A New Class of Functions for Abstract Interpretation

Abstract

In the context of denotational style abstract interpretation it is crucial to have an efficient fixed point solver. In general, however, finding a fixed point requires exponential time. One approach to improving the efficiency is the use of special classes of functions. A well-known example for such a class are additive functions, which allow the reduction to quadratic runtime. In this paper, we demonstrate that additive functions are not suited in a higher-order context. To overcome this deficiency, we introduce the class of component-wise additive functions, which are an extension of the class of additive functions. Component-wise additive functions allow us to solve many higher-order equation systems in polynomial time. We stress the usefulness of our class by presenting a package for implementing abstract interpretations using our theoretical results. Furthermore, experimental results taken in a case study for escape analysis are presented to relate our approach to other approaches