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Section: New Results

Formalization of Higher-Order Process Calculi

Participants : Guillaume Ambal, Sergueï Lenglet, Alan Schmitt.

Guillaume Amabal, Sergueï Lenglet, Alan Schmitt have continued exploring how to formalize HO$\pi$ in Coq, in particular how to deal with the different kinds of binders used in the calculus. We have studied and compared several approaches, such as locally nameless, De Bruijn indices, and nominal binders. We have discovered that the locally nameless approach introduces a lot of complexity, as name restriction allows reduction under binders, introducing the need for numerous renaming lemmas. The nominal approach is quite elegant and very close to the pen and paper definitions, but it still requires many technical lemmas to be proven. The de Bruijn approach is the most concise. A first version of this work has been published at CPP 2018 [18] and a journal version is submitted for publication. The Coq scripts can be found at http://passivation.gforge.inria.fr/hopi/.