Graph grammars and operational semantics

Transformations of graphlike expressions are called correct if they preserve a given functional semantics of the expressions. Combining the algebraic theories of graph grammars (cf. [10]) and programming language semantics (cf. [1]) it will be proved that the correctness of transformation rules carries over to the correctness of derivations via such rules. Applying this result to LISP we show that a LISP interpreter represented by a graph grammar is correct with respect to the functional semantics of graphlike LISP expressions.