The algebraic structure of interfaces

In this paper we examine formally the idea that the architecture of a system can be modelled by the structure of its interface expressed in terms of the interfaces for its components. Thus,System Interface Architecture=Structured set of Sub-system Interfaces.We specify an abstract model for interface definition languages (IDLs) based on this idea and the idea that anInterface=Name+Imports+Body.A set of interfaces is a repository. An interface architecture is a repository with some primary interfaces identified; the import dependencies between the interfaces of a repository are used to determine its structure. The abstract model uses algebraic specifications to define the abstract syntax of a general IDL, and interface transformations using structural induction. We examine a flattening process which assembles a system interface from its components. We use the general model to derive a simple IDL suitable for the design phase of object-oriented software development. This requires us to specify a form of Body that treats both data types and state, and in Body we explicitly distinguish between methods with and without side-effects, by commands and queries, respectively. We also consider alternative proposals for Body that yield new IDLs, including other object-oriented design languages and data type specification languages.