new slides

[Vladimir Voevodsky]

Hello,

I have uploaded to me homepage the slides of my lecture at HLF 2016 with a discussion of the Univalent Foundations and some discussion of the UniMath library. See https://www.math.ias.edu/vladimir/Lectures .

Vladimir.

[Martin Escardo]

On 22/09/16 20:46, Vladimir Voevodsky wrote:
> I have uploaded to me homepage the slides of my lecture at HLF 2016 with a discussion of the Univalent Foundations and some discussion of the UniMath library. See https://www.math.ias.edu/vladimir/Lectures .

I like the recognition of the usefulness, and, more importantly, the
intrinsic interest in the constructive aspect, given in your presentation.

Like you, I am impressed by the work in Cubical Type Theory to make this
to successfully work in univalent extensions of constructive type theories.

In my view, an important part of the intimate connection of intuition
with rigorous mathematics (your slide 3) is precisely constructivity.
Perhaps not everybody wants to be constructive all the time, but we do
need a good, precise mathematical language that supports constructivity
directly, without ruling out non-constructive arguments (by seeing them
as arguments that just give much less information one would like to,
which potentially one would like to uncover with further refinement).

The Cubical-Type-Theory rendering of UF is such a language.

Best,
Martin

[Dimitris Tsementzis]

On the fourth bullet point of slide 12 it is claimed that it might be easier to solve the problem of infinite objects in CTT. Why is that the case?

Is this related to the third bullet point, namely because it might be easier to implement a strict equality in CTT? (I still don’t understand why implementing a strict equality in CTT is easier than in MLTT+UA, but at least this way I see the connection with the problem of infinite objects.)

Dimitris

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[Vladimir Voevodsky]

No, it is more related to another idea that I am not quite ready to explain yet.

Vladimir.