Complete Types in an Extension of the System AF2

International audienceIn this paper, we extend the system AF2 in order to have the subject reduction for the $\beta\eta$-reduction. We prove that the types with positive quantifiers are complete for models that are stable by weak-head expansion

Les types de données syntaxiques du système F

International audienceWe give in this paper a purely syntactical definition of input and output types of system 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

Un R\'esultat de Compl\'etude pour les Types ∀+\forall^+ du Syst\`eme F

We presente in this note a completeness result for the types with positive quantifiers of the J.-Y. Girard type system F. This result generalizes a theorem of R. Labib-Sami

Un Résultat de Complétude pour les Types ∀+\forall^+ du Système F

International audienceWe presente in this note a completeness result for the types with positive quantifiers of the J.-Y. Girard type system F. This result generalizes a theorem of R. Labib-Sami

Résultats de complétude pour des classes de types du système AF2

International audienceJ.-L. Krivine introduced the AF2 type system in order to obtain programs ($\lambda$-terms) which calculate functions, by writing demonstrations of their totalities. We present in this paper two results of completness for some types of AF2 and for many notions of reductions. These results generalize a theorem of R. Labib-Sami established in the system F of J.-Y. Girard