Coalgebraic Components in a Many-Sorted Microcosm
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Ichiro Hasuo, Chris Heunen, Bart Jacobs, and Ana Sokolova
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Abstract:
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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.
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