A Calculational Approach to Control-Flow Analysis by Abstract Interpretation

  • Authors:
  • Jan Midtgaard;Thomas Jensen

  • Affiliations:
  • INRIA Rennes - Bretagne Atlantique,;CNRS IRISA, Rennes Cedex, France 35042

  • Venue:
  • SAS '08 Proceedings of the 15th international symposium on Static Analysis
  • Year:
  • 2008

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Abstract

We present a derivation of a control-flow analysis by abstract interpretation. Our starting point is a transition system semantics defined as an abstract machine for a small functional language in continuation-passing style. We obtain a Galois connection for abstracting the machine states by composing Galois connections, most notable an independent-attribute Galois connection on machine states and a Galois connection induced by a closure operator associated with a constituent-parts relation on environments. We calculate abstract transfer functions by applying the state abstraction to the collecting semantics, resulting in a novel characterization of demand-driven 0-CFA.