Cellular Monads from Positive GSOS Specifications
Tom Hirschowitz (Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS,, LAMA, 73000 Chamb\'ery, France)
TL;DR
This paper introduces an abstract framework using cellular monads for operational semantics, demonstrating that Positive GSOS specifications produce compositional free algebras and ensuring bisimilarity as a congruence.
Contribution
It establishes a novel connection between cellular monads and Positive GSOS specifications, showing that these specifications generate compositional free algebras.
Findings
Positive GSOS specifications generate cellular monads
Free algebras are compositional
Bisimilarity is a congruence in the generated systems
Abstract
We give a leisurely introduction to our abstract framework for operational semantics based on cellular monads on transition categories. Furthermore, we relate it for the first time to an existing format, by showing that all Positive GSOS specifications generate cellular monads whose free algebras are all compositional. As a consequence, we recover the known result that bisimilarity is a congruence in the generated labelled transition system.
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