arXiv subjects
Publications and source records attributed to Samir Farkh.
We 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.
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. Girard.
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.
In this paper, we extend the system AF2 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.