Combining Norms to Prove Termination

  • Authors:
  • Samir Genaim;Michael Codish;John P. Gallagher;Vitaly Lagoon

  • Affiliations:
  • -;-;-;-

  • Venue:
  • VMCAI '02 Revised Papers from the Third International Workshop on Verification, Model Checking, and Abstract Interpretation
  • Year:
  • 2002

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Abstract

Automatic termination analysers typically measure the size of terms applying norms which are mappings from terms to the natural numbers. This paper illustrates howt o enable the use of size functions defined as tuples of these simpler norm functions. This approach enables us to simplify the problem of deriving automatically a candidate norm with which to prove termination. Instead of deriving a single, complex norm function, it is sufficient to determine a collection of simpler norms, some combination of which, leads to a proof of termination. We propose that a collection of simple norms, one for each of the recursive data-types in the program, is often a suitable choice. We first demonstrate the power of combining norm functions and then the adequacy of combining norms based on regular types.