Abstract Interpretation using a Language of Symbolic Approximation

The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework, based on symbolic expressions used both as an abstraction of the program, and as the input analyzed by abstract domains. We demonstrate new applications of the framework: an abstract domain that efficiently propagates constraints across the whole program; a new formalization of functor domains as approximate translation, which allows the production of approximate programs, on which we can perform classical symbolic techniques. We used these to build a complete analyzer for embedded C programs, that demonstrates the practical applicability of the framework.