Iteration theories: the equational logic of iterative processes
Iteration theories: the equational logic of iterative processes
Terms and Infinite Trees as Monads Over a Signature
TAPSOFT '89/CAAP '89 Proceedings of the International Joint Conference on Theory and Practice of Software Development, Volume 1: Advanced Seminar on Foundations of Innovative Software Development I and Colloquium on Trees in Algebra and Programming
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Infinite trees and completely iterative theories: a coalgebraic view
Theoretical Computer Science
Terminal coalgebras and free iterative theories
Information and Computation
Mathematical Structures in Computer Science
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
Semantics of higher-order recursion schemes
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra 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
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Iterative monads were introduced by Calvin Elgot in the 1970's and are those ideal monads in which every guarded system of recursive equations has a unique solution. We prove that every ideal monad has an iterative reflection, that is, an embedding into an iterative monad with the expected universal property. We also introduce the concept of iterativity for algebras for the monad , following in the footsteps of Evelyn Nelson and Jerzy Tiuryn, and prove that is iterative if and only if all free algebras for are iterative algebras.