Loader and Urzyczyn Are Logically Related
Résumé
In simply typed \lam-calculus with one ground type the following theorem due to Loader holds. $(i)$ Given the full model $\cF$ over a finite set, %with at least seven elements, the question whether some element $f\in\cF$ is \lam-definable is undecidable. In the \lam-calculus with intersection types based on countably many atoms, the following is proved by Urzyczyn. $(ii)$ It is undecidable whether a type is inhabited. Both statements are major results presented in \cite{Bare2}. We show that $(i)$ and $(ii)$ follow from each other in a natural way, by interpreting intersection types as continuous functions logically related to elements of $\cF$. From this, and a result by Joly on \lam-definability, we get that \Urz's theorem already holds for intersection types with at most two atoms.
Domaines
Langage de programmation [cs.PL]Origine | Fichiers produits par l'(les) auteur(s) |
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