Hypergraph rewriting and Causal structure of $\lambda-$calculus

TL;DR

This paper develops a categorical framework for hypergraph rewriting to understand causality, introduces an algorithm for causal analysis in lambda calculus, and extends these concepts to general lambda expressions.

Contribution

It presents a novel categorical approach to hypergraph rewriting and causality, along with an algorithm for causal relations in lambda calculus, extending to arbitrary lambda expressions.

Findings

Categorical framework for hypergraph rewriting and causality

Algorithm for determining causal relations in lambda calculus

Extension of causal analysis to arbitrary lambda expressions

Abstract

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.