A new abstraction framework for affine transformers

Abstract

This paper addresses the problem of abstracting a set of affine transformers (Formula presented.), where (Formula presented.) and (Formula presented.) represent the pre-state and post-state, respectively. We introduce a framework to harness any base abstract domain B in an abstract domain of affine transformations. Abstract domains are usually used to define constraints on the variables of a program. In this paper, however, abstract domain B is re-purposed to constrain the elements of C and (Formula presented.) —thereby defining a set of affine transformers on program states. This framework facilitates intra- and interprocedural analyses to obtain function and loop summaries, as well as to prove program assertions.