From: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
To: "Joyal, André" <"joyal..."@uqam.ca>
Cc: David Roberts <drober...@gmail.com>,
Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>,
Michael Shulman <shu...@sandiego.edu>,
Steve Awodey <awo...@cmu.edu>,
"homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] Identity versus equality
Date: Sat, 9 May 2020 20:43:13 +0200 [thread overview]
Message-ID: <20200509184313.GB28841@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <8C57894C7413F04A98DDF5629FEC90B1652F55C8@Pli.gst.uqam.ca>
Dear Andr'e,
> By the way, if type theory is not very effective in practice, why do we insist that it should always compute?
> The dream of a formal system in which every proof leads to an actual computation may be far off.
> Not that we should abandon it, new discoveries are always possible.
> Is there a version of type theory for proving and verifying, less
> for computing?
In my opinion the currenrly implemented type theories are essentially
for proving and not for computing.
But if you haven't mechanized PART of equational reasoning it would be
much much more painful than it still is.
But that is "only" a pragmatic issue.
> The notations of type theory are very useful in homotopy theory.
> But the absence of simplicial types is a serious obstacle to applications.
In cubical type theory they sort of live well with cubes not being
fibrant... They have them as pretypes. But maybe I misunderstand...
Thomas
next prev parent reply other threads:[~2020-05-09 18:43 UTC|newest]
Thread overview: 61+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-05-05 8:47 Ansten Mørch Klev
2020-05-06 16:02 ` [HoTT] " Joyal, André
2020-05-06 19:01 ` Steve Awodey
2020-05-06 19:18 ` Michael Shulman
2020-05-06 19:31 ` Steve Awodey
2020-05-06 20:30 ` Joyal, André
2020-05-06 22:52 ` Thorsten Altenkirch
2020-05-06 22:54 ` Thorsten Altenkirch
2020-05-06 23:29 ` Joyal, André
2020-05-07 6:11 ` Egbert Rijke
2020-05-07 6:58 ` Thorsten Altenkirch
2020-05-07 9:04 ` Ansten Mørch Klev
2020-05-07 10:09 ` Thomas Streicher
2020-05-07 16:13 ` Joyal, André
2020-05-07 21:41 ` David Roberts
2020-05-07 23:43 ` Joyal, André
2020-05-07 23:56 ` David Roberts
2020-05-08 6:40 ` Thomas Streicher
2020-05-08 21:06 ` Joyal, André
2020-05-08 23:44 ` Steve Awodey
2020-05-09 2:46 ` Joyal, André
2020-05-09 3:09 ` Jon Sterling
[not found] ` <CADZEZBY+3z6nrRwsx9p-HqYuTxAnwMUHv7JasHy8aoy1oaGPcw@mail.gmail.com>
2020-05-09 2:50 ` Steve Awodey
2020-05-09 8:28 ` Thomas Streicher
2020-05-09 15:53 ` Joyal, André
2020-05-09 18:43 ` Thomas Streicher [this message]
2020-05-09 20:18 ` Joyal, André
2020-05-09 21:27 ` Jon Sterling
2020-05-10 2:19 ` Joyal, André
2020-05-10 3:04 ` Jon Sterling
2020-05-10 9:09 ` Thomas Streicher
2020-05-10 11:59 ` Thorsten Altenkirch
2020-05-10 11:46 ` Thorsten Altenkirch
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:20 ` Nicolai Kraus
2020-05-10 14:34 ` Michael Shulman
2020-05-10 14:52 ` Nicolai Kraus
2020-05-10 15:16 ` Michael Shulman
2020-05-10 15:23 ` Nicolai Kraus
2020-05-10 16:13 ` Nicolai Kraus
2020-05-10 16:28 ` Michael Shulman
2020-05-10 18:18 ` Nicolai Kraus
2020-05-10 19:15 ` Thorsten Altenkirch
2020-05-10 19:20 ` Thorsten Altenkirch
2020-05-10 12:53 ` Ulrik Buchholtz
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:27 ` Nicolai Kraus
2020-05-10 15:35 ` Ulrik Buchholtz
2020-05-10 16:30 ` Michael Shulman
2020-05-10 18:56 ` Nicolai Kraus
2020-05-10 18:04 ` Joyal, André
2020-05-11 7:33 ` Thomas Streicher
2020-05-11 14:54 ` Joyal, André
2020-05-11 16:37 ` stre...
2020-05-11 16:42 ` Michael Shulman
2020-05-11 17:27 ` Thomas Streicher
2020-05-10 16:51 ` Nicolai Kraus
2020-05-10 18:57 ` Michael Shulman
2020-05-10 19:18 ` Nicolai Kraus
2020-05-10 20:22 ` Michael Shulman
2020-05-10 22:08 ` Joyal, André
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=20200509184313.GB28841@mathematik.tu-darmstadt.de \
--to="stre..."@mathematik.tu-darmstadt.de \
--cc="Thorsten...."@nottingham.ac.uk \
--cc="awo..."@cmu.edu \
--cc="drober..."@gmail.com \
--cc="homotopyt..."@googlegroups.com \
--cc="joyal..."@uqam.ca \
--cc="shu..."@sandiego.edu \
/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).