Algebraic approaches to program semantics
Algebraic approaches to program semantics
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Infinite trees and completely iterative theories: a coalgebraic view
Theoretical Computer Science
Free iterative theories: a coalgebraic view
Mathematical Structures in Computer Science
On tree coalgebras and coalgebra presentations
Theoretical Computer Science
Completely iterative algebras and completely iterative monads
Information and Computation
On the final sequence of a finitary set functor
Theoretical Computer Science
Terminal coalgebras and free iterative theories
Information and Computation
Algebras with parametrized iterativity
Theoretical Computer Science
Bases for parametrized iterativity
Information and Computation
A Description of Iterative Reflections of Monads (Extended Abstract)
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Elgot Theories: A New Perspective of Iteration Theories (Extended Abstract)
Electronic Notes in Theoretical Computer Science (ENTCS)
Complete iterativity for algebras with effects
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Semantics of higher-order recursion schemes
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Recursive Program Schemes and Context-Free Monads
Electronic Notes in Theoretical Computer Science (ENTCS)
Iterative reflections of monads
Mathematical Structures in Computer Science
Equational properties of iterative monads
Information and Computation
Elgot theories: A new perspective on the equational properties of iteration
Mathematical Structures in Computer Science
From corecursive algebras to corecursive monads
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Multi-Linear Iterative K-Σ-Semialgebras
Electronic Notes in Theoretical Computer Science (ENTCS)
Well-Pointed coalgebras (extended abstract)
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
A complete logical system for the equality of recursive terms for sets
Logic and Program Semantics
Sound and Complete Axiomatizations of Coalgebraic Language Equivalence
ACM Transactions on Computational Logic (TOCL)
How iterative reflections of monads are constructed
Information and Computation
A parameterized graph transformation calculus for finite graphs with monadic branches
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
Electronic Notes in Theoretical Computer Science (ENTCS)
Base modules for parametrized iterativity
Theoretical Computer Science
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Iterative theories, which were introduced by Calvin Elgot, formalise potentially infinite computations as unique solutions of recursive equations. One of the main results of Elgot and his coauthors is a description of a free iterative theory as the theory of all rational trees. Their algebraic proof of this fact is extremely complicated. In our paper we show that by starting with ‘iterative algebras’, that is, algebras admitting a unique solution of all systems of flat recursive equations, a free iterative theory is obtained as the theory of free iterative algebras. The (coalgebraic) proof we present is dramatically simpler than the original algebraic one. Despite this, our result is much more general: we describe a free iterative theory on any finitary endofunctor of every locally presentable category $\cal{A}$.Reportedly, a blow from the welterweight boxer Norman Selby, also known as Kid McCoy, left one victim proclaiming,‘It's the real McCoy!’.