Strategic programming on graph rewriting systems

Rewriting [4] is a computation model used in computer science, algebra, logic and linguistics, amongst others. Its purpose is to transform syntactic objects (words, terms, programs, proofs, graphs, etc., which we will call generally expressions), by applying rewrite rules until a suitable simplied form is obtained. Given an expression and a set of rewrite rules, it is often the case that several different rules can be applied, and the same rule can be applied to different sub-expressions. To control the rewriting process, a strategy of application of rules is used. In this paper we focus on graph rewriting [11, 27]. Graphs are widely used for describing complex structures in a visual and intuitive way, e.g., UML diagrams, representation of proofs, microprocessor design, XML documents, communication networks, data and control flow, neural networks, biological systems, etc. Graph rewriting has many applications in specification, programming, and simulation tools, amongst others [12, 13]. Several graph-transformation languages and tools have been developed, such as PROGRES [28], AGG [14], Fujaba [23], GROOVE [26], GrGen [17] and GP [25], only to mention a few. When the graphs are large or growing along transformations, or when the number of graph rewriting rules is large, visualisation becomes crucial to understand the graph evolution. PORGY [1] is a visual environment that allows users to define graphs and graph rewriting rules, and to experiment with a graph rewriting system in a visual and interactive way. For instance, one may want to apply a rule r on a graph G at the positions described by the subgraph P to study different rewriting derivations for G. To control the application of graph rewriting rules, PORGY uses a strategy language. In this paper we describe this strategy language and show how it can be used to write high-level declarative programs in several application areas. Strategies for rewriting have been well studied in the case of terms: there are languages that allow the user to specify and apply strategies controlling the use of term rewrite rules (see for instance [9, 29, 6]). For graph rewriting, some of the languages and tools mentioned above also allow users to guide the rewriting engine, for instance by specifying the order in which rules will