Motivated by issues in designing practical total functional programming languages, we are interested in structured recursive equations that uniquely describe a function not because of the properties of the coalgebra marshalling the recursive call arguments but thanks to the algebra assembling their results. Dualizing the known notions of recursive and wellfounded coalgebras, we call an algebra of a functor corecursive, if from any coalgebra of the same functor there is a unique map to this algebra, and antifounded, if it admits a bisimilarity principle. Differently from recursiveness and wellfoundedness, which are equivalent conditions under mild assumptions, corecursiveness and antifoundedness turn out to be generally inequivalent. © 2009 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Capretta, V., Uustalu, T., & Vene, V. (2009). Corecursive algebras: A study of general structured corecursion. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5902 LNCS, pp. 84–100). https://doi.org/10.1007/978-3-642-10452-7_7
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