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.

[img]
Preview
PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Available under Licence Creative Commons Attribution.
Download (510kB) | Preview

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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published in: 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)/ editors Delia Kesner and Brigitte Pientka, article No. 6, p. 6:1–6:16.
Keywords: Normalisation by evaluation, dependent types, internal type theory, logical relations, Agda
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Computer Science
Depositing User: Altenkirch, Thorsten
Date Deposited: 22 Jun 2016 11:06
Last Modified: 14 Sep 2016 13:05
URI: http://eprints.nottingham.ac.uk/id/eprint/34287

Actions (Archive Staff Only)

Edit View Edit View