Typed connector families and their semantics.

Typed models of connector/component composition specify interfaces describing ports of components and connectors. Typing ensures that these ports are plugged together appropriately, so that data can flow out of each output port and into an input port. These interfaces typically consider the direction of data flow and the type of values flowing. Components, connectors, and systems are often parameterised in such a way that the parameters affect the interfaces. Typing such connector families is challenging. This paper takes a first step towards addressing this problem by presenting a calculus of connector families with integer and boolean parameters. The calculus is based on monoidal categories, with a dependent type system that describes the parameterised interfaces of these connectors. We use families of Reo connectors as running examples, and show how this calculus can be applied to Petri Nets and to BIP systems. The paper focuses on the structure of connectors—well-connectedness—and less on their behaviour, making it easily applicable to a wide range of coordination and component-based models. A type-checking algorithm based on constraints is used to analyse connector families, supported by a proof-of-concept implementation.