Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Altenkirch, Thorsten; Kaposi, Ambrus http://www.dagstuhl.de/lipics License
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Normalisation by Evaluation for Dependent Types

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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.

BibTeX - Entry

@InProceedings{altenkirch_et_al:LIPIcs:2016:5972,
  author =	{Thorsten Altenkirch and Ambrus Kaposi},
  title =	{{Normalisation by Evaluation for Dependent Types}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Delia Kesner and Brigitte Pientka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5972},
  URN =		{urn:nbn:de:0030-drops-59727},
  doi =		{10.4230/LIPIcs.FSCD.2016.6},
  annote =	{Keywords: normalisation by evaluation, dependent types, internal type theory, logical relations, Agda}
}

Keywords: normalisation by evaluation, dependent types, internal type theory, logical relations, Agda
Seminar: 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)
Issue date: 2016
Date of publication: 2016


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