Coalgebraic Representation Theory of Fractals
Electronic Notes in Theoretical Computer Science (ENTCS)
From corecursive algebras to corecursive monads
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Language constructs for non-well-founded computation
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
Adjoint folds and unfolds-An extended study
Science of Computer Programming
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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.