Complete sets of cooperations.

C. Kupke, J.J.M.M. Rutten

Research output: Contribution to JournalArticleAcademicpeer-review


The structure map turning a set into the carrier of a final coalgebra is not unique. This fact is well known, but commonly elided. In this paper, we argue that any such concrete representation of a set as a final coalgebra is potentially interesting on its own. We discuss several examples, in particular, we consider different coalgebra structures that turn the set of infinite streams into the carrier of a final coalgebra. After that we focus on coalgebra structures that are made up using so-called cooperations. We say that a collection of cooperations is complete for a given set X if it gives rise to a coalgebra structure that turns X into the carrier set of a subcoalgebra of a final coalgebra. Any complete set of cooperations yields a coalgebraic proof and definition principle. We exploit this fact and devise a general definition scheme for constants and functions on a set X that is parametrical in the choice of the complete set of cooperations for X. © 2010 Published by Elsevier Inc.
Original languageEnglish
Pages (from-to)1398-1420
Number of pages22
JournalInformation and Computation
Issue number12
Publication statusPublished - 2010


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