On the structure of categories of coalgebras
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Combining a monad and a comonad
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Mongruences and Cofree Coalgebras
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Bialgebraic Modelling of Timed Processes
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LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A Comparison of Additivity Axioms in Timed Transition Systems.
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Category theory for operational semantics
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Electronic Notes in Theoretical Computer Science (ENTCS)
Tensors of Comodels and Models for Operational Semantics
Electronic Notes in Theoretical Computer Science (ENTCS)
Bialgebraic methods and modal logic in structural operational semantics
Information and Computation
The microcosm principle and concurrency in coalgebra
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
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We give a coalgebraic formulation of timed processes and their operational semantics. We model time by a monoid called a "time domain", and we model processes by "timed transition systems", which amount to partial monoid actions of the time domain or, equivalently, coalgebras for an "evolution comonad" generated by the time domain. All our examples of time domains satisfy a partial closure property, yielding a distributive law of a monad for total monoid actions over the evolution comonad, and hence a distributive law of the evolution comonad over a dual comonad for total monoid actions. We show that the induced coalgebras are exactly timed transition systems with delay operators. We then integrate our coalgebraic formulation of time qua timed transition systems into Turi and Plotkin's formulation of structural operational semantics in terms of distributive laws. We combine timing with action via the more general study of the combination of two arbitrary sorts of behaviour whose operational semantics may interact. We give a modular account of the operational semantics for a combination induced by that of each of its components. Our study necessitates the investigation of products of comonads. In particular, we characterise when a monad lifts to the category of coalgebras for a product comonad, providing constructions with which one can readily calculate.