Foundations of a Module Concept for Distributed Object Systems

This thesis provides a logical and mathematical foundation for object-oriented specification languages with a further modularisation unit between the system and object classes. The unit is denoted object-oriented module, or module for short, and initially described in an informal way. Modules offer a better approach to reusability and provide better structuring of large, complex and distributed systems. In our approach, systems and single modules are represented by theory presentations in a module logic. These presentations, also called module specifications, are pairs consisting of a module signature and a set of module axioms. The axioms are formulae in a newly developed module logic MDTL (Module Distributed Temporal Logic). This is a true-concurrent branching-time discrete distributed first-order temporal logic that is interpreted over labelled event structures. Winskel et al. introduced certain event structure morphisms to organise event structures into a category ev with limits. Here we present a second notion of morphism between event structures, so-called communication event structure morphisms, that result in a different category cev with just the right colimits for our purposes. Crucially, in some cases a morphism in ev has a corresponding reverse morphism in cev. A categorical construction is presented which uses limits in ev and colimits in cev. The construction may be used to model several module operations in a uniform way. In particular, we consider concurrent composition (synchronous, asynchronous, or mixed), parameter actualisation, refinement, restriction (hiding) and renaming.