Term Graph Rewriting

Term graph rewriting is concerned with the representation of functional expressions as graphs, and the evaluation of these expressions by rule-based graph transformation. Representing expressions as graphs allows to share common subexpressions, improving the efficiency of term rewriting in space and time. Besides efficiency, term graph rewriting differs from term rewriting in properties like termination and confluence. This chapter surveys (acyclic) term graph rewriting, where emphasis is given to the relations between term and term graph rewriting. We focus on soundness of term graph rewriting with respect to term rewriting, on completeness for proving validity of equations and for computing term normal forms, on termination and confluence, and on term graph narrowing.