A Case Study of Completion Modulo Distributivity and Abelian Groups

We propose an approach for building equational theories with the objective of improving the performance of the completion procedure, even though there exist canonical rewrite systems for these theories. As a test case of our approach, we show how to build the free Abelian groups and distributivity laws in the completion procedure. The empirical results of our experiment on proving many identities in alternative rings show clearly that the gain of this approach is substantial. More than 30 identities which are valid in any alternative ring are taken from the book “Rings that are nearly associative” by K.A. Zhevlakov et al., and include the Moufang identities and the skew-symmetry of the Kleinfeld function. The proofs of these identities are obtained by Herky, a descendent of RRL and a high-performance rewriting-based theorem prover.

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