J.-L. Krivine introduced the AF2 type system in order to obtain programs (λ-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.… (More)
In this paper, we extend the system AF 2 in order to have the subject reduction for the βη-reduction. We prove that the types with positive quantifiers are complete for models that are stable by weak-head expansion. KEYWORDS: system AF 2, type with positive quantifier, complete type.