On the structure of categories of coalgebras
Theoretical Computer Science
Combining a monad and a comonad
Theoretical Computer Science
Mongruences and Cofree Coalgebras
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
Bialgebraic Modelling of Timed Processes
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Real-Time Behaviour of Asynchronous Agents
CONCUR '90 Proceedings of the Theories of Concurrency: Unification and Extension
An Overview and Synthesis on Timed Process Algebras
CAV '91 Proceedings of the 3rd International Workshop on Computer Aided Verification
Towards a Mathematical Operational Semantics
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A Comparison of Additivity Axioms in Timed Transition Systems.
A Comparison of Additivity Axioms in Timed Transition Systems.
Category theory for operational semantics
Theoretical Computer Science - Selected papers of CMCS'03
Combining effects: sum and tensor
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Modularity of Behaviours for Mathematical Operational Semantics
Electronic Notes in Theoretical Computer Science (ENTCS)
Structural operational semantics for weighted transition systems
Semantics and algebraic specification
A categorical view of timed weak bisimulation
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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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.