We show that coinductive predicates expressing behavioural properties of infinite objects can be themselves expressed as final coalgebras in a category of relations. The well-known case of bisimulation will simply be a special case of such final predicates. We will show how some useful pointwise and mixed properties of streams can be modelled in this way.
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Institute of Cybernetics at Tallinn University of Technology
R. Matthes , T. Uustalu
Mending the Unending: Machine Assisted Reasoning with Infinite Objects
Workshop on Fixed Points in Computer Science
Computer Security

Niqui, M., & Rutten, J. (2009). Coinductive Predicates as Final Coalgebras. In R. Matthes & T. Uustalu (Eds.), 6th Workshop on Fixed Points in Computer Science, FICS 2009, Coimbra, Portugal, 12--13 September 2009. Proceedings. (pp. 79–85). Institute of Cybernetics at Tallinn University of Technology.