It is pointed out that the incremental cost of a change to a program is often disproportionately high because of inadequate means of determining the semantic effects of the change. A practical logical technique for finding the semantic effects of changes through a direct analysis of the program is presented. The programming language features considered include parametrized modules, procedures, and global variables. The logic described is approximate in that weak (conservative) results sometimes are inferred. Isolating the exact effects of a change is undecidable in general. The basis for an approximation is a structural interpretation of the information-flow relationships among program objects. The approximate inference system is concise, abstract, extensible, and decidable, giving it significant advantages over the main alternative formalizations. The authors' implementation of the logic records the justification for each dependency to facilitate the interpretation of results.>

We consider languages whose operational semantics is given by a set of rewrite rules. For such languages, it is important to be able to determine that there are enough rules to completely reduce all meaningful expressions, but not so many that the system of rules is inconsistent. We develop a formal framework in which to give a precise treatment of these soundness and completeness issues. We believe our approach to be novel in that we make heavy use of denotational semantics in our proof of completeness. The particular language for which we answer these questions is an extended version of the functional programming language FP; however the applicability of these techniques extends beyond the realm of FP rewriting systems.