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.

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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.

Item Type: Conference or Workshop Item (Paper)
RIS ID: https://nottingham-repository.worktribe.com/output/793447
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 > Faculty of Science > School of Computer Science
Depositing User: Altenkirch, Thorsten
Date Deposited: 22 Jun 2016 11:06
Last Modified: 04 May 2020 17:55
URI: http://eprints.nottingham.ac.uk/id/eprint/34287

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