Specification and programming (by graph transformation)

In this tutorial, some basic ideas will be outlined and exempliied how graph transformation can be employed in speciication and programming. In particular, some of the respective achievements of the COMPUGRAPH project will be pointed out. Graphs are widely used in many areas of Computer Science and beyond to describe complex system states, structured objects, networks and relations among components. Rules are even wider used to deene permitted actions, updates , transitions and transformations. Typical examples can be found in functional and logical programming, term rewriting, theorem proving, Petri nets, etc. Graphs and rules together yield the paradigm of graph transformation of which one encounters quite a variety of approaches in the literature (see, e.g. 3,8,9,7,24]). Graph transformation provides a natural way to model systems and to analyze their behaviour. In this tutorial, some basic ideas will be outlined and exempliied how graph transformation can be employed in speciication and programming. In particular, some of the respective achievements of the COMPUGRAPH project will be pointed out. Three lines of recent investigations will be discussed in more detail. 1. Term graph and jungle rewriting As functional expressions and logical formulas can be represented by (hyper)-graphs, their evaluation can be eeciently implemented by (hyper)graph rewriting. This observation has led to the introduction and study of term graph and jungle rewriting (see, e.g., 2,10,27]). More recent development concern the use of functional term graph rewriting as a speciication language, sub-typing with inheritance, optimization, critical pairs and memorization (cf.