Theoretical Computer Science
Infinite trees and completely iterative theories: a coalgebraic view
Theoretical Computer Science
Free iterative theories: a coalgebraic view
Mathematical Structures in Computer Science
On the final sequence of a finitary set functor
Theoretical Computer Science
From Iterative Algebras to Iterative Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
A general final coalgebra theorem
Mathematical Structures in Computer Science
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Terminal coalgebras and free iterative theories
Information and Computation
Mathematical Structures in Computer Science
The category-theoretic solution of recursive program schemes
Theoretical Computer Science - Algebra and coalgebra in computer science
Comonadic Notions of Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Equational properties of iterative monads
Information and Computation
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Completely iterative theories of Calvin Elgot formalize (potentially infinite) computations as solutions of recursive equations. One of the main results of Elgot and his coauthors is that infinite trees form a free completely iterative theory. Their algebraic proof of this result is extremely complicated. We present completely iterative algebras as a new approach to the description of free completely iterative theories. Examples of completely iterative algebras include algebras on complete metric spaces. It is shown that a functor admits an initial completely iterative algebra iff it has a final coalgebra. The monad given by free completely iterative algebras is proved to be the free completely iterative monad on the given endofunctor. This simplifies substantially all previous descriptions of these monads. Moreover, the new approach is much more general than the classical one of Elgot et al. A necessary and sufficient condition for the existence of a free completely iterative monad is proved.