Semantics as a Tool of Thought: Provenance-Aware Dimensional Checking in a Reactive Array IR
This program is tentative and subject to change.
Array language runtimes discard semantic metadata at the evaluation boundary. A Reynolds number and a Courant number are indistinguishable buffers to the runtime; torque and energy, both carrying dimension M L² T⁻², are equally anonymous. Dimensional analysis confirms their structure; it cannot confirm their meaning.
We present the Three-Graph Reactive Unit Array IR, which extends Iverson’s subordination principle to semantic provenance. The authoring surface is a computational pidgin: users write in noun phrases — reynolds number, population density, courant number — which are interned to canonical integer token IDs at the parse boundary. Strings do not re-enter the computational core. Three co-indexed flat arrays — Concept Graph, Data Graph, Computation Graph — share this integer namespace. Four static judgments are checked at materialization time, before any kernel executes: dimensional compatibility, provenance matching for formation history, shape and broadcast compatibility, and mutability rebind. Dimensionless quantities are distinguished by the physical measurements and operations that produced them, not by name; a user-defined ratio with the Reynolds formation receives the Reynolds kind ID automatically.
The IR executes in the browser within a 5ms per-frame budget, providing immediate edit-to-feedback response at 60fps. A 26-case judgment suite validates all four judgment forms; median reconstitution times of 0.003–0.018ms confirm the semantic checks consume a small fraction of the budget, leaving the remainder for rendering and application logic.
This program is tentative and subject to change.
Tue 16 JunDisplayed time zone: Mountain Time (US & Canada) change
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