Hans-Jörg Kreowski

Graph transformation for specification and programming

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.

ALGEBRAIC IMPLEMENTATION OF ABSTRACT DATA TYPES

Abstract Starting with a review of the theory of algebraic specifications in the sense of the ADJ-group a new theory for algebraic implementations of abstract data types is presented. While main concepts of this new theory were given already at several conferences this paper provides the full theory of algebraic implementations developed in Berlin except of complexity considerations which are given in a separate paper. The new concept of algebraic implementations includes implementations for algorithms in specific programming languages and on the other hand it meets also the requirements for stepwise refinement of structured programs and software systems as introduced by Dijkstra and Wirth. On the syntactical level an algebraic implementation corresponds to a system of recursive programs while the semantical level is defined by algebaic constructions, called synthesis, restriction and identification . Moreover the concept allows composition of implementations and a rigorous study of correctness. The main results of the paper are different kinds of correctness criteria which are applied to a number of illustrating examples including the implementation of sets by hash-tables. Algebraic implementations of larger systems like a histogram or a parts system are given in separate case studies which, however, are not included in this paper.

May we introduce to you: hyperedge replacement

In this kind of tutorial note, we explain how graphs can be rewritten by edge replacement. The formal definitions are accompanied by intuitive descriptions and a series of examples.

Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement

Hyperedge replacement systems are introduced as a device for generating hypergraph languages including graph languages and string languages (where the strings are uniquely represented as certain graphs). Our concept combines a context-free type of rewriting with a comparatively large generative power. The former is indicated, for example, by a pumping lemma, the latter by the examples (among them you find the refinement of Petri nets, the analysis of flow diagrams, the structural description of molecules and some typical non-context-free string languages).

From Graph Grammars to High Level Replacement Systems

The algebraic approach to graph grammars — well-known in the literature for several types of graphs and structures — is extended to include several new types of replacement systems, especially the replacement of algebraic specifications which were recently introduced for a rule-based approach to modular system design.

An Integrated Semantics for UML Class, Object and State Diagrams Based on Graph Transformation

This paper studies the semantics of a central part of the Unified Modeling Language UML. It discusses UML class, object and state diagrams and presents a new integrated semantics for both on the basis of graph transformation. Graph transformation is a formal technique having some common ideas with the UML. Graph transformation rules are associated with the operations in class diagrams and with the transitions in state diagrams. The resulting graph transformations are combined into a one system in order to obtain a single coherent semantic description.

Parameter passing in algebraic specification languages

Abstract In this paper we study the semantics of the parameter passing mechanism in algebraic specification languages. More precisely, this problem is studied for parameterized data types and parameterized specifications. The given results include the extension of the model functor (which is useful for correctness proofs) and the semantic properties of the result of inserting actual parameters into parameterized specifications. In particular, actual parameters can be parameterized and the result is nested parameterized specification. Correctness of an applied ( matrix ( int )) or a nested ( bintree ( string ())) parameterized specification is shown given correctness of the parts. The formal theory in this paper is restricted to the basic algebraic case where only equations are allowed in the parameter declaration and parameter passing is given by specification morphisms. But we also give the main ideas of a corresponding theory with requirements where we allow different kinds of restrictions in the parameter declaration.

Graph Transformation Units with Interleaving Semantics

Abstract. 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.

Stepwise Specification and Implementation of Abstract Data Types

The algebraic approach to specification and implementation of abstract data type in the sense of Goguen, Thatcher and Wagner is extended to study problems of stepwise specification and implementation. Two different concepts are introduced: 1. Stepwise specification by enrichment 2. Stepwise specification and implementation by functors

A Comparison Between Petri-Nets and Graph Grammars

A graph grammar is constructed from a given Petri-net so that direct derivation steps in the grammar correspond to firings of transitions in the net. This close relationship between Petri-nets and graph grammars allows to compare the concurrency concepts of the two theories. As an illustrating example the well-known dining-philosophers problem is discussed.