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normalisation by evaluation for dependent types

descriptionPublicationkeyboard_double_arrow_right Other literature type , Conference object , Article 01 Jan 2016 Germany, United Kingdom Publisher:Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

Authors: Altenkirch, Thorsten; Kaposi, Ambrus;

doi: 10.4230/lipics.fscd.2016.6

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.

Countries

Germany, United Kingdom

Related Organizations

Leibniz Association
Germany
Nottingham Trent University
United Kingdom
Schloss Dagstuhl – Leibniz Center for Informatics
Germany

Keywords

logical relations, dependent types, internal type theory, normalisation by evaluation, Agda, 004, ddc: ddc:004

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