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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Official URL: https://lmcs.episciences.org/4005

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:

https://doi.org/10.23638/LMCS-13(4:1)2017

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