Coalgebraic components in a many-sorted microcosm

Authors:
Ichiro Hasuo;Chris Heunen;Bart Jacobs;Ana Sokolova
Affiliations:
RIMS, Kyoto University, Japan and PRESTO Research Promotion Program, Japan Science and Technology Agency;Radboud University Nijmegen, The Netherlands;Radboud University Nijmegen, The Netherlands;University of Salzburg, Austria
Venue:
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Year:
2009

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Abstract

The microcosm principle, advocated by Baez and Dolan and formalized for Lawvere theories lately by three of the authors, has been applied to coalgebras in order to describe compositional behavior systematically. Here we further illustrate the usefulness of the approach by extending it to a many-sorted setting. Then we can show that the coalgebraic component calculi of Barbosa are examples, with compositionality of behavior following from microcosm structure. The algebraic structure on these coalgebraic components corresponds to variants of Hughes' notion of arrow, introduced to organize computations in functional programming.