Generic bidirectional typing for dependent type theories - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Generic bidirectional typing for dependent type theories

Résumé

Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be used. Bidirectional typing has been fruitfully studied and bidirectional systems have been developed for many type theories. However, the formal development of bidirectional typing has until now been kept confined to specific theories, with general guidelines remaining informal. In this work, we give a generic account of bidirectional typing for a general class of dependent type theories. This is done by first giving a general definition of type theories (or equivalently, a logical framework), for which we define declarative and bidirectional type systems. We then show, in a theory-independent fashion, that the two systems are equivalent. This equivalence is then explored to establish the decidability of typing for weak normalizing theories, yielding a generic type-checking algorithm that has been implemented in a prototype and used in practice with many theories.
Fichier principal
Vignette du fichier
doc.pdf (438.92 Ko) Télécharger le fichier
tech.pdf (474.9 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Format : Autre
Commentaire : Technical report

Dates et versions

hal-04270368 , version 1 (04-11-2023)

Licence

Paternité

Identifiants

Citer

Thiago Felicissimo. Generic bidirectional typing for dependent type theories. 2023. ⟨hal-04270368⟩
90 Consultations
78 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More