Work

On Intersection Types and Probabilistic Lambda Calculi

Year: 2018

Type: conference-paper

Abstract: We define two intersection type systems for the pure, untyped, 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.

Source: International Symposium on Principles and Practice of Declarative Programming (PPDP)

DOI: 10.1145/3236950.3236968

Authors: Flavien Breuvart, Ugo Dal Lago

Institutions: Laboratoire d'Informatique de Paris-Nord, Institut national de recherche en sciences et technologies du numérique, University of Bologna

Language: English

Topic: Logic, programming, and type systems

Subfield: Software

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: G1871999087, Expanding Logical Ideas for Complexity Analysis, G7558042017, Reliable and Privacy-Aware Software Systems via Bisimulation Metrics