Résultats de complétude pour des classes de types du système AF2

• Main Authors: Farkh, Samir, Nour, Karim
• Other Authors: Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB Université de Savoie Université de Chambéry )
• Format: Article in Journal/Newspaper
• Language: French
• Published: HAL CCSD 1998
• Subjects: [MATH.MATH-LO]Mathematics [math]/Logic [math.LO]; Lambda; sami
• Online Access: https://hal.archives-ouvertes.fr/hal-00381155; https://hal.archives-ouvertes.fr/hal-00381155/document; https://hal.archives-ouvertes.fr/hal-00381155/file/THESE.pdf

International audience J.-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.