Compositional Re nement of Interactive Systems

We describe systems and their components by functional speci cation techniques We de ne notions of interface and interaction re nement for interactive systems and their components These notions of re nement allow one to change both the syntactic the number of channels and sorts of messages at the channels and the semantic interface causality ow between messages and interaction granularity of an interactive system component We prove that these notions of re nement are compositional with respect to sequential and parallel composition of system components communication feedback and recursive declarations of system components According to these proofs re nements of networks can be accomplished in a modular way by re ning their components We generalize the notions of re nement to re ning contexts Finally full abstraction for speci cations is de ned and compositionality with respect to this abstraction is shown too This work was partially sponsored by the German Sonderforschungsbereich Werk zeuge f ur die Nutzung paralleler Architekturen