Procedural Generalization: A Resource-Sensitive Account of Knowing-How

Standard learning theory usually treats generalization as a statement about error: a learned hypothesis is reliable if it returns correct predictions on fresh samples. This view is incomplete when the learned object is a procedure. A solver, planner, prover, or tool-using agent may return correct answers either because it has learned a reusable way of acting, or because it spends enough computation to compensate for not having one. This paper proposes an operational account of procedural knowledge in learned systems. A learned procedure embodies knowing-how when evidence from examples, search, or synthesis is compiled into reusable control over future computation. Runtime is then not merely an engineering metric. Holding correctness fixed, reduced computation is evidence that the learner inferred structure that makes future solving easier. We formalize this idea through runtime-aware learning and define procedural knowledge gain as correctness-preserving speedup from an uncompiled baseline procedure to a compiled learned procedure. A SAT-backdoor example illustrates the concept: correctness is supplied by a complete fallback solver, while knowing-how consists in learning which structural shortcut to compile. The result reframes generalization for learned procedures: they should not merely return correct outputs, but generalize as reusable ways of acting.