Normalisation by evaluation for dependent types - Altenkirch, Thorsten; Kaposi, Ambrus (2016)
We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated using internal type theory using quotient inductive types. We use a typed presentation hence there are no preterms or realizers in our construction. NBE for simple types is using a logical relation between the syntax and the presheaf interpretation. In our construction, we merge the presheaf interpretation and the logical relation into a proof-relevant logical predicate. We have formalized parts of the construction in Agda.