Algebraic Constructions: A Simple Framework for Complex Dependencies and Parameterisation

We propose a simple framework of algebraic constructions for software specification, modular design and development. Algebraic constructions generalise (parameterised) modules by allowing on one hand a rather arbitrary collection of elements to form the parameter and on the other hand dependencies between the module elements to be spelled out explicitly. Algebraic constructions are specified in a very natural way by means of ordinary algebraic specifications. They are combined using a sum operation which captures as special cases various operations on (parameterised) modules offered by standard specification and development frameworks. We show the expected composability result for the sum of algebraic constructions and of their specifications.