Interoperability remains a significant challenge in service-oriented computing. After proposing a pivot architecture to solve three interoperability problems, namely adaptation, integration and coordination problems between clients and servers, we explore the theoretical foundations for this architecture. A pivot architecture requires a universal language for orchestrating services and a universal language for interfacing resources. Since there is no evidence today that Web Services technologies can provide this basis, we propose a new language called Criojo and essentially show that it can be considered as a pivot language. We formalize the language Criojo and its operational semantics, by resorting to a chemical abstract machine, and give an account of formal translations into Criojo: in a distributed context, we deal with idiomatic languages for four major programming paradigms: imperative programming, logic programming, functional programming and concurrent programming.