The microcosm principle and concurrency in coalgebra

Authors:
Ichiro Hasuo;Bart Jacobs;Ana Sokolova
Affiliations:
Radboud University Nijmegen, The Netherlands and RIMS, Kyoto University, Japan and PRESTO Research Promotion Program, Japan Science and Technology Agency;Radboud University Nijmegen, The Netherlands and Technical University Eindhoven, The Netherlands;University of Salzburg, Austria
Venue:
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Year:
2008

Citing 13
Cited 7

Communicating sequential processes

Communicating sequential processes
Notions of computation and monads

Information and Computation
Universal coalgebra: a theory of systems

Theoretical Computer Science - Modern algebra and its applications
Communication and Concurrency

Communication and Concurrency
Towards a Mathematical Operational Semantics

LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
An Axiomatics for Categories of Transition Systems as Coalgebras

LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Coalgebraic semantics for timed processes

Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Discrete Lawvere theories and computational effects

Theoretical Computer Science - Algebra and coalgebra in computer science
Bialgebraic Operational Semantics and Modal Logic

LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
From Bialgebraic Semantics to Congruence Formats

Electronic Notes in Theoretical Computer Science (ENTCS)
Trace Semantics for Coalgebras

Electronic Notes in Theoretical Computer Science (ENTCS)
A syntactic commutativity format for SOS

Information Processing Letters
Generic forward and backward simulations

CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory

A Rule Format for Associativity

CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Coalgebraic components in a many-sorted microcosm

CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Traces, executions and schedulers, coalgebraically

CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Categorifying Computations into Components via Arrows as Profunctors

Electronic Notes in Theoretical Computer Science (ENTCS)
Arrows are strong monads

Proceedings of the third ACM SIGPLAN workshop on Mathematically structured functional programming
Traces for coalgebraic components

Mathematical Structures in Computer Science
The microcosm principle and compositionality of GSOS-based component calculi

CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Coalgebras are categorical presentations of state-based systems. In investigating parallel composition of coalgebras (realizing concurrency), we observe that the same algebraic theory is interpreted in two different domains in a nested manner, namely: in the category of coalgebras, and in the final coalgebra as an object in it. This phenomenon is what Baez and Dolan have called the microcosm principle, a prototypical example of which is "a monoid in a monoidal category." In this paper we obtain a formalization of the microcosm principle in which such a nested model is expressed categorically as a suitable lax natural transformation. An application of this account is a general compositionality result which supports modular verification of complex systems.