License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2023.5
URN: urn:nbn:de:0030-drops-183800
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18380/
Accattoli, Beniamino ;
Blanc, Horace ;
Sacerdoti Coen, Claudio
Formalizing Functions as Processes
Abstract
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.
BibTeX - Entry
@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/opus/volltexte/2023/18380},
URN = {urn:nbn:de:0030-drops-183800},
doi = {10.4230/LIPIcs.ITP.2023.5},
annote = {Keywords: Lambda calculus, pi calculus, proof assistants, binders, Abella}
}
