We present a formalization of HO $$\pi $$ π 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 $$\lambda $$ 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 bisimilarity 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.

中文翻译：

---

Coq 中的 HO$$\pi $$

我们在 Coq 中提出了 HO $$\pi $$ π 的形式化，这是一种消息携带过程的过程演算。这种高阶微积分具有两种截然不同的绑定器：过程输入，类似于 $$\lambda $$ λ -抽象，以及名称限制，其范围可以通过通信扩展。对于后者，我们比较了四种表示绑定器的方法：局部无名、de Bruijn 索引、名义和高阶抽象语法。在每种情况下，我们都将强上下文双相似性形式化并证明它是兼容的，即在每个上下文下都是封闭的，使用 Howe 的方法，基于我们在前一篇论文中开发的几个证明方案。