Arrays and References in Resource Aware ML

This article introduces a technique to accurately perform static prediction of resource usage for ML-like functional programs with references and arrays. Previous research successfully integrated the potential method of amortized analysis with a standard type system to automatically derive parametric resources bounds. Due to its type-based nature, the analysis is naturally compositional and the resource consumption of functions can be abstracted using potential-annotated types. The soundness theorem of the analysis guarantees that type derivations prove that the derived bounds are correct with respect to the resource usage defined by a cost semantics. Type inference can be efficiently automated using off-the-shelf LP solvers, even if the derived bounds are polynomials. However, side effects and aliasing of heap references make it notoriously difficult to derive bounds that depend on mutable structures, such as arrays and references. As a result, existing automatic amortized analysis systems cannot derive bounds for programs whose resource consumption is dependent on data in such structures. This article extends the potential method to handle mutable structures with minimal changes to the type rules while preserving the stated advantages of amortized analysis. To do so, we introduce the notion of a reference collection, which gathers all unique locations pointed to by a reference in a given program. Apart from the design of the system, the main contribution is the proof of the soundness of the extended analysis system.