Web Operating Systems can be seen as an extension of traditional Operating Systems where the addresses used to manage files and execute programs (via the basic load/execution mechanism) are extended from local filesystem path-names to URLs. A first consequence is that, similarly as for traditional web technologies, executing a program at a given URL can be done in two modalities: either the execution is performed client-side at the invoking machine (and relative URL addressing in the executed program set to refer to the invoked URL) or it is performed server-side at the machine addressed by the invoked URL (as, e.g., for a web service). Moreover in this context, user identification for access to programs and files and workow-based composition of service programs is naturally based on token/session-like mechanisms. We propose a middleware based on client-server protocols and on a set primitives, for managing files/resources and executing programs (in the form of client-side/server-side components/services) in Web Operating Systems, based on an extension of the REST architecture. In order to provide an unambiguous specification, we formally define the semantics of such middleware by first introducing a process algebra for standard REST and then extending it to the whole middleware.