A first-order calculus for allegories

Authors:
Bahar Aameri;Michael Winter
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Ontario, Canada;Department of Computer Science, Brock University, St. Catharines, Ontario, Canada
Venue:
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Year:
2011

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Abstract

In this paper we present a language and first-order calculus for formal reasoning about relations based on the theory of allegories. Since allegories are categories, the language is typed in Church-style. We show soundness and completeness of the calculus and demonstrate its usability by presenting the RelAPS system; a proof assistant for relational categories based on the calculus presented here.