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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].

paper (cordiverse/paper)

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Paper
What is this?This is an academic preprint (arXiv:2608.25512 [cs.PL]) that proposes a formal programming paradigm called the 'context paradigm' for building software that can dynamically add, remove, and interleave components (like plugins or self-evolving agent harnesses) without breaking each other.
Is this a research paper or something I can run as code?It is just the paper itself (text and citation info), not a runnable project. The ideas are implemented separately in a framework called Cordis.
Where do I actually read the paper?Read it on arXiv at the link in the README (arXiv:2608.25512); the arXiv version is kept up to date with the latest revisions.
Is the paper finished, or could the content still change?It is explicitly marked as a preprint under active revision, so details may change between versions; cite the arXiv version rather than this repo.
Who is this paper written for?Programming-language researchers and framework authors working on plugin systems, hot module replacement, or dynamic multi-component architectures (including AI agent harnesses) who need a rigorous model for safe composition.
What is Cordis?Cordis is the meta-framework that implements the paper's ideas in practice: a core library with effect tracking and coeffect resolution, plus a declarative component loader with configuration reconciliation and hot module replacement.
What are revertible effects?They are context transformations where the runtime keeps an inverse for every change a component makes, so removing the component can completely undo its side effects. This gives 'temporal composability' local to one component.
What are reactive coeffects?They are a mechanism where every context change is checked against a component's declared coeffect specification, automatically driving when that component activates or deactivates. This gives 'spatial composability' between components.
Why does this matter for AI agent harnesses?Self-evolving agent harnesses and plugin systems constantly add and remove capabilities at runtime; the paper's context paradigm gives a formal guarantee that these dynamic changes can be cleanly composed and reverted without components interfering with each other.
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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