No-counterexample interpretation et spécification des théorèmes de l'arithmétique

Denis Bonnay (1)

1 PPS - Preuves, Programmes et Systèmes

This paper presents two different ways of extracting the computational content of formal proofs in arithmetic. The first one corresponds to Kreisel's No-counterexample Interpretation. based on Ackermann consistency proof. We show the link with recent work by Krivine on classical realizability. Finally, we discuss the various degrees of modularity of both approaches.

Mots clés: realizability; epsilon calculus; lambda calculus; specification; Curry Howard isomorphism

Domaines: Logique [math.LO]

Denis Bonnay. No-counterexample interpretation et spécification des théorèmes de l'arithmétique. 2005. ⟨hal-00004054⟩