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.

模式语言是许多领域中的一种普遍手段，可以以抽象的方式捕获重复出现的问题的经过验证的解决方案。为了提高可重用性，它们从特定技术或环境等实现细节中进行抽象。然而，虽然这种抽象提供了显着的好处，因为可以应用模式来解决一般问题的不同表现形式，但是当必须应用模式时，这也会导致耗时的工作，因为必须一遍又一遍地详细阐述和实现具体的解决方案。此外，由于模式旨在与其他模式结合应用，因此各个具体解决方案也必须聚合成一个整体解决方案。然而，这极大地增加了必要的专业知识、所需的努力和复杂性。因此，我们提出了一种系统方法，允许（i）重用和（ii）根据选定的模式序列组合已经开发的具体解决方案。我们建立了解代数理论，将具体解和聚合算子视为数学对象。因此，特定于领域的运算符允许组合和聚合模式的具体解决方案，我们在几个不同的领域中对其进行验证。