Outputs (2)

Two-level type theory and applications (2023)
Journal Article
Annenkov, D., Capriotti, P., Kraus, N., & Sattler, C. (2023). Two-level type theory and applications. Mathematical Structures in Computer Science, 33(8), 688-743. https://doi.org/10.1017/s0960129523000130

We define and develop two-level type theory (2LTT), a version of Martin-Löf type theory which combines two different type theories. We refer to them as the ‘inner’ and the ‘outer’ type theory. In our case of interest, the inner theory is homotopy typ... Read More about Two-level type theory and applications.

Type-theoretic approaches to ordinals (2023)
Journal Article
Kraus, N., Nordvall Forsberg, F., & Xu, C. (2023). Type-theoretic approaches to ordinals. Theoretical Computer Science, 957, Article 113843. https://doi.org/10.1016/j.tcs.2023.113843

In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences is constructively incompatible with deciding extensi... Read More about Type-theoretic approaches to ordinals.