In modern cloud-based architectures, containers play a central role: they provide powerful isolation mechanisms such that developers can focus on the logic and dependencies of applications while system administrators can focus on deployment and management issue. In this work, we propose a formal model for container-based systems, using the framework of Bigraphical Reactive Systems (BRSs). We first introduce local directed bigraphs, a graph-based formalism which allows us to deal with localized resources. Then, we define a signature for modelling containers and provide some examples of bigraphs modelling containers. These graphs can be analysed and manipulated using techniques from graph theory: properties about containers can be formalized as properties of the corresponding bigraphic representations. Moreover, it turns out that the composition of containers as performed by e.g. docker-compose, corresponds precisely to the composition of the corresponding bigraphs inside an "environment bigraph" which in turn is obtained directly from the YAML file used to define the composition of containers.

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