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A Programming Paradigm for Spatiotemporal Composability

Read the paper on arXiv · arXiv:2608.25512 [cs.PL]

This is a preprint under active revision. The arXiv page above always serves the latest version; please cite accordingly.

Abstract

Modern software—from plugin systems to self-evolving agent harnesses—increasingly requires dynamic composition, yet its formal foundations remain underdeveloped. We identify two orthogonal dimensions of the problem: temporal composability, the ability to completely revert a component's side effects upon removal, and spatial composability, the ability to declare and reactively manage inter-component dependencies. We address the two dimensions by lifting classical effect and coeffect concepts to runtime mechanisms. In particular, we formalize revertible effects, in which every context transformation carries an inverse that the runtime holds, establishing temporal composability local to one component. We formalize reactive coeffects, in which every context change is classified against a component's coeffect specification to drive its activation and deactivation, establishing spatial composability local to one component. We then unify the effect context and the coeffect context into a single context type and mediate every effect and coeffect through it, yielding a discipline we call the context paradigm; the mediation induces an observational equivalence up to which the effects of distinct components interleave without disturbing one another. Combining these mechanisms into the notion of a component, we give a calculus of dynamic composition whose metatheory carries spatiotemporal composability from a single component to a whole system of interleaved components. We implement these ideas in Cordis, a meta-framework of spatiotemporal composability that provides a core library with effect tracking and coeffect resolution, as well as a declarative component loader with configuration reconciliation and hot module replacement.

Citation

@misc{shi2026cordis,
  title         = {A Programming Paradigm for Spatiotemporal Composability},
  author        = {Shi, Yifan and Zhang, Wei and Cui, Tianyi},
  year          = {2026},
  eprint        = {2608.25512},
  archivePrefix = {arXiv},
  primaryClass  = {cs.PL},
  url           = {https://arxiv.org/abs/2608.25512},
}

Acknowledgments

We thank @TZZheng and @thwfhk for their feedback and corrections on earlier drafts of this paper.

Contact

Questions, comments, and corrections about the paper are welcome by email: [email protected].

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这是什么？这是一篇学术预印本（arXiv:2608.25512 [cs.PL]），提出了一种名为「上下文范式」的形式化编程范式，用于构建能动态添加、删除和交错组合组件（如插件或自演化的智能体框架）而互不破坏的软件。
这是一篇研究论文，还是能当代码运行的东西？它只是论文本身（正文和引用信息），不是可运行的项目。这些思想在另一个名为 Cordis 的框架中单独实现。
到底去哪里读这篇论文？通过 README 中的链接在 arXiv 上阅读（arXiv:2608.25512）；arXiv 版本会随最新修订持续更新。
论文已经定稿了吗，内容还可能变动吗？它被明确标注为仍在积极修订中的预印本，细节可能在版本间变动；引用时请引用 arXiv 版本而不是这个仓库。
这篇论文是为谁写的？面向从事插件系统、热模块替换或动态多组件架构（包括 AI 智能体框架）研究、需要安全组合的严格模型的编程语言研究者和框架作者。
Cordis 是什么？Cordis 是在实践中实现论文思想的元框架：一个带效应追踪和协效应解析的核心库，外加一个支持配置调和与热模块替换的声明式组件加载器。
什么是可回退效应（revertible effects）？这是一类上下文变换：运行时会为组件所做的每个改动保留一个逆操作，因此移除组件就能完全撤销其副作用。这为单个组件带来了「时间维度的可组合性」。
什么是响应式协效应（reactive coeffects）？这是一种机制：每次上下文变更都会对照组件声明的协效应规范进行检查，从而自动决定该组件何时激活或停用。这在组件之间实现了「空间维度的可组合性」。
这为什么对 AI 智能体框架很重要？自演化的智能体框架和插件系统会在运行时不断添加和移除能力；论文的上下文范式提供了形式化保证，使这些动态变更能够干净地组合与回退，组件之间互不干扰。
What are similar projects?context-language-models, dsh-explore, Attention-Residuals, Tiersense, KISS-Knowledge-Infrastructure-for-Scientific-Simulation, Deepgraph, MSA, XRAG
Which topics is it in?software-architecture, declarative, arxiv, paper, programming-language, academic, architecture, harness, plugin-system, computer-science, academic-research, agents
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