cient Computation of Fixpoints that Arise in Complex Program Analysis

This paper proposes a model for studying the computation of xpoints that arise in complex program analysis based on abstract interpretation, and presents an e cient algorithm for computing xpoints based on the model. Abstract interpretation provides a uni ed framework for handling interprocedural analysis of programs with unrestricted pointer manipulation, higher-order functions, and continuations. In the general case, the structure of the xpoint computation is not known before analysis; that is, the ow graph cannot be determined from the syntax of a program. Abstract interpretation handles this situation easily. In our algorithm, the entailment graph, representing the structure of the xpoint computation, is developed during analysis. The strategies for determining the evaluation order, which underlie the algorithm, are described. Based on the strategies, local knowledge of the entailment graph at each node is exploited to determine dynamically an e ective order of evaluation. The algorithm behaves like those based upon interval analysis of a ow graph, but without requiring the interprocedural control ow graph to be given a priori. The algorithm has been implemented, and experiments have been conducted to compare it to other iterative algorithms for solving such problems. The results show that the algorithm is exible, e cient, and consistently better than the others.