Behavioural Types for Synchronous Software Composition 1

Digital signal–processing (DSP) development tools such as Ptolemy, LabView and iConnect allow application developers to assemble reactive systems by connecting predefined components in generalised dataflow graphs and by hierarchically building new components by encapsulating sub–graphs. We follow the literature in calling this approach dataflow-oriented development. Previous work has shown how a novel process calculus, CaSE, can provide a model for this form of software, and how this can be used as the basis for a system of behavioural types. Well-typedness in this system implies reactivity (non-termination) in terms of a generalisation to the dataflow principle of consistency, which was previously unable to handle, in general, statefulness and non-determinism. In the previous presentation the typing rules were parameterised in a semantic behavioural equivalence, temporal observation congruence, which specialises CCS’s notion of weak bisimulation to this setting. In this work, we show how a complete axiom system for CaSE allows these equivalences to be reduced to a syntactic check, which is more fitting to a type system.