Solving Equations by Graph Transformation

We review the concept of term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with rst-order term uni cation. This mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and conuent. This includes, in particular, all convergent term rewriting systems. Completeness means that for every solution of a given equation, term graph narrowing can nd an equivalent or more general solution. The general motivation for using term graphs instead of terms is to improve eÆciency: sharing common subterms saves space and avoids the repetition of computations.