Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Iteration theories: the equational logic of iterative processes
Iteration theories: the equational logic of iterative processes
On the greatest fixed point of a set functor
Theoretical Computer Science
Initial Algebra Semantics and Continuous Algebras
Journal of the ACM (JACM)
Theoretical Computer Science
Automata and Algebras in Categories
Automata and Algebras in Categories
On varieties and covarieties in a category
Mathematical Structures in Computer Science
Free iterative theories: a coalgebraic view
Mathematical Structures in Computer Science
Explicit substitutions and higher-order syntax
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Nordic Journal of Computing
Theoretical Computer Science - Logic, semantics and theory of programming
Substitution in non-wellfounded syntax with variable binding
Theoretical Computer Science - Selected papers of CMCS'03
Completely iterative algebras and completely iterative monads
Information and Computation
A general final coalgebra theorem
Mathematical Structures in Computer Science
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Distributive laws for the coinductive solution of recursive equations
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Explicit substitutions and higher-order syntax
Higher-Order and Symbolic Computation
Terminal coalgebras and free iterative theories
Information and Computation
Mathematical Structures in Computer Science
The category-theoretic solution of recursive program schemes
Theoretical Computer Science - Algebra and coalgebra in computer science
Comonadic Notions of Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Initial Algebra Semantics for Cyclic Sharing Structures
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
From Iterative Algebras to Iterative Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
Recursive Coalgebras from Comonads
Electronic Notes in Theoretical Computer Science (ENTCS)
Relating Two Approaches to Coinductive Solution of Recursive Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
Completely iterative algebras and completely iterative monads
Information and Computation
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Distributive laws for the coinductive solution of recursive equations
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Recursive Program Schemes and Context-Free Monads
Electronic Notes in Theoretical Computer Science (ENTCS)
Higher-order Algebras and Coalgebras from Parameterized Endofunctors
Electronic Notes in Theoretical Computer Science (ENTCS)
Iterative reflections of monads
Mathematical Structures in Computer Science
Equational properties of iterative monads
Information and Computation
The Recursion Scheme from the Cofree Recursive Comonad
Electronic Notes in Theoretical Computer Science (ENTCS)
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
The essence of dataflow programming
APLAS'05 Proceedings of the Third Asian conference on Programming Languages and Systems
On the semantics of coinductive types in martin-löf type theory
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Context-free languages via coalgebraic trace semantics
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Equational logic of recursive program schemes
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
The category theoretic solution of recursive program schemes
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
CIA structures and the semantics of recursion
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Electronic Notes in Theoretical Computer Science (ENTCS)
Base modules for parametrized iterativity
Theoretical Computer Science
Hi-index | 5.23 |
Infinite trees form a free completely iterative theory over any given signature--this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has final coalgebras for all functors H(-) + X, then those coalgebras, TX, form a monad. This monad is completely iterative, i.e., every guarded system of recursive equations has a unique solution. And it is a free completely iterative monad on H. The special case of polynomial endofunctors of the category Set is the above mentioned theory, or monad, of infinite trees.This procedure can be generalized to monoidal categories satisfying a mild side condition: if, for an object H, the endofunctor H ⊗ _ + I has a final coalgebra, T, then T is a monoid. This specializes to the above case for the monoidal category of all endofunctors.