On Intersection Types and Probabilistic Lambda Calculi

Flavien Breuvart (1) , Ugo Dal Lago (2, 3)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
3 FOCUS - Foundations of Component-based Ubiquitous Systems

We define two intersection type systems for the pure, un-typed, probabilistic λ-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.

Domaines: Logique en informatique [cs.LO]

Flavien Breuvart, Ugo Dal Lago. On Intersection Types and Probabilistic Lambda Calculi. 20th International Symposium on Principles and Practice of Declarative Programming, Sep 2018, Frankfurt am Main, Germany. ⟨10.1145/3236950.3236968⟩. ⟨hal-01926420⟩