Internal and external logics of abstract interpretations

  • Authors:

  • David A. Schmidt

  • Affiliations:

  • Kansas State University, Manhattan, Kansas

  • Venue:
  • VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
  • Year:
  • 2008

  • Safer unsafe code for .NET

    Proceedings of the 23rd ACM SIGPLAN conference on Object-oriented programming systems languages and applications

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Abstract

We show that every abstract interpretation possesses an internal logic, whose proof theory is defined by the partial ordering on the abstract domain's elements and whose model theory is defined by the domain's concretization function. We explain how program validation and transformation depend on this logic. Next, when a logic external to the abstract interpretation is imposed, we show how to synthesize a sound, underapproximating, set-based variant of the external logic and give conditions when the underapproximating logic can be embedded within the original abstract domain, inverted. We show how model-checking logics depend on this construction. The intent of this paper is tutorial, to integrate little-publicized results into a standard framework that can be used by practitioners of static analysis.