超图重写与$\lambda-$演算的因果结构
Hypergraph rewriting and Causal structure of $λ-$calculus
AI总结：
该研究从范畴论角度研究超图重写以定义事件并构建图重写因果基础，还研究λ演算中事件的因果判定算法并尝试将其扩展到任意λ表达式。
摘要：
本文首先用范畴论术语研究超图重写，旨在定义事件概念并为图重写中的因果性奠定基础。我们在粘合范畴的double-pushout（双推出）重写框架内引入了新概念。其次，我们研究$\lambda-$演算中的事件概念，构建了一种算法，用于在满足特定条件的$\lambda-$表达式求值后确定事件间的因果关系。最后，我们尝试将该定义扩展到任意$\lambda-$表达式。
英文摘要：
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 $λ-$calculus, wherein we construct an algorithm to determine causal relations between events following the evaluation of a $λ-$expression satisfying certain conditions. Lastly, we attempt to extend this definition to arbitrary $λ-$expressions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
