The framework of graph transformation combines the potentials and advantages of both, graphs and rules, to a single computational paradigm. In this paper we present some recent developments in applying graph transformation as a rule-based framework for the specification and development of systems, languages, and tools. After reviewing the basic features of graph transformation, we discuss a selection of applications, including the evaluation of functional expressions, the specification of an interactive graphical tool, an example specification for abstract data types, and the definition of a visual database query language. The case studies indicate the need for suitable structuring principles which are independent of a particular graph transformation approach. To this end, we present the concept of a transformation unit, which allows systematic and structured specification and programming based on graph transformation.

Sharing graphs are the structures introduced by Lamping to implement optimal reductions of lambda calculus. Gonthier's reformulation of Lamping's technique inside Geometry of Interaction, and Asperti and Laneve's work on Interaction Systems have shown that sharing graphs can be used to implement a wide class of calculi. Here, we give a general characterization of sharing graphs independent from the calculus to be implemented. Such a characterization rests on an algebraic semantics of sharing graphs exploiting the methods of Geometry of Interaction. By this semantics we can de ne an unfolding partial order between proper sharing graphs, whose minimal elements are unshared graphs. The least-shared instance of a sharing graph is the unique unshared graph that the unfolding partial order associates to it. The algebraic semantics allows to prove that we can associate a semantical read-back to each unshared graph and that such a read-back can be computed