Iteration theories: the equational logic of iterative processes
Iteration theories: the equational logic of iterative processes
Additions and corrections to “Terminal coalgebras in well-founded set theory”
Theoretical Computer Science
Theoretical Computer Science
Automata and Algebras in Categories
Automata and Algebras in Categories
Category Theory and Computer Science
On final coalgebras of continuous functors
Theoretical Computer Science - Category theory and 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
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
From Iterative Algebras to Iterative Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
Mathematical Structures in Computer Science
The category-theoretic solution of recursive program schemes
Theoretical Computer Science - Algebra and coalgebra in computer science
Coequational Logic for Finitary Functors
Electronic Notes in Theoretical Computer Science (ENTCS)
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)
Iterative reflections of monads
Mathematical Structures in Computer Science
Coequational logic for accessible functors
Information and Computation
Elgot theories: A new perspective on the equational properties of iteration
Mathematical Structures in Computer Science
How iterative reflections of monads are constructed
Information and Computation
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Every finitary endofunctor H of Set can be represented via a finitary signature Σ and a collection of equations called "basic". We describe a terminal coalgebra for H as the terminal Σ-coalgebra (of all Σ-trees) modulo the congruence of applying the basic equations potentially infinitely often. As an application we describe a tree iterative theory on H (in the sense of Calvin Elgot) as the theory of all rational Σ-trees modulo the analogous congruence. This yields a number of new examples of iterative theories, e.g., the theory of all strongly extensional, rational, finitely branching trees, free on the finite power-set functor, or the theory of all binary, rational unordered trees, free on one commutative binary operation.