Constrained Tree Grammars to Pilot Automated Proof by Induction

In this paper, we develop a new approach for mechanizing induction on complex data structures (like bags, sorted lists, trees, powerlists. . . ) by adapting and generalizing works in tree automata with constraints. The key idea of our approach is to compute a tree grammar with constraints which describes the initial model of the given specification. This grammar is used as an induction schema for the generation of subgoals during the proof. Our procedure is sound and refutationally complete even when the axioms for constructors are not left-linear, constrained, non-terminating. Moreover, it subsumes all test set induction approaches. Based on several examples, our method seems to yield very natural proofs.