Induction proofs with partial functions
In this paper we present a method for automated induction proofs about partial functions. We show that most well-known techniques developed for (explicit) induction theorem proving are unsound when dealing with partial functions. But surprisingly, by slightly restricting the application of these techniques, it is possible to develop a calculus for automated induction proofs with partial functions. In particular, under certain conditions one may even generate induction schemes from the recursions of nonterminating algorithms. The need for such induction schemes and the power of our calculus have been demonstrated on a large collection of nontrivial theorems (including Knuth and Bendix's critical pair lemma). In this way, existing induction theorem provers can be directly extended to partial functions without major changes of their logical framework.
induction partial functions automated theorem proving