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Many of us working on homotopy type theory believe that it will be a better framework for doing math, and in particular computer-checked math, than set theory or classical higher-order logic or non-univalent type theory. One reason we believe this … Continue reading
(guest post by Jesse McKeown) A short narative of a brief confusion, leading to yet-another-reason-to-think-about-univalence, after which the Author exposes his vaguer thinking to derision. The Back-story In the comments to Abstract Types with Isomorphic Types, Dan Licata mentioned O(bservational)TT, … Continue reading
Here’s a cute little example of programming in HoTT that I worked out for a recent talk. Abstract Types One of the main ideas used to structure large programs is abstract types. You give a specification for a component, and … Continue reading
I recently had occasion to define the simplex category inside of type theory. For some reason, I decided to use an inductive definition of each type of simplicial operators , rather than defining them as order-preserving maps of finite totally … Continue reading
Many updates have been made to the various other pages on the site: Code, Events, Links, People, References. For example, there are several new items on models of the Univalence Axiom on the References page.
From a homotopical perspective, Coq’s built-in sort Prop is like an undecided voter, wooed by both the extensional and the intensional parties. Sometimes it leans one way, sometimes the other, at times flirting with inconsistency.