Cost Analysis Using Automatic Size and Time Inference

Abstract

Cost information can be exploited in a variety of contexts, including parallelizing compilers, autonomic GRIDs and real-time systems. In this paper, we introduce a novel type and effect system — the sized time system that is capable of determining upper bounds for both time and space costs, and which we initially intend to apply to determining good granularity for parallel tasks. The analysis is defined for a simple, strict, higher-order and polymorphic functional language, $\mathcal{L}$ , incorporating arbitrarily-sized list data structures. The inference algorithm implementing this analysis constructs cost- and size-terms for $\mathcal{L}$-expressions, plus constraints over free size and cost variables in those terms that can be solved to produce information for higher-order functions. The paper presents both the analysis and the inference algorithm, providing examples that illustrate the primary features of the analysis.