A logic-based approach to program flow analysis

Abstract

A formalism is presented for tracking assertions which hold universally, i.e., at the end of all the execution paths to a given program point, and assertions which hold existentially, i.e., at the end of some execution paths. In the formalism, the assertions which hold at a given execution path are uniformly defined by an entry environment which contains the assertions which hold when the execution of the program begins and an environment transformer for every program construct. The novel aspect of our formalism is that Horn clauses are used to specify the consistent environments and the meaning of program constructs. The best iterative algorithm (a notion defined by P. Cousot and R. Cousot) for tracking universal and existential assertions simultaneously is given. Conditions are presented under which the best iterative algorithm can be efficiently implemented. The formalism is applied to the pointer equality problem in Pascal. It is shown that universal pointer equalities may be used to reduce the number of superfluous existential equalities, and that existential equalities may be used to obtain more universal equalities. Recent empirical results indicate that tracking the combination of may and must equalities leads to substantial improvements in the result of the analysis. For programs without recursively defined records, the best iterative algorithm can be effectively implemented. These results apply to multiple levels of pointers and can be extended to handle possibly recursive procedures. However, for programs with recursively defined data types further approximations are necessary, e.g., by using a finite graph to model all the possible pointer equalities. For simplicity, this paper does not present an analysis algorithm for this case.