On the algebraic properties of concrete solution aggregation

Abstract

Pattern languages are a pervasive means in many domains to capture proven solutions for recurring problems in an abstract manner. To improve reusability, they abstract from implementation details such as specific technologies or environments. However, while this abstraction provides a significant benefit as patterns can be applied to solve different manifestations of the general problem, this also leads to time-consuming efforts when patterns have to be applied as concrete solutions have to be elaborated and implemented over and over again. Moreover, as patterns are intended to be applied in combination with other patterns, the individual concrete solutions have to be aggregated into an overall solution, too. However, this immensely increases necessary expertise, required effort, and complexity. Therefore, we present a systematic approach that allows to (i) reuse and (ii) combine already developed concrete solutions on the basis of selected sequences of patterns. We establish the theory of solution algebras, which perceive concrete solutions and aggregation operators as mathematical objects. Thereby, domain-specific operators allow to combine and aggregate concrete solutions of patterns, which we validate in several different domains.