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

Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)

Collections: Computer Technologies and Information Sciences