The aim of the paper is to introduce the notion of a transformation unit together with its interleaving semantics and to study it as a means of constructing large graph transformation systems from small ones in a structured and systematic way. A transformation unit comprises a set of rules, descriptions of initial and terminal graphs, and a control condition. Moreover, it may import other transformation units for structuring purposes. Its semantics is a binary relation between initial and terminal graphs which is given by interleaving sequences. As a generalization of ordinary derivations, an interleaving sequence consists of direct derivation steps interleaved with calls of imported transformation units. It must obey the control condition and may be seen as a kind of structured derivation. The introduced framework is independent of a particular graph transformation approach and, therefore, it may enhance the usefulness of graph transformations in many contexts.

Currently existing graph grammar-based specification languages have serious problems with supporting any kind of "specification-in-the-large" activities. More precisely, they have deficiences with respect to modeling hierarchical data structures or specifying meta activities like manipulation of graph schemata. Furthermore, already proposed graph grammar module concepts are still too abstract to be useful in practice. Our contribution addresses these problems by introducing a new hierarchical graph data model with an infinite number of schema, meta-schema, etc. layers. It forms the base for a forthcoming concrete modular graph grammar specification language where in addition information hiding aspects like explicit export and import interfaces are expressible.

In this chapter we use a three-level approach for analyzing module concepts for graph transformation systems. Based on the observation that module architectures consist of basic specifications like body or export interface and relations like the implementation relation between them, or the import relation between a client and a server module, module concepts are characterized by answering the questions 1. What are the basic specifications? 2. Which relations between specifications are used? 3. How are specifications and relations combined to module architectures? These three questions are investigated for five module concepts available in the literature. As a reference example, a sample modular specification of resource management in distributed operating systems is presented.

This is a survey of the main aims and results of the ESPRIT Basic Research Working Group COMPUTING BY GRAPH TRANSFORMATION II, 1992 - 1996, following up the first phase of COMPUGRAPH, 1989 - 1992. The research goals and main results are presented within the following three research areas: Foundations, Concurrency, and Graph Transformations for Specification and Programming. 1 Introduction The research area of graph grammars or graph transformations is a relatively young discipline of computer science. Its origins date back to the early seventies. Nevertheless, methods, techniques, and results from the area of graph transformations have already been studied and applied in many fields of computer science such as formal language theory, pattern recognition and generation, compiler construction, software engineering, concurrent and distributed systems modeling, database design and theory, logical and functorial programming, AI etc. This wide applicability is due to the fact that graphs ar...

A basic construct of the graph and rule centered language GRACE, currently under development, is the transformation unit. In the paper transformation units together with their interleaving semantics are introduced, and the idea of programming with transformation units in a systematic and structured way is illustrated in an example. Furthermore, two operations on transformation units are presented that construct a normal form without changing the interleaving semantics.

Semantics Various ways have been proposed to define the semantics of a GTS. They include semantics based on derivation sequences (abstract or concrete), processes and event structures. We aim at further investigating them, in order to get a better insight in the possibilities and drawbacks of the various approaches, especially in the light of research about modularity and concurrency. Topics to be investigated include the study of categories of derivations and processes, at different levels of abstractions, and corresponding normal forms; of abstraction mechanisms preserving compositionality [12]; of the relations with event structure semantics [3]; of observation mechanisms and observational equivalence for derivations sequences and processes; and of algebraic domains for a denotational semantics of GTS. The main formal frameworks to be used in this area are Algebra and Universal Algebra, Logic, Category Theory. e) Concurrency Aspects The aim of this focus area is the description o...

This paper presents a systematic approach for classifying and comparing modularity concepts that have been proposed for graph transformation systems. The approach is based on the following observation: Modules and module interconnections consist of basic specifications (forming, e.g., a module's body, import, or export interface), and relations between such specifications, like the implementation relation between export and body of a module. Hence, a natural approach for characterizing a module concept is to answer the following three questions: 1. What are the basic specifications? 2. Which relations between specifications are used? 3. How are specifications and relations combined to modules and interconnections? In this paper, these questions are considered in some detail for the following module concepts for graph transformation systems.

This is a survey of the main aims and results of the ESPRIT Basic Research Working Group COMPUTING BY GRAPH TRANSFORMATION with main emphasize on COMPUGRAPH II, 1992 - 1996, following up the first phase of COMPUGRAPH, 1989 - 1992. Starting with an overview of the history of graph grammars and graph transformations the research goals and main results are presented within the following three research areas: Foundations, Concurrency, and Graph Transformations for Specification and Programming.