When developing complex software and systems, contracts provide a means for controlling the complexity by dividing the responsibilities among the components of the system in a hierarchical fashion. In specific application areas, dedicated contract theories formalise the notion of contract and the operations on contracts in a manner that supports best the development of systems in that area. At the other end, contract meta-theories attempt to provide a systematic view on the various contract theories by axiomatising their desired properties. However, there exists a noticeable gap between the most well-known contract meta-theory of Benveniste et al., which focuses on the design of embedded and cyber-physical systems, and the established way of using contracts when developing general software, following Meyer's design-by-contract methodology. At the core of this gap appears to be the notion of procedure: while it is a central unit of composition in software development, the meta-theory does not suggest an obvious way of treating procedures as components. In this paper, we provide a first step towards a contract theory that takes procedures as the basic building block, and is at the same time an instantiation of the meta-theory. To this end, we propose an abstract contract theory for sequential programming languages with procedures, based on denotational semantics. We show that, on the one hand, the specification of contracts of procedures in Hoare logic, and their procedure-modular verification, can be cast naturally in the framework of our abstract contract theory. On the other hand, we also show our contract theory to fulfil the axioms of the meta-theory. In this way, we give further evidence for the utility of the meta-theory, and prepare the ground for combining our instantiation with other, already existing instantiations.

中文翻译：

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带程序的程序的抽象契约理论

在开发复杂的软件和系统时，合同提供了一种通过以分层方式在系统组件之间划分职责来控制复杂性的方法。在特定的应用领域中，专用的合同理论将合同和合同操作的概念形式化，以最好地支持该领域系统的开发。另一方面，契约元理论试图通过公理它们的期望属性来提供各种契约理论的系统观点。但是，在Benveniste等人的最著名的合同元理论（着重于嵌入式和网络物理系统的设计）与遵循Meyer的方法开发通用软件时使用合同的既定方式之间，存在明显的差距。合同设计方法。差距的核心似乎是过程的概念：尽管它是软件开发中组成的核心单元，但元理论并未提出将过程视为组件的明显方法。在本文中，我们提供了迈向合同理论的第一步，该合同理论以程序为基本构建块，同时也是元理论的实例化。为此，我们提出了一种基于指称语义的带有程序的顺序编程语言的抽象契约理论。我们证明，一方面，Hoare逻辑中的过程契约规范及其过程模块化验证可以自然地在我们抽象契约理论的框架内进行。另一方面，我们也展示了我们的契约理论来满足元理论的公理。通过这种方式，