A New Abstraction Framework for Affine Transformers
Tushar Sharma and Thomas Reps
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.
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University of Wisconsin