On Graph Rewritings.
Jean-Claude Raoult · 1983
Abstract The purpose of the present paper is twofold: Firstly, show that it is possible to rewrite graphs in a way equivalent to, and in fact slightly more powerful than that of Ehrig, Pfender and Schneider (1973), which has, since then, been developed mainly by the Berlin school. Our method consists in using a single push-out of partial morphisms and is described in Section 3. Section 1 is devoted to the elementary definitions concerning graphs and related terms. Section 2 contains the set-theoretic prerequisites for the sequel but the proofs have been moved into an appendix, for easier reading. Secondly, we indicate in Section 4 why this method is not really fit for rewriting graphs that represent collapsed terms (i.e., sharing common subterms) and we introduce pushouts of total functions, which are not morphisms everywhere on their domain. This method is connected to the classical rewriting of the corresponding terms. The adequacy of these new rewriting rules is then tested to prove a local confluence criterion a la Knuth-Bendix (1970) in Section 5, the proof of which turns out to be very short.