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Efficient Graph Rewriting and Its Implementation (Lecture Notes in Computer Science)

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Graph rewriting systems have come of age. In autumn 1994, the 25th anniversary of the first publication in this area was celebrated at the 5th Workshop on Graph Grammars and their Applications to Computer Science. In the interim, the subject has evolved. The current situation can be described by a three-stage model. At the very low level there is a common idea of graph rewriting as the basic mechanism, where a graph is transformed by the application of a rewriting rule.

In the second stage, this mechanism is expressed in several ways. Usually, two so called approaches are distinguished: the algorithmic (or set-theoretic) and the algebraic approach. Both provide a formalisation of graph rewriting. They give a precise semantics to the idea of graph transformation and, hence, allow for a formal treatment. In that sense, they are similar to the semantics of programming languages.

The upper stage is partitioned into several branches. At one extreme, theoretical studies on the generational power, on semantic constructs, or on restricted formalisms are undertaken. At the other extreme, specifications of real-world systems, or imple mentations of rewriting environments are developed. Because the individual problems to solve are complicated enough, the branches are not very aware of each other.

The monograph builds bridges between various areas of interest: 1) it studies a class of graph rewriting systems which is very suitable for an efficient execution; 2) it presents a compilation approach to the implementation of an environment for graph rewriting; 3) it develops an implementation of a functional programming language to show that and how the presented ideas apply to real-world problems.

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