This paper presents a study of causality in a reversible, concurrent setting. There exist various notions of causality in π-calculus, which differ in the treatment of parallel extrusions of the same name. Hence, by using a parametric way of bookkeeping the order and the dependencies among extruders it is possible to map different causal semantics into the same framework. Starting from this simple observation, we present a uniform framework for reversible π-calculi that is parametric with respect to a data structure that stores information about the extrusion of a name. Different data structures yield different approaches to the parallel extrusion problem. We map three well-known causal semantics into our framework. We prove causal-consistency for the three instances of our framework. Furthermore, we prove a causal correspondence between the appropriate instances of the framework and the Boreale-Sangiorgi semantics and an operational correspondence with the reversible π-calculus causal semantics.

本文提出了在可逆的并发设置中因果关系的研究。π演算中存在因果关系的各种概念，在同名平行挤压的处理上有所不同。因此，通过使用参数化方式记账顺序和挤出机之间的依存关系，可以将不同的因果语义映射到同一框架中。从这个简单的观察开始，我们为参数的可逆π-计算提供了一个统一的框架关于存储有关名称扩展的信息的数据结构。不同的数据结构产生了不同的方法来解决并行挤压问题。我们将三种众所周知的因果语义映射到我们的框架中。我们证明了我们框架的三个实例的因果一致性。此外，我们证明了框架的适当实例与Boreale-Sangiorgi语义之间的因果关系以及与可逆π-演算因果语义之间的可操作对应关系。