We develop an embedded domain specific language inside the dependently typed functional programming language Agda for specifying and verifying properties of functional reactive programs. For this purpose, we embed the temporal logic CTL (computation tree logic) inside dependent type theory.
Our EDSL offers all the standard stream programming primitives, and enriches them with two crucial aspects:
This article presents Rhine, an FRP library written in Haskell. The implementation at https://github.com/turion/rhine is usable. The article has been submitted to Haskell Symposium 2018.
An introductory course to Haskell in German.
Ein Haskell-Einführungskurs. Enthält Beamer-Folien und einige Aufgaben mit Lösungen.
I went to Erlangen to learn all about Cartan Geometry from Derek Wise. I also learned about spin network quantisation, and we tried to combine the two. Unfortunately we didn't really finish this project. Still, the thesis serves as an introduction to Cartan geometry and some thoughts about quantisation.
There is an excellent question on mathoverflow asking whether there is category theory with a half-twist as graphical calculus. It turns out there is. Basically, the half-twist is a square root of the twist in a balanced braided category. The most general treatment I know of is Jeff Egger's article On Involutive Monoidal Categories.
A new library for functional reactive programming. It allows for specifying the clock (sampling rate) of a signal function in the type. A framework for specifying resampling strategies and scheduling is included.
The notion of finite dimensional spectral triples internal to an involutive monoidal dagger category is defined. It makes the definition of a noncommutative geometry with symmetry quantum group possible. Surprising relations to two-dimensional extended TQFTs with line defects are uncovered.