HO$$\pi $$ in Coq

We present a formalization of HOπ in Coq, a process calculus where messages carry processes. Such a higher-order calculus features two very different kinds of binder: process input, similar to λ-abstraction, and name restriction, whose scope can be expanded by communication. For the latter, we compare four approaches to represent binders: locally nameless, de Bruijn indices, nominal, and Higher-Order Abstract Syntax. In each case, we formalize strong context bisimi-larity and prove it is compatible, i.e., closed under every context, using Howe's method, based on several proof schemes we developed in a previous paper.