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A Programming Paradigm for Spatiotemporal Composability

Read the paper (PDF) · Draft of August 13, 2026

This is a preprint under active revision. The content may change substantially; please cite the latest version and check back before relying on specific results.

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.<br>We address the two dimensions by lifting classical effect and coeffect concepts to runtime mechanisms.<br>In particular, we formalize revertible effects, in which every context transformation carries an inverse that the runtime tracks.<br>We formalize reactive coeffects, in which each change of the context notifies a component against its coeffect specification.<br>We unify the effect context and the coeffect context into a single context type, which constitutes a programming paradigm.<br>After that, we combine these mechanisms into the notion of a component and give a calculus of dynamic composition, whose metatheory carries spatiotemporal composability from a single component to a whole system of interleaved components.<br>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.

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