Component algebra

Abstract

An axiomatic algebraic calculus of components is given that is based on the operators combination, hiding and taking the visible interfaces. The theory model of this component algebra is constructed and discussed. Several variations of the component algebra are investigated, each corresponding to a different approach for dealing with name clashes. The work is closely related to the module algebra of Bergstra, Heering and Klint but signatures are handled in a way similar to modern component interfaces. This has the effect that both provides and requires interfaces are explicitly manipulated. The paper investigates whether the same algebraic laws as module algebra can be made true, in particular the idempotency, associativity and commutativity of combination ($\text{+}$). Of course, distributivity of hiding over combination, $\text{p}\text{□}\text{(X+Y)=(p}\text{□}\text{X)+(p}\text{□}\text{Y)}$, does not hold in general (here $\text{p}$ is a so-called portfolio, a generalisation of the concept of signature). It is investigated, however, whether a conditional version can be made true, similar to the conditional law E4 of Bergstra, Heering and Klint.