Abstract
This chapter introduces the notion of a final coalgebra relative to an endofunctor and corecursion on a final coalgebra via the paradigm examples of a particular kind of tree. The notion is dual to the more familiar notion of an initial algebra and structural recursion on an initial algebra. The chapter starts with the paradigm syntactic examples of initial algebras, the term algebras.
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References
Peter Aczel, Non-well-founded Sets, CSLI, (1988). 85
Peter Aczel, Jiri Adamek and Jiri Velebil, A Coalgebraic View of Infinite Trees and Iteration, in Electronic Notes in Theoretical Computer Science 44.1 (2001). See http://www.elsevier.nl/gej-ng/31/29/23/73/23/show/Products/notes/index.htt. 88
Larry Paulson, Final Coalgebras as greatest fixed points in ZF set theory, in Mathematical Structures in Computer Science, pp 545–567, (1999). 85
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© 2002 Springer-Verlag Berlin Heidelberg
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Aczel, P. (2002). Algebras and Coalgebras. In: Backhouse, R., Crole, R., Gibbons, J. (eds) Algebraic and Coalgebraic Methods in the Mathematics of Program Construction. Lecture Notes in Computer Science, vol 2297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47797-7_3
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DOI: https://doi.org/10.1007/3-540-47797-7_3
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