univalent

I am much more partial to the univalent approach and in particular univalent implementation that compute e.g.

It's worth noting that Univalent Foundations (and type theory in general) really has nothing to do with computers.

Well, all right, but then if you interpret the type system using a univalent approach, what do you get?

So it seems like this univalent axiom is saying that this does not happen, and so a is b.

The univalent foundations developments make use of various axioms that have no known constructive meaning (e.g.

If Coq can be used with Vladimir Voevodsky's theory of univalent foundations, can Mizar also be based on them as well?

Most of the work in Univalent Foundations has been directly aimed at addressing that skepticism.

Oddly enough, they're neither the standard (first-order, that is, predicate logic based) ZFC theory, nor the Univalent foundations.

The Growth of Univalent Foundations/ Homotopy Type Theory.

And one of the ideas behind univalent type theory is to find a type system rich enough that you can use this for talking about all of mathematics.

As a PL theorist and kind-of-mathematician, I think the work going on in the Univalent Foundations project to be really interesting and extremely beautiful.

So I wonder what he thinks of this new univalent foundation.

Some other people in the "univalent foundations" project that Voevodsky started have also done some developments in Agda.

Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky’s univalence axiom and higher inductive types.

However you try to construct mathematics, either your system will just be broken or else there will be questions it can't resolve.) "Univalent foundations" is an entirely different approach.

The usual path from raw sets to the mathematical objects we're familiar with -- which is not relevant to "univalent foundations", so skip this if you like -- goes like this.