Discussion of Homotopy Type Theory and Univalent Foundations
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From: Michael Shulman <shulman@sandiego.edu>
To: Martin Escardo <escardo.martin@gmail.com>
Cc: "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?

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  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

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Discussion of Homotopy Type Theory and Univalent Foundations

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