Context-exploiting shapes for diagram transformation

Abstract. DIAPLAN is a language for programming with graphs representing diagrams that is currently being developed. The computational model of the languages, nested graph transformation, supports nested structuring of graphs, and graph variables, but is—hopefully—still intuitive. This paper is about structural typing of nested graphs and nested graph transformation systems by shape rules. We extend the context-free shape rules proposed in earlier work to context-exploiting shape rules by which many relevant graph structures can be specified. The conformance of a nested graph to shape rules is decidable. If a transformation system conforms to shape rules as well, it can be shown to preserve shape conformance of the graphs it is applied to. This sets up a static type discipline for nested graph transformation. Key words: Graph transformation; diagram language; visual programming; data type 1