This note is about work in progress on the topic of "internal type theory" where we investigate the internal formalization of the categorical metatheory of constructive ...
This work expounds the notion that (structured) categories are syntax free presentations of type theories, and shows some of the ideas involved in deriving categorical semantics f...
We consider the problem of providing formal support for working tract syntax involving variable binders. Gabbay and Pitts have shown in their work on Fraenkel-Mostowski (FM) set th...
racting these leads us to introduce the notion of a path object category. This is a relatively simple axiomatic framework, which is nonetheless sufficiently strong to allow the con...
There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language th...
Sooraj Bhat, Ashish Agarwal, Richard W. Vuduc, Ale...