We define two intersection type systems for the pure, untyped, probabilistic lambda-calculus, and prove that type derivations precisely reflect the probability of convergence of the underlying term. We first define a simple system of oracle intersection types in which derivations are annotated by binary strings and the probability of termination can be computed by combining all the different possible annotations. Although inevitable due to recursion theoretic limitations, the fact that (potentially) infinitely many derivations need to be considered is of course an issue when seeing types as a verification methodology. We thus develop a more complex system: the monadic intersection type system. In this second system, the probability of termination of a term is shown to be the least upper bound of the weights of its type derivations.
On Intersection Types and Probabilistic Lambda Calculi
Lago, Ugo Dal
2018
Abstract
We define two intersection type systems for the pure, untyped, probabilistic lambda-calculus, and prove that type derivations precisely reflect the probability of convergence of the underlying term. We first define a simple system of oracle intersection types in which derivations are annotated by binary strings and the probability of termination can be computed by combining all the different possible annotations. Although inevitable due to recursion theoretic limitations, the fact that (potentially) infinitely many derivations need to be considered is of course an issue when seeing types as a verification methodology. We thus develop a more complex system: the monadic intersection type system. In this second system, the probability of termination of a term is shown to be the least upper bound of the weights of its type derivations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.