License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2019.4
URN: urn:nbn:de:0030-drops-130682
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13068/
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Altenkirch, Thorsten ; Geniet, Colin

Big Step Normalisation for Type Theory

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LIPIcs-TYPES-2019-4.pdf (0.5 MB)

Abstract

Big step normalisation is a normalisation method for typed lambda-calculi which relies on a purely syntactic recursive evaluator. Termination of that evaluator is proven using a predicate called strong computability, similar to the techniques used to prove strong normalisation of β-reduction for typed lambda-calculi. We generalise big step normalisation to a minimalist dependent type theory. Compared to previous presentations of big step normalisation for e.g. the simply-typed lambda-calculus, we use a quotiented syntax of type theory, which crucially reduces the syntactic complexity introduced by dependent types. Most of the proof has been formalised using Agda.

BibTeX - Entry

@InProceedings{altenkirch_et_al:LIPIcs:2020:13068,
  author =	{Thorsten Altenkirch and Colin Geniet},
  title =	{{Big Step Normalisation for Type Theory}},
  booktitle =	{25th International Conference on Types for Proofs and Programs (TYPES 2019)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-158-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{175},
  editor =	{Marc Bezem and Assia Mahboubi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13068},
  URN =		{urn:nbn:de:0030-drops-130682},
  doi =		{10.4230/LIPIcs.TYPES.2019.4},
  annote =	{Keywords: Normalisation, big step normalisation, type theory, dependent types, Agda}
}

Keywords: Normalisation, big step normalisation, type theory, dependent types, Agda
Collection: 25th International Conference on Types for Proofs and Programs (TYPES 2019)
Issue Date: 2020
Date of publication: 24.09.2020
Supplementary Material: https://github.com/colingeniet/big-step-normalisation

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