Re: [HoTT] two's complement integers

[Michael Shulman <shulman@sandiego.edu>]

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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