Attributed Graph Transformation via Rule Schemata: Church-Rosser Theorem

We present an approach to attributed graph transformation which requires neither infinite graphs containing data algebras nor auxiliary edges that link graph items with their attributes. Instead, we use the double-pushout approach with relabelling and extend it with rule schemata which are instantiated to ordinary rules prior to application. This framework provides the formal basis for the graph programming language GP 2. In this paper, we abstract from the data algebra of GP 2, define parallel independence of rule schema applications, and prove the Church-Rosser Theorem for our approach. The proof relies on the Church-Rosser Theorem for partially labelled graphs and adapts the classical proof by Ehrig and Kreowski, bypassing the technicalities of adhesive categories.