We present a dimensional type system whose annotations remain available through the stages that require them, allowing numeric representation and deterministic memory management to be resolved within a single Program Semantic Graph (PSG). Based on Andrew Kennedy's Units of Measure, dimensions constrain admissible operations and the application of domain laws, forming our Native Type Universe (NTU). Range analysis combines those constraints with values, guards, and declared boundaries. A covering representation then determines word width and memory footprint, which participate in allocation and transfer decisions alongside lifetime and target constraints. Our Dimensional Type System (DTS) extends Hindley-Milner inference with abelian-group unification. Within that algebraic fragment, inference is decidable and admits principal types. Measures form part of source-level type identity, while numeric width and storage layout are coeffects resolved from context. A known range that exceeds every available representation produces an error at representation commitment. During program elaboration, unresolved facts can remain pending while further context is supplied. Deterministic Memory Management (DMM) uses the same graph to relate escape paths to storage lifetimes. Closure capture, return, and by-reference use supply different lifetime requirements. Allocation follows the lifetime classification and the platform's declared storage capabilities. Our unique implementation of a posit quire illustrates the interaction: exact accumulation requires a suitable numeric format, adequate capacity, and storage that persists across the accumulation. We also examine how these constraints would apply to automatic differentiation. A shared graph would allow language services to present dimensional resolution and proof status alongside the reasons for representation and placement decisions.

翻译：暂无翻译