Normalisation by evaluation for dependent types
Altenkirch, Thorsten and Kaposi, Ambrus (2016) Normalisation by evaluation for dependent types. In: FSCD 2016: 1st International Conference on Formal Structures for Computation and Deduction, 22-26 June 2016, Porto, Portugal.
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.
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