018-06-01 17:43 ` Eric Finster
2018-06-01 19:55 ` Martín Hötzel Escardó
2018-06-01 20:59 ` András Kovács
2018-06-01 21:06 ` Martín Hötzel Escardó
2018-06-01 21:23 ` Michael Shulman
2018-06-01 21:53 ` Eric Finster
2018-06-01 22:09 ` Michael Shulman
2018-06-02 15:06 ` Eric Finster
2018-06-05 20:04 ` Michael Shulman
2018-06-02 5:13 ` Thomas Streicher
2018-06-01 21:52 ` Jasper Hugunin [this message]
2018-06-01 22:00 ` Eric Finster
2018-06-01 21:27 ` Matt Oliveri
2018-06-02 5:21 ` Ambrus Kaposi
2018-06-02 6:01 ` Thomas Streicher
2018-06-02 14:35 ` Thorsten Altenkirch
2018-05-30 13:30 ` Jon Sterling
2018-06-05 7:52 ` Andrej Bauer
2018-06-05 8:37 ` David Roberts
2018-06-05 9:46 ` Gabriel Scherer
2018-06-05 22:19 ` Martín Hötzel Escardó
2018-06-05 22:54 ` Martín Hötzel Escardó
2018-06-05 22:12 ` Richard Williamson
2018-06-06 15:05 ` Thorsten Altenkirch
2018-06-06 19:25 ` Richard Williamson
2018-05-29 14:00 ` Jon Sterling
2018-05-30 22:35 ` Michael Shulman
2018-05-31 10:48 ` Martín Hötzel Escardó
2018-05-31 11:09 ` Michael Shulman
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to='CAGTS-a8gXmo4=JuHAFLhqVSvfZjYemgtbpC+79EVY=L2UmTgEw@mail.gmail.com' \
--to="jas..."@cs.washington.edu \
--cc=HomotopyTypeTheory@googlegroups.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).