## Equalizing Terms by Difference Reduction Techniques (1997)

Venue: | In Proceedings Gramlich, B., Kirchner, H. (Eds.) Workshop on Strategies in Automated Deduction |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Hutter97equalizingterms,

author = {Dieter Hutter},

title = {Equalizing Terms by Difference Reduction Techniques},

booktitle = {In Proceedings Gramlich, B., Kirchner, H. (Eds.) Workshop on Strategies in Automated Deduction},

year = {1997}

}

### OpenURL

### Abstract

In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for a hierarchical planning of proofs. Also rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. 1 Introduction In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling ...

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Citation Context ...[SuSu95]. For example, SAM's lemma [GOBS69] is fully automatically proven by the system in less than a second. The ternary Boolean algebra problem EQ-3 (f(x; g(x); y) = y holds if axiom 3 is removed) =-=[LuMC93]-=- is proven using the path-abstraction on y and the described DR-techniques to refine the abstract solution. This example illustrates how abstractions are used to overcome local minima of the differenc... |

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Citation Context ...eleton As we have seen in the previous section, the abstraction to maximal symbols preserves to less information to plan in advance several deduction steps in the abstract space. The next abstraction =-=[Aut96]-=- suggests to equate the paths in both terms 12 Equalising Terms by from the top-level to a specific part of the skeleton. In case of success the symbols on this path will be added to the skeleton in t... |

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Citation Context ...corresponding literals upon which we want to resolve. A more general framework to decompose proof problems to problems of equalising terms can be obtained by using the approach of Negrete-Yankelevich =-=[Neg96]-=- which covers also non-first order logics. 9 Further Work Although the approach presented in this paper is able to proof some challenging equality problems (cf. the proof of SAM's lemma in the appendi... |