Formalizing Functions as Processes

Authors Beniamino Accattoli , Horace Blanc, Claudio Sacerdoti Coen

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Beniamino Accattoli
  • Inria & LIX, École Poytechnique, Palaiseau, France
Horace Blanc
  • Independent researcher, Paris, France
Claudio Sacerdoti Coen
  • Alma Mater Studiorum - University of Bologna, Italy

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Beniamino Accattoli, Horace Blanc, and Claudio Sacerdoti Coen. Formalizing Functions as Processes. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We present the first formalization of Milner’s classic translation of the λ-calculus into the π-calculus. It is a challenging result with respect to variables, names, and binders, as it requires one to relate variables and binders of the λ-calculus with names and binders in the π-calculus. We formalize it in Abella, merging the set of variables and the set of names, thus circumventing the challenge and obtaining a neat formalization. About the translation, we follow Accattoli’s factoring of Milner’s result via the linear substitution calculus, which is a λ-calculus with explicit substitutions and contextual rewriting rules, mediating between the λ-calculus and the π-calculus. Another aim of the formalization is to investigate to which extent the use of contexts in Accattoli’s refinement can be formalized.

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
  • Theory of computation → Process calculi
  • Theory of computation → Operational semantics
  • Theory of computation → Automated reasoning
  • Lambda calculus
  • pi calculus
  • proof assistants
  • binders
  • Abella


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