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Complete Bidirectional Typing for the Calculus of Inductive Constructions

Meven Lennon-Bertrand 1, 2
1 GALLINETTE - Gallinette : vers une nouvelle génération d'assistant à la preuve
LS2N - Laboratoire des Sciences du Numérique de Nantes, Inria Rennes – Bretagne Atlantique
Abstract : This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence of computation in types. 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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https://hal.archives-ouvertes.fr/hal-03139924
Contributor : Meven Lennon-Bertrand Connect in order to contact the contributor
Submitted on : Monday, April 19, 2021 - 3:59:47 PM
Last modification on : Wednesday, April 27, 2022 - 3:54:37 AM

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Meven Lennon-Bertrand. Complete Bidirectional Typing for the Calculus of Inductive Constructions. ITP 2021 - 12th International Conference on Interactive Theorem Proving, Jun 2021, Rome, Italy. pp.1-19, ⟨10.4230/LIPIcs.ITP.2021.24⟩. ⟨hal-03139924v2⟩

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