We consider the problem of modularizing control flow in a generic abstract interpretation framework. A generic abstract interpretation framework is not truly flexible if it does not allow interpreting with different path- and flow-sensitivities, by going forwards or backwards, and over- or under-approximately. Most interpreters inherently intertwine syntax and semantics, making the implementation antagonistic to modularity. Current approaches to modular designs require the use of complex data structures (e.g., monad transformers), providing modularity but often proving unwieldy (e.g., lifts). We observe that leveraging scoped effects within an interpreter facilitates the accumulation of semantic fragments against a fixed syntax. In this paper, we define cumulative abstract semantics, illustrating the potential for creating multiple dynamic evaluators and static analyses from one interpreter. This modularity is achieved by grouping effects into two categories: syntax elimination and domain-semantic introduction handlers. Our contribution shows the benefits of using effects as an instrument for designing a clean, elegant, and modular abstract interpretation framework.

翻译：我们探讨在通用抽象解释框架中模块化控制流的问题。若一个通用抽象解释框架无法通过前向或后向、过近似或欠近似的方式，以不同的路径敏感性和流敏感性进行解释，则其并非真正灵活。大多数解释器本质上将语法与语义交织在一起，导致实现与模块化相抵触。当前模块化设计的方法需要使用复杂的数据结构（例如单子变换器），虽提供了模块化但往往显得笨拙（例如提升操作）。我们观察到，在解释器中利用作用域效应有助于在固定语法下累积语义片段。本文定义了累积抽象语义，展示了从单一解释器创建多个动态求值器和静态分析的潜力。这种模块化通过将效应分为两类实现：语法消除处理器和领域语义引入处理器。我们的贡献展示了使用效应作为工具来设计清晰、优雅且模块化的抽象解释框架的优势。