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CALCO
2009
Springer

Complete Iterativity for Algebras with Effects

14 years 5 months ago
Complete Iterativity for Algebras with Effects
Abstract. Completely iterative algebras (cias) are those algebras in which recursive equations have unique solutions. In this paper we study complete iterativity for algebras with computational effects (described by a monad). First, we prove that for every analytic endofunctor on Set there exists a canonical distributive law over any commutative monad M, hence a lifting of that endofunctor to the Kleisli category of M. Then, for an arbitrary distributive law λ of an endofunctor H on Set over a monad M we introduce λ-cias. The cias for the corresponding lifting of H (called Kleisli-cias) form a full subcategory of the category of λ-cias. For various monads of interest we prove that free Kleisli-cias coincide with free λ-cias, and these free algebras are given by free algebras for H. Finally, for three concrete examples of monads we prove that Kleisli-cias and λ-cias coincide and give a characterisation of those algebras. Key words: iterative algebra, monad, distributive law, initia...
Stefan Milius, Thorsten Palm, Daniel Schwencke
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CALCO
Authors Stefan Milius, Thorsten Palm, Daniel Schwencke
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