Resources, garbage-collection and the π-calculus

Techniques such as mobility and distribution are often used to overcome limitations of resources such as the amount of memory or the necessity for specialised devices. Indeed, questions related to such limitations are crucial in matters of security, compilation and quality of service. However, few attempts have been made at formalising this notion of resource limitation in presence of mobility, distribution or concurrency. In this paper, we present a formalisation of resource usage, resource limitations and garbage-collection, using as a support a variant of the π-calculus, the controlled π-calculus. We use this calculus to study formally the notion of garbage-collection and to produce an effective proof system for respect of resource bounds, aware of resource transfer between processes and resource reuse thanks to finalisation. We also present an example of transformation of a protocol for compliance with such limitations and we confront informally our definitions with commonly-used garbage-collectors such as those of OCaml, Java and C#.