Modular algebraic specifications

Abstract

Module, import, export and detail hiding are well-known notions in software engineering. If algebraic specifications together with their operational semantics of term rewriting should be useful as a programming language, similar concepts must be developed to cope with very large specifications. Especially the concept of detail hiding is important, since many problems and their efficient solutions require hidden sorts or hidden functions.

In this paper we discuss a module concept for algebraic specifications. A module consists of an algebraic specification, the body specification, together with import and export specifications. The semantics is given by a free functor from the class of import algebras to the class of body algebras followed by a subalgebra restriction according to the export signature. A module is correct, if its semantics does not change the reexport part of any import algebra. The reexport specification is the common part of import and export specifications. This requirement is much weaker than the requirements for module correctness we find in other approaches, e.g. in [EW

This makes module specifications more suitable for software engineering purposes. For instance there is no need for explicit error handling in the body specification if the export restricts data to non-error data only. The example of a specification of a process scheduler demonstrates the usefulness of this concept. On the other hand, theoretic results concerning correctness of the semantics can be carried over to the new module concept. In this paper, we show that some basic constructions on modules preserve correctness and that the composition of correct modules yields a correct module.