Decidability results for primitive recursive algorithms
Résumé
In this paper I use the notion of trace to extend T.Coquand's constructive proof of the ultimate obstination theorem of L. Colson to the case when mutual recursion is allowed. As a by product I get an algorithm that computes the value of a primitive recursive combinator applied to lazy integers (infinite or partially undefined arguments may appear). I also get, as T. Coquand got from his proof, that, even when mutual recursion is allowed, there is no primitive recursive definition f such that $f(S^{n}(\bot ))=S^{n^{2}}(\bot )$.
Origine : Fichiers produits par l'(les) auteur(s)