The Semantics of Shared Submodules Specifications

After reviewing the concept of module specification with import and export interfaces introduced by H. Ehrig for the modular development of software systems, precise definitions of submodule and union of modules specifications are given along with some basic results on their compatibility and semantics. The notion of amalgamated sum is used for the semantics of unions of modules and some connections are made with parametrized specifications. The results are restricted to the basic algebraic case.