T1: Type Systems for Array Programming
Array programming is foundational for data science and deep learning. Most array programming languages and frameworks (e.g. APL, Numpy, Pytorch) are untyped. On the other hand, recent research developed approaches to array programming that not only prevent type errors, but also out-of-bounds accesses.
For the seminar, first try out either the Dex or Futhark programming language, which use the type system to keep track of an array's shape. Then, look into the paper Structuring Arrays with Algebraic Shapes, where array indices don't have to be numbers, and compare with related work.