On Intersection Types and Probabilistic Lambda Calculi

Flavien Breuvart 1 Ugo Dal Lago 2, 3
3 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : 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.
Document type :
Conference papers
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01926420
Contributor : Ugo Dal Lago <>
Submitted on : Monday, November 19, 2018 - 4:07:56 PM
Last modification on : Thursday, February 7, 2019 - 4:55:34 PM
Long-term archiving on : Wednesday, February 20, 2019 - 1:58:29 PM

File

main.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

51

Files downloads

180