Partial Evaluation for Program Analysis

Preface This report documents the scientific work carried out during the part A of the Ph.D. studies of author at BRICS 1. The main topic of interest is programming languages, focusing on partial evaluation and program transformation. One of the ideas explored in the period was to assess the impact of partial evaluation on program analysis. The present report makes an account of the results obtained, from both theoretical and practical points of view. The report presents a case study of partial evaluation in program analysis. Starting from the observation that abstract interpretation incurs an interpretive overhead in the same way as a standard interpretation, we explore the benefits that can be obtained from specializing an abstract interpretation-based program analysis with respect to the source program. The contribution of our work is to present a complete formal account of Shivers's 0-CFA implementation and specialization. In the first chapters of the report, we point out a missing link between the formal specification of Shivers's 0-CFA and its implementation. We fill this gap by formally relating the specification with the formalization of the implementation. Both implementation and specialization are formalized within a unified programming-language framework. We formally specify an implementation language, thus making it possible to prove correctness of both implementation and specialization. The former is done by formally relating the semantics of the program implementing the analysis to the specification of the analysis. The later is done by establishing meaning-preserving program transformations which lead to program specialization. We thus obtain a correct specialized analyzer by means of simple program transformations. The motivation of this work is to build a complete theoretical foundation of an idea which can prove useful in practice. Our approach constructs a formal connection between a mathematical solution to a problem, its practical implementation, and the improvement obtained by specialization. Acknowledgments I would like to thank my supervisor Olivier Danvy for the numerous discussions and for his valuable comments about my work. I am also grateful to Andrzej Filinski for his courses at DAIMI and for his numerous suggestions. Thanks are also due to Dominique Boucher, who generously provided the source of his benchmarks. I would also like to thank Torben Amtoft for his collaboration during his stay at BRICS. Finally I thank Bernd Grobauer and Zhe Yang for both their help and enjoyable company.