Inside 206-105

Existential Pontification and Generalized Abstract Digressions

Type Theory

Equality, roughly speaking

In Software Foundations, equality is defined in this way: Even Coq's equality relation is not built in. It has (roughly) the following inductive definition. Inductive eq0 {X:Type} : X -> X -> Prop := refl_equal0 : forall x, eq0 x x. Why the roughly? Well, as it turns out, Coq defines equality a little differently […]

HoTT exercises in Coq (in progress)

I spent some of my plane ride yesterday working on Coq versions of the exercises in The HoTT book. I got as far as 1.6 (yeah, not very far, perhaps I should make a GitHub repo if other folks are interested in contributing skeletons. Don't know what to do about the solutions though). All of […]

(Homotopy) Type Theory: Chapter One

In what is old news by now, the folks at the Institute for Advanced Study have released Homotopy Type Theory: Univalent Foundations of Mathematics. There has been some (meta)commentary (Dan Piponi, Bob Harper, Andrej Bauer, Fran├žois G. Dorais, Steve Awodey, Carlo Angiuli, Mike Shulman, John Baez) on the Internet, though, of course, it takes time […]