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Normalisation by Evaluation for Dependent Types

Authors Thorsten Altenkirch, Ambrus Kaposi

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Thorsten Altenkirch
Ambrus Kaposi

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Thorsten Altenkirch and Ambrus Kaposi. Normalisation by Evaluation for Dependent Types. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSCD.2016.6

Abstract

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.

Subject Classification

Keywords
  • normalisation by evaluation
  • dependent types
  • internal type theory
  • logical relations
  • Agda

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References

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