Recursive coalgebras from comonads
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Recursive Coalgebras from Comonads
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic Observations and Valuations
Electronic Notes in Theoretical Computer Science (ENTCS)
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
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TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
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Abstract: We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. The universal property gives rise to an analogue of primitive recursion for defining computable functions on the interval. We use this to define basic arithmetic operations and to verify equations between them. We test the notion in categories of interest. In the category of sets, any closed and bounded interval of real numbers is an interval object. In the category of topological spaces, the interval objects are closed and bounded intervals with the Euclidean topology. We also prove that an interval object exists in any elementary topos with natural numbers object.