Discussion of Homotopy Type Theory and Univalent Foundations
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From: Michael Shulman <shulman@sandiego.edu>
To: Nicolai Kraus <nicolai.kraus@gmail.com>
Cc: "HomotopyTypeTheory@googlegroups.com"
	<HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] two's complement integers
Date: Thu, 4 Mar 2021 18:27:02 -0800
Message-ID: <CAOvivQwtAMVnOG7D_A_s1EMAum4fv_x945MLB+01Y_pMdEKC2w@mail.gmail.com> (raw)
In-Reply-To: <58a0a515-d8fa-4eb2-9555-d3a41fdee728@gmail.com>

On Thu, Mar 4, 2021 at 3:16 PM Nicolai Kraus <nicolai.kraus@gmail.com> wrote:
> I'm not sure what the precise thing is that you're looking for because, without further specification, any standard definition of Z would qualify :-)

Yes, that seems to be what Martin suggested too with ℕ + ℕ.  It seemed
to me as though the distance between ℕ + ℕ and my ℤ is greater than
the distance between his 𝔹 and 𝔹', but maybe not in any important
way.

> The HIT is neat, but wouldn't it in practice behave pretty similar to a standard representation via binary lists? E.g. something like Unit + Bool * List(Bool), where inl(*) is zero, the first Bool is the sign, and you add a 1 in front of the list in order to get a positive integer. What's the advantage of the HIT - maybe one can avoid case distinctions?

Is there a non-HIT binary representation that can be interpreted as
two's-complement (thereby avoiding case distinctions on sign)?  I
haven't been able to figure out a way to do that with mere lists of
booleans.

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  reply	other threads:[~2021-03-05  2:27 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
2021-03-04 22:42     ` Martin Escardo
2021-03-04 23:16     ` Nicolai Kraus
2021-03-05  2:27       ` Michael Shulman [this message]
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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