From graph grammars to high level replacement systems

Abstract

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 roplacement of algebraic specifications which were recently introduced for a rule-based approach to modular system design. This leads to the new concept of high level replacement systems which is formulated in an axiomatic algebraic framework based on categories and double-pushouts. In this paper only basic notions like productions, derivations, parallel and sequential independence are introduced for high-level replacement systems leading to Chorch-Rosser and Parallelism Theorems previously shown in the literature for special cases only.