Program–value separability: the structural precondition for compilation, caching, and dense journaling in a DSL runtime

This paper is an analytic theory contribution in the sense of Gregor's (2006) theory for analyzing (Type I): it introduces a structural construct — program-value separability — and the binary taxonomy it induces, states a necessary-condition claim about the runtime consequences that follow from it, and presents one realization in production as an existence proof that the construct is realizable — not the design-science evaluation of an artifact (Hevner, March, Park, a fourth, replication-bounded entropy, follows from the same precondition and is taken up in a companion paper. We characterize one concrete realization in a CQRS + Actor + Event Sourcing runtime — the same Puppeteer framework introduced in the prior paper of this series — and report empirical magnitudes from two independent open-source DDD aggregates (dotnet/eShop's Order and kgrzybek/modular-monolith's SubscriptionPayment): a compiled-versus-interpreted speedup that scales with DSL-bound work (roughly 1.5× to 3.1×); a cold compile cost amortized within several hundred invocations; and a journal that stored, on each of the two aggregates, about 99.8% of parametric entries as compact action references — 3.5× and 5.6× denser than the equivalent literal-script storage. The journal-density values are exact per-host counts and the speedups carry run-to-run variation; all are reported as illustrations of the structural property on the cases measured, not as estimates of its magnitude in general. The principle generalizes beyond any one runtime: program-value separability characterizes the structural condition any DSL runtime must satisfy to admit compilation, caching, and dense persistence at all.