Generating Counterexamples for Structural Inductions by Exploiting Nonstandard Models
- Cite this paper as:
- Blanchette J.C., Claessen K. (2010) Generating Counterexamples for Structural Inductions by Exploiting Nonstandard Models. In: Fermüller C.G., Voronkov A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science, vol 6397. Springer, Berlin, Heidelberg
Induction proofs often fail because the stated theorem is noninductive, in which case the user must strengthen the theorem or prove auxiliary properties before performing the induction step. (Counter)model finders are useful for detecting non-theorems, but they will not find any counterexamples for noninductive theorems. We explain how to apply a well-known concept from first-order logic, nonstandard models, to the detection of noninductive invariants. Our work was done in the context of the proof assistant Isabelle/HOL and the counterexample generator Nitpick.
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