Rewriting induction (Reddy, 1989) is an automated inductive theorem proving method for term rewriting systems. An automated lemma generation method for automated inductive theorem proving is said to be sound if it does not produce incorrect lemmas. Divergence critic (Walsh, 1996) is a well-known automated lemma generation method for the rewriting induction, but it is unsound. In this paper, we propose a sound variant of the divergence critic applicable for monomorphic term rewriting systems by incorporating sound generalization (Urso and Kounalis, 2004) in a part of its procedure. We implement these three automated lemma generation methods on a rewriting induction system with disproof to evaluate effectiveness of these methods. Our experiment reveals that the (sound) divergence critic and the sound generalization are often effective for different kinds of conjectures. Thus, the sound divergence critic can be combined with the sound generalization to obtain a more powerful automated sound lemma generation method for rewriting induction.
|Number of pages||15|
|Publication status||Published - 2009 Jul 29|
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