From: Michael Shulman <firstname.lastname@example.org> To: Nicolai Kraus <email@example.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: <firstname.lastname@example.org> On Thu, Mar 4, 2021 at 3:16 PM Nicolai Kraus <email@example.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. -- 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 HomotopyTypeTheoryfirstname.lastname@example.org. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAOvivQwtAMVnOG7D_A_s1EMAum4fv_x945MLB%2B01Y_pMdEKC2w%40mail.gmail.com.
next prev parent 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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