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We provide an algorithm that automatically derives many provable theorems in the equational theory of allegories. This was accomplished by noticing properties of an existing decision algorithm that could be extended to provide a derivation in addition to a decision certi cate. We also suggest improvements and corrections to previous research in order to motivate further work on a complete derivation mechanism. The results presented here are signi cant for those interested in relational theories, since we essentially have a subtheory where automatic proof-generation is possible. This is also relevant to program veri cation since relations are well-suited to describe the behaviour of computer programs. It is likely that extensions of the theory of allegories are also decidable and possibly suitable for further expansions of the algorithm presented here.
About the author
Joel Glanfield was raised in Welland, Ontario, Canada. He completed his Master of Science degree at Brock University under the supervision of Dr. Michael Winter. Joel is currently pursuing his PhD in Computer Science at Dalhousie University in Halifax, Nova Scotia, Canada.
