论文标题
架构的数学语法
The Mathematical Syntax of Architectures
论文作者
论文摘要
尽管有几个（接受的）标准，但在信息技术或系统工程体系结构中通常采用的核心概念缺乏逻辑，代数和其他数学分支中遇到的精确和确切的基础。 在此贡献中，我们以数学上严格的方式定义了术语架构一词的句法方面。 We motivate our particular choice by demonstrating (i) how commonly understood and expected properties of an architecture -- as defined by various standards -- can be suitably identified or derived within our formalization, (ii) how our concept is fully compatible with real life (business) architectures, and (iii) how our definition complements recent foundational work in this area (Wilkinson 2018, Dickersen 2020, Efatmaneshnik 2020). 此外，我们基于同构的概念，形成了严格的建筑相似性概念，从而使架构类别被视为一个类别，Arch。我们通过得出对某些类型的体系结构的分类定理来证明我们的概念对理论的适用性。除此之外，我们得出了一个No Go定理，证明，与N层体系结构相比，一个人不能仅在句法层面上明智地定义通用的建筑模块。
Despite several (accepted) standards, core notions typically employed in information technology or system engineering architectures lack the precise and exact foundations encountered in logic, algebra, and other branches of mathematics. In this contribution we define the syntactical aspects of the term architecture in a mathematically rigorous way. We motivate our particular choice by demonstrating (i) how commonly understood and expected properties of an architecture -- as defined by various standards -- can be suitably identified or derived within our formalization, (ii) how our concept is fully compatible with real life (business) architectures, and (iii) how our definition complements recent foundational work in this area (Wilkinson 2018, Dickersen 2020, Efatmaneshnik 2020). We furthermore develop a rigorous notion of architectural similarity based on the notion of homomorphisms allowing the class of architectures to be regarded as a category, Arch. We demonstrate the applicability of our concepts to theory by deriving theorems on the classification of certain types of architectures. Inter alia, we derive a no go theorem proving that, in contrast to n-tier architectures, one cannot sensibly define generic architectural modularity on the syntactical level alone.
