In this paper, we first study hypergraph rewriting in categorical terms in an attempt to define the notion of events and develop foundations of causality in graph rewriting. We introduce novel concepts within the framework of double-pushout rewriting in adhesive categories. Secondly, we will study the notion of events in $\lambda-$calculus, wherein we construct an algorithm to determine causal relations between events following the evaluation of a $\lambda-$expression satisfying certain conditions. Lastly, we attempt to extend this definition to arbitrary $\lambda-$expressions.

翻译：本文首先从范畴论角度研究超图重写，旨在定义事件概念并建立图重写中的因果性理论基础。我们在黏着范畴的双推出重写框架内引入了若干新概念。其次，我们将研究λ演算中的事件概念，针对满足特定条件的λ表达式求值过程，构建判定事件间因果关系的算法。最后，我们尝试将该定义推广至任意λ表达式。