Semantics of higher-order recursion schemes

Authors:
Jiří Adámek;Stefan Milius;Jiří Velebil
Affiliations:
Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Faculty of Electrical Engineering, Czech Technical University of Prague, Czech Republic
Venue:
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Year:
2009

Citing 12
Cited 4

Algebraic Semantics

Algebraic Semantics
Automata and Algebras in Categories

Automata and Algebras in Categories
Higher type program schemes and their tree languages

Proceedings of the 3rd GI-Conference on Theoretical Computer Science
Abstract Syntax and Variable Binding

LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A unified category theoretic approach to variable binding

MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Substitution in non-wellfounded syntax with variable binding

Theoretical Computer Science - Selected papers of CMCS'03
Iterative algebras at work

Mathematical Structures in Computer Science
Second-Order and Dependently-Sorted Abstract Syntax

LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Corrigendum: Corrigendum to: “The category theoretic solution of recursive program schemes” [Theoret. Comput. Sci. 366 (2006) 3-59]

Theoretical Computer Science
Completely iterative algebras and completely iterative monads

Information and Computation
Program schemes, recursion schemes, and formal languages

Journal of Computer and System Sciences
A finite semantics of simply-typed lambda terms for infinite runs of automata

CSL'06 Proceedings of the 20th international conference on Computer Science Logic

Recursive Program Schemes and Context-Free Monads

Electronic Notes in Theoretical Computer Science (ENTCS)
Iterative reflections of monads

Mathematical Structures in Computer Science
Elgot theories: A new perspective on the equational properties of iteration

Mathematical Structures in Computer Science
Sound and Complete Axiomatizations of Coalgebraic Language Equivalence

ACM Transactions on Computational Logic (TOCL)

Quantified Score

Hi-index	0.00

Visualization

Abstract

Higher-order recursion schemes are equations defining recursively new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of λ-calculus in which the terminals are interpreted as continuous operations. For the uninterpreted semantics based on infinite λ-terms we follow the idea of Fiore, Plotkin and Turi and work in the category of sets in context, which are presheaves on the category of finite sets. Whereas Fiore et al proved that the presheaf Fλ of λ-terms is an initial Hλ-monoid, we work with the presheaf Rλ of rational infinite λ-terms and prove that this is an initial iterative Hλ-monoid. We conclude that every guarded higher-order recursion scheme has a unique uninterpreted solution in Rλ.