Compiling high-level specifications of program analyses

Abstract

In this thesis, we address two problems in compiling high-level static analysis specifications into executable analyzers: how to check the correctness of the specifications and how to achieve the efficiency of the generated analyzers. Our research is motivated from our work on a static program-analyzer generating system (named Zoo), in which the specification of static analysis (input to Zoo) consists of finite-height lattice definitions and function definitions over the lattices. In order to make our system be used in practice, we need to generate a correct and efficient program analyzer. We present a static analysis to examine the extensivity of functions as a solution of the first problem, how to check the correctness of the specifications. One of the sufficient conditions for terminating program analysis is the extensivity of analysis function. Once extensivity of the function is ascertained, the generated analyzer is guaranteed to terminate. The extensivity analysis consists of a syntax-driven deductive rules whose satisfiability check is done by a constraint solving procedure. We also present a differential fixpoint iteration method as a solution of the second problem, how to achieve the efficiency of the generated analyzers. Computing a static program analysis is done by the fixpoint iterations ("repeat until no-change"), and by "differential" we mean that the method tries to compute only the difference between iterations in order to avoid redundancies. Our method is fully automatic and does not require that the given analysis function or its input/output lattices should be distributive. By subtracting previous results from intermediate results, we can reduce the differences as small as possible and, by transforming the given program analysis function into differential one, we can automatically eliminate use-less computations caused by differential method.