Abstract
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 language | English |
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Pages (from-to) | 1398-1420 |
Number of pages | 22 |
Journal | Information and Computation |
Volume | 208 |
Issue number | 12 |
DOIs | |
Publication status | Published - 2010 |