Normalisation by evaluation for type theory, in type theory

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Altenkirch, Thorsten and Kaposi, Ambrus (2017) Normalisation by evaluation for type theory, in type theory. Logical Methods in Computer Science, 13 (4:1). pp. 1-26. ISSN 1860-5974

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Abstract

We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no preterms or realizers in our construction, and every construction respects the conversion relation. NBE for simple types uses 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 prove normalisation, completeness, stability and decidability of definitional equality. Most of the constructions were formalized in Agda.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/888899
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
Identification Number: 10.23638/LMCS-13(4:1)2017
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URL Type
https://lmcs.episciences.org/
UNSPECIFIED
Depositing User: Altenkirch, Thorsten
Date Deposited: 30 Oct 2017 11:16
Last Modified: 04 May 2020 19:13
URI: https://eprints.nottingham.ac.uk/id/eprint/47642

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