Completely iterative algebras and completely iterative monads

DOI10.1016/j.ic.2004.05.003zbMath1062.68075OpenAlexW2082232201MaRDI QIDQ1767976

Stefan Milius

Publication date: 8 March 2005

Published in: Information and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ic.2004.05.003

zbMATH Keywords

CoalgebraMonadCompletely iterative algebraCompletely iterative theory

Mathematics Subject Classification ID

Semantics in the theory of computing (68Q55) Categorical semantics of formal languages (18C50)

Related Items (31)

Monads for behaviour ⋮ Complete Iterativity for Algebras with Effects ⋮ The coinductive resumption monad ⋮ Recursive Program Schemes and Context-Free Monads ⋮ The category-theoretic solution of recursive program schemes ⋮ Unnamed Item ⋮ How iterative reflections of monads are constructed ⋮ Equational properties of iterative monads ⋮ Recursive coalgebras of finitary functors ⋮ Unnamed Item ⋮ On second-order iterative monads ⋮ Unifying Guarded and Unguarded Iteration ⋮ Friends with Benefits ⋮ On functors preserving coproducts and algebras with iterativity ⋮ Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot ⋮ Elgot theories: a new perspective on the equational properties of iteration ⋮ Initial algebras and terminal coalgebras in many-sorted sets ⋮ The Recursion Scheme from the Cofree Recursive Comonad ⋮ Recursive coalgebras from comonads ⋮ Terminal coalgebras and free iterative theories ⋮ A metalanguage for guarded iteration ⋮ On the Key Dependent Message Security of the Fujisaki-Okamoto Constructions ⋮ Semantics of Higher-Order Recursion Schemes ⋮ Long-term values in Markov decision processes, (co)algebraically ⋮ Steps and traces ⋮ On algebras with effectful iteration ⋮ Categorical Büchi and parity conditions via alternating fixed points of functors ⋮ A new foundation for finitary corecursion and iterative algebras ⋮ Unnamed Item ⋮ Corecursive algebras in nature ⋮ Comonadic Notions of Computation

Cites Work

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• On Rational Monads and Free Iterative Theories
• On Iteratable Endofunctors
• Free iterative theories: a coalgebraic view
• Coproducts of Ideal Monads
• A Perspective View of Discrete Automata and Their Design
• Parametric corecursion

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