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Issue RAIRO-Theor. Inf. Appl.
Volume 35, Number 3, May-June 2001
Page(s) 207 - 221
DOI 10.1051/ita:2001117

DOI: 10.1051/ita:2001117


Theoret. Informatics Appl. 35, 207-221 (2001)

LES TYPES DE DONNÉES SYNTAXIQUES DU SYSTÈME ${\cal F}$

Samir Farkh and Karim Nour

LAMA, Équipe de Logique, Université de Savoie, 73376 Le Bourget du Lac Cedex, France; (knour@univ-savoie.fr)

(Reçu le 12 avril 1999. Accepté le 30 mars 2001.)

Abstract
We give in this paper a purely syntactical definition of input and output types of system ${\cal F}$. We define the syntactical data types as input and output types. We show that any type with positive quantifiers is a syntactical data type and that an input type is an output type. We give some restrictions on the $\forall$-elimination rule in order to prove that an output type is an input type.

Résumé
Nous présentons dans ce papier une définition purement syntaxique des types entrées et des types sorties du système ${\cal F}$. Nous définissons les types de données syntaxiques comme étant des types entrées et sorties. Nous démontrons que les types à quantificateurs positifs sont des types de données syntaxiques et qu'un type entrée est un type sortie. Nous imposons des restrictions sur la règle d'élimination des quantificateurs pour démontrer qu'un type sortie est un type entrée.


AMS Subject: 03B40, 68Q60.

Key words: Input type -- output type -- data type -- system ${\cal F}$.


© EDP Sciences 2001


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