A New Abstraction Framework for Affine Transformers

Tushar Sharma, Thomas W. Reps

Abstract: This paper addresses the problem of abstracting a set of affine transformers $$\overrightarrow{v}' = \overrightarrow{v} \cdot C + \overrightarrow{d}$$ , where $$\overrightarrow{v}$$ and $$\overrightarrow{v}'$$ represent the pre-state and post-state, respectively. We introduce a framework to harness any base abstract domain $$\mathcal {B}$$ 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 $$\mathcal {B}$$ is re-purposed to constrain the elements of C and $$\overrightarrow{d}$$ —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.