Two Cotensors in One: Presentations of Algebraic Theories for Local State and Fresh Names
Electronic Notes in Theoretical Computer Science (ENTCS)
Relating coalgebraic notions of bisimulation: with applications to name-passing process calculi
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
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Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rule-based definitions and proof techniques for congruenceresults. We formulate these principles in the general context of categorical logic. From this general formulation we recover precise results for particular language idioms by interpreting the logic inparticular categories. For instance, results for first-order calculi, such as CCS, arise from considering the general results in the category of sets. Results for languages involving substitution and name generation, such as the pi-calculus, arise from considering the general results in categories of sheaves and group actions. As an extended example, we develop a tyft/tyxt-like rule format for open bisimulation in the pi-calculus.