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Induction Proofs with Partial Functions \Lambda URGEN GIESL

Summary: Induction Proofs with Partial Functions \Lambda
J ¨
Dept. of Computer Science, Darmstadt University of Technology, Alexanderstr. 10,
64283 Darmstadt, Germany, e­mail: giesl@informatik.tu­darmstadt.de
Abstract. In this paper we present a method for automated induction proofs about
partial functions. We show that most well­known 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 par­
ticular, 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' critical pair lemma). In this way, existing
induction theorem provers can be directly extended to partial functions without
major changes of their logical framework.
Key words: induction, automated theorem proving, partial functions
1. Introduction
Induction is the essential proof method for the verification of func­
tional programs. For that reason, several techniques 1 have been devel­


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


Collections: Computer Technologies and Information Sciences