Fractals everywhere
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
Theoretical Computer Science
Algebraic Semantics
Automata and Algebras in Categories
Automata and Algebras in Categories
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
Theoretical Computer Science - Logic, semantics and theory of programming
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
Electronic Notes in Theoretical Computer Science (ENTCS)
The category theoretic solution of recursive program schemes
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
A Mezei-Wright theorem for categorical algebras
Theoretical Computer Science
Complete iterativity for algebras with effects
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)
CIA structures and the semantics of recursion
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Algebraic synchronization trees and processes
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Electronic Notes in Theoretical Computer Science (ENTCS)
Hi-index | 0.00 |
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with "enough final coalgebras" we show how to formulate, solve, and study recursive program schemes. Our general theory is algebraic and so avoids using ordered or metric structures. Our work generalizes the previous approaches which do use this extra structure by isolating the key concepts needed to study substitution in infinite trees, including second-order substitution. As special cases of our interpreted solutions we obtain the usual denotational semantics using complete partial orders, and the one using complete metric spaces. Our theory also encompasses implicitly defined objects which are not usually taken to be related to recursive program schemes. For example, the classical Cantor two-thirds set falls out as an interpreted solution (in our sense) of a recursive program scheme.