Abstract Behavior Types: A Foundation Model for Components and Their Composition

The notion of Abstract Data Type (ADT) has served as a foundation model for structured and object-oriented programming for some thirty years. An ADT defines an algebra of operations with well-defined semantics, without specifying any detail about the implementation of those operations or the data structures they operate on to realize them. ADT is a powerful abstraction and encapsulation mechanism that groups data together with their related operations into logically coherent and loosely-dependent entities, such as objects, yielding better structured programs.

The current trend in software engineering toward component based systems requires a foundation model as well. The immense success of object-oriented techniques has distracted proper attention from the fact that the most basic inherent property of an ADT, i.e., that it provides a set of operations, subverts some highly desirable properties in emerging formal models for components. This is already evident in the current attempts at extending the object-oriented models into the realm of components.

We introduce the notion of an Abstract Behavior Type (ABT) as a higher-level alternative to ADT and propose it as a proper foundation model for both components and their composition. An ABT defines an abstract behavior as a relation among a set of timed-data-streams, without specifying any detail about the operations that may be used to implement such behavior or the data types it may manipulate for its realization. In contrast with the algebraic underpinnings of the ADT model, the (generally) infinite streams that are the elements of behavior in the ABT model naturally lend themselves to the coalgebraic techniques and the coinduction reasoning principle that have recently been developed as a general theory to describe the behavior of dynamic systems. The ABT model supports much looser coupling than is possible with ADT and is inherently amenable to exogenous coordination. We propose that both of these are highly desirable, if not essential, properties for components and their composition.

In our view, a component based system consists of component instances and their connectors (i.e., the "glue code"), both of which are uniformly modeled as ABTs. As a concrete instance of the application of the ABT model, we present Reo: a channel-based exogenous coordination model wherein complex coordinators, called "connectors" are compositionally built out of simpler ones. The simplest connectors in Reo are a set of channels with well-defined behavior supplied by users. Reo can be used as a "glue language" for compositional construction of connectors that orchestrate component instances in a component-based system. We demonstrate the surprisingly expressive power of connector composition in Reo through a number of examples. Because all Reo connectors are ABTs, we show how the semantics of channel composition in Reo can be defined in terms of a calculus of ABT composition.  

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