All Outputs (2)

Big Step Normalisation for Type Theory (2020)
Journal Article
Altenkirch, T., & Geniet, C. (2020). Big Step Normalisation for Type Theory. LIPIcs, 2020, Article 4. https://doi.org/10.4230/LIPIcs.TYPES.2019.4

Big step normalisation is a normalisation method for typed lambda-calculi which relies on a purely syntactic recursive evaluator. Termination of that evaluator is proven using a predicate called strong computability, similar to the techniques used to... Read More about Big Step Normalisation for Type Theory.

The Integers as a Higher Inductive Type (2020)
Conference Proceeding
Altenkirch, T., & Scoccola, L. (2020). The Integers as a Higher Inductive Type. In LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science (67-73). https://doi.org/10.1145/3373718.3394760

We consider the problem of defining the integers in Homotopy Type Theory (HoTT). We can define the type of integers as signed natural numbers (i.e., using a coproduct), but its induction principle is very inconvenient to work with, since it leads to... Read More about The Integers as a Higher Inductive Type.