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DOI: 10.4230/LIPIcs.ITP.2021.24

Complete Bidirectional Typing for the Calculus of Inductive Constructions

Authors: Meven Lennon-Bertrand

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract

This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). The key property of the system is its completeness with respect to the usual undirected one, which has been formally proven in Coq as a part of the MetaCoq project. Although it plays an important role in an ongoing completeness proof for a realistic typing algorithm, the interest of bidirectionality is wider, as it gives insights and structure when trying to prove properties on CIC or design variations and extensions. In particular, we put forward constrained inference, an intermediate between the usual inference and checking judgements, to handle the presence of computation in types.

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Meven Lennon-Bertrand. Complete Bidirectional Typing for the Calculus of Inductive Constructions. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lennonbertrand:LIPIcs.ITP.2021.24,
  author =	{Lennon-Bertrand, Meven},
  title =	{{Complete Bidirectional Typing for the Calculus of Inductive Constructions}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.24},
  URN =		{urn:nbn:de:0030-drops-139194},
  doi =		{10.4230/LIPIcs.ITP.2021.24},
  annote =	{Keywords: Bidirectional Typing, Calculus of Inductive Constructions, Coq, Proof Assistants}
}

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Complete Bidirectional Typing for the Calculus of Inductive Constructions

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