## Induction Proofs with Partial Functions (1998)

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- [www.inferenzsysteme.informatik.tu-darmstadt.de]
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Venue: | Journal of Automated Reasoning |

Citations: | 5 - 4 self |

### BibTeX

@TECHREPORT{Giesl98inductionproofs,

author = {Jürgen Giesl},

title = {Induction Proofs with Partial Functions},

institution = {Journal of Automated Reasoning},

year = {1998}

}

### OpenURL

### Abstract

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 non-terminating algorithms. The need for such induction schemes and the power of our calculus have been demonstrated on a large collection of non-trivial 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.