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Solvability in a Probabilistic Setting (Invited Talk)

Authors Simona Ronchi Della Rocca, Ugo Dal Lago, Claudia Faggian

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Simona Ronchi Della Rocca
  • Dipartimento di Informatica, Università di Torino, Italy
Ugo Dal Lago
  • Dipartimento di Informatica, Università di Bologna, Italy
Claudia Faggian
  • Université de Paris, IRIF, CNRS, France

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Simona Ronchi Della Rocca, Ugo Dal Lago, and Claudia Faggian. Solvability in a Probabilistic Setting (Invited Talk). In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 1:1-1:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSCD.2020.1

Abstract

The notion of solvability, crucial in the λ-calculus, is conservatively extended to a probabilistic setting, and a complete characterization of it is given. The employed technical tool is a type assignment system, based on non-idempotent intersection types, whose typable terms turn out to be precisely the terms which are solvable with nonnull probability. We also supply an operational characterization of solvable terms, through the notion of head normal form, and a denotational model of Λ_⊕, itself induced by the type system, which equates all the unsolvable terms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
  • Theory of computation → Models of computation
Keywords
  • Probabilistic Computation
  • Lambda Calculus
  • Solvability
  • Intersection Types

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