Discussion of Homotopy Type Theory and Univalent Foundations
 help / color / mirror / Atom feed
From: Michael Shulman <shulman@sandiego.edu>
To: Martin Escardo <escardo.martin@gmail.com>
Cc: "HomotopyTypeTheory@googlegroups.com"
	<homotopytypetheory@googlegroups.com>
Subject: Re: [HoTT] two's complement integers
Date: Thu, 4 Mar 2021 14:05:21 -0800
Message-ID: <CAOvivQwsn-MLHzw=W5wxZ49Bp+HS9nr261YQJLgQ9E60K2Pcmg@mail.gmail.com> (raw)
In-Reply-To: <9eefbc82-ba49-b101-433d-c3c1e452ecda@googlemail.com>

On Thu, Mar 4, 2021 at 1:11 PM Martin Escardo <escardo.martin@gmail.com> wrote:
> I wonder if your definition of the integers with the HIT is isomorphic
> to an inductively defined version without a HIT as above, and this is
> how you proved it to be a set.

No, I just did an encode-decode.  I formalized most of it, up to some
obviously true lemmas about squares and cubes.

I thought for a little bit about whether there is an equivalent
"lower" inductive version, but nothing immediately occurred to me.  Do
you have a suggestion?

-- 
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/CAOvivQwsn-MLHzw%3DW5wxZ49Bp%2BHS9nr261YQJLgQ9E60K2Pcmg%40mail.gmail.com.

  reply	other threads:[~2021-03-04 22:05 UTC|newest]

Thread overview: 8+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2021-03-04 20:43 Michael Shulman
2021-03-04 21:11 ` Martin Escardo
2021-03-04 22:05   ` Michael Shulman [this message]
2021-03-04 22:42     ` Martin Escardo
2021-03-04 23:16     ` Nicolai Kraus
2021-03-05  2:27       ` Michael Shulman
2021-03-05  3:02         ` Jason Gross
2021-03-05  4:41           ` 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='CAOvivQwsn-MLHzw=W5wxZ49Bp+HS9nr261YQJLgQ9E60K2Pcmg@mail.gmail.com' \
    --to=shulman@sandiego.edu \
    --cc=escardo.martin@gmail.com \
    --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

Discussion of Homotopy Type Theory and Univalent Foundations

This inbox may be cloned and mirrored by anyone:

	git clone --mirror https://inbox.vuxu.org/hott

	# If you have public-inbox 1.1+ installed, you may
	# initialize and index your mirror using the following commands:
	public-inbox-init -V1 hott hott/ https://inbox.vuxu.org/hott \
		homotopytypetheory@googlegroups.com
	public-inbox-index hott

Example config snippet for mirrors.
Newsgroup available over NNTP:
	nntp://inbox.vuxu.org/vuxu.archive.hott


AGPL code for this site: git clone https://public-inbox.org/public-inbox.git