On the Taylor Expansion of Probabilistic lambda-terms

Authors Ugo Dal Lago, Thomas Leventis

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Ugo Dal Lago
  • University of Bologna, Italy
  • INRIA Sophia Antipolis, France
Thomas Leventis
  • INRIA Sophia Antipolis, France

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Ugo Dal Lago and Thomas Leventis. On the Taylor Expansion of Probabilistic lambda-terms. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We generalise Ehrhard and Regnier’s Taylor expansion from pure to probabilistic lambda-terms. We prove that the Taylor expansion is adequate when seen as a way to give semantics to probabilistic lambda-terms, and that there is a precise correspondence with probabilistic Böhm trees, as introduced by the second author. We prove this adequacy through notions of probabilistic resource terms and explicit Taylor expansion.

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
  • Theory of computation → Equational logic and rewriting
  • Probabilistic Lambda-Calculi
  • Taylor Expansion
  • Linear Logic


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