A Graph Syntax for Processes and Services

We propose a class of hierarchical graphs equipped with a simple algebraic syntax as a convenient way to describe the configurations of languages equipped with inherently hierarchical features such as sessions, fault-handling scopes, transactions or locations. The graph syntax can be seen as an intermediate representation language, that facilitates the encoding of algebraic specifications and, in particular, of process calculi, since it provides primitives for nesting, name restriction and parallel composition. The syntax is based on an algebraic presentation of graphs that faithfully characterises families of hierarchical graphs, meaning that each term of the language identifies uniquely an equivalence class of graphs (modulo graph isomorphism). Proving soundness and correctness of an encoding with respect to graph isomorphism (i.e. proving that congruent processes are mapped to isomorphic graphs) is then facilitated and can be done by structural induction. Summing up, the graph syntax facilitates the definition of faithful encodings, yet allowing a precise visual representation. We instantiate our proposal by offering the graphical encoding of a workflow language and a service-oriented calculus.