Vendredi 9 Juin
Heure: 
11:00  12:30 
Lieu: 
Salle B107, bâtiment B, Université de Villetaneuse 
Résumé: 
An interpretation of system F through bar recursion 
Description: 
Valentin Blot There are two possible computational interpretations of secondorder arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a fundamentally different computational behavior and their relationship is not well understood. We make a step towards a comparison by defining the first translation of system F into a simplytyped total language with a variant of bar recursion. This translation relies on a realizability interpretation of secondorder arithmetic. Due to Gödel's incompleteness theorem there is no proof of termination of system F within secondorder arithmetic. However, for each individual term of system F there is a proof in secondorder arithmetic that it terminates, with its realizability interpretation providing a bound on the number of reduction steps to reach a normal form. Using this bound, we compute the normal form through primitive recursion. Moreover, since the normalization proof of system F proceeds by induction on typing derivations, the translation is compositional. The flexibility of our method opens the possibility of getting a more direct translation that will provide an alternative approach to the study of polymorphism, namely through bar recursion. 

