 
Summary: Partial Functions in Induction Theorem Proving ?
 Extended Abstract 
J¨urgen Giesl
Dept. of Computer Science, Darmstadt University of Technology, Alexanderstr. 10,
64283 Darmstadt, Germany, Email: giesl@informatik.tudarmstadt.de
Abstract. We present an approach for automated induction proofs with
partial functions. Most wellknown techniques developed for (explicit)
induction theorem proving are unsound when dealing with partial func
tions. But surprisingly, by slightly restricting the application of these
techniques, it is possible to develop a calculus for automated induc
tion proofs with partial functions. In particular, under certain condi
tions one may even generate induction schemes from the recursions of
nonterminating algorithms. The need for such induction schemes and
the power of our approach have been demonstrated on a large collec
tion of nontrivial theorems (including Knuth and Bendix' critical pair
lemma). In this way, existing induction theorem provers can be directly
extended to partial functions without changing their logical framework.
1 Introduction
The most important proof method for software verification is induction. There
fore, several techniques 1 have been developed to compute suitable induction
