Thorsten Altenkirch ; Ambrus Kaposi - Normalisation by Evaluation for Type Theory, in Type Theory

lmcs:2588 - Logical Methods in Computer Science, October 23, 2017, Volume 13, Issue 4 - https://doi.org/10.23638/LMCS-13(4:1)2017
Normalisation by Evaluation for Type Theory, in Type Theory

Authors: Thorsten Altenkirch ; Ambrus Kaposi

We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no preterms or realizers in our construction, and every construction respects the conversion relation. NBE for simple types uses 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 prove normalisation, completeness, stability and decidability of definitional equality. Most of the constructions were formalized in Agda.


Volume: Volume 13, Issue 4
Published on: October 23, 2017
Accepted on: October 23, 2017
Submitted on: September 4, 2017
Keywords: Computer Science - Logic in Computer Science,F.4.1


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