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.
@InProceedings{accattoli_et_al:LIPIcs.ITP.2023.5, author = {Accattoli, Beniamino and Blanc, Horace and Sacerdoti Coen, Claudio}, title = {{Formalizing Functions as Processes}}, booktitle = {14th International Conference on Interactive Theorem Proving (ITP 2023)}, pages = {5:1--5:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-284-6}, ISSN = {1868-8969}, year = {2023}, volume = {268}, editor = {Naumowicz, Adam and Thiemann, Ren\'{e}}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.5}, URN = {urn:nbn:de:0030-drops-183800}, doi = {10.4230/LIPIcs.ITP.2023.5}, annote = {Keywords: Lambda calculus, pi calculus, proof assistants, binders, Abella} }
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