A Full Formalisation of pi-Calculus Theory in the Calculus of Constructions

A formalisation of π-calculus in the Coq system is presented. Based on a de Bruijn notation for names, our implementation exploits the mechanisation of some proof techniques described by Sangiorgi in [San95b] to derive several results of classical π-calculus theory, including congruence, structural equivalence and the replication theorems. As the proofs are described, insight is given to the main implementational issues that arise in our study, without entering too much the technical details. Possible extensions of this work include the full verification for the “functions as processes” paradigm, as well as the design of a system to check bisimilarities for processes.

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