A New Abstraction Framework for Affine Transformers

Abstract. This paper addresses the problem of abstracting a set of affine transformers v' = v C + d, where v and v' 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 d---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