Analysis of a Guard Condition in Type Theory (Preliminary Report)

Abstract : We present a realizability interpretation of co-inductive types based on partial equivalence relations (per's). We extract from the per's interpreta- tion sound rules to type recursive definitions. These recursive definitions are needed to introduce «infinite» and «total» objects of co-inductive type such as an infinite stream or a non-terminating process. We show that the proposed type system enjoys the basic syntactic properties of subject reduction and strong normalization with respect to a confluent rewriting system first studied by Gimenez. We also compare the proposed type system with those studied by Coquand and Gimenez. In particular, we provide a semantic reconstruction of Gimenez's system which suggests a rule to type nested recursive definitions.
Type de document :
Rapport
RR-3300, INRIA. 1997
Liste complète des métadonnées

Littérature citée [1 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00073388
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 12:41:02
Dernière modification le : samedi 27 janvier 2018 - 01:30:56
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:29:01

Fichiers

Identifiants

  • HAL Id : inria-00073388, version 1

Collections

Citation

Roberto M. Amadio, Solange Coupet-Grimal. Analysis of a Guard Condition in Type Theory (Preliminary Report). RR-3300, INRIA. 1997. 〈inria-00073388〉

Partager

Métriques

Consultations de la notice

98

Téléchargements de fichiers

111