Combining Norms to Prove Termination

Samir Genaim, Michael Codish, John Gallagher and Vitaly Lagoon   

Third International Workshop on Verification, Model Checking and Abstract Interpretation; 2002


Automatic termination analysers typically measure the size of terms applying norms which are mappings from terms to the natural numbers. This paper illustrates how to 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.

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Michael Codish
The Department of Computer Science
Ben-Gurion University of the Negev
PoB 653, Beer-Sheva, 84105, Israel

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