Static determination of quantitative resource usage for higher-order programs

Abstract

We describe a new automatic static analysis for determining upper-bound functions on the use of quantitative resources for strict, higher-order, polymorphic, recursive programs dealing with possibly-aliased data. Our analysis is a variant of Tarjan's manual amortised cost analysis technique. We use a type-based approach, exploiting linearity to allow inference, and place a new emphasis on the number of references to a data object. The bounds we infer depend on the sizes of the various inputs to a program. They thus expose the impact of specific inputs on the overall cost behaviour.The key novel aspect of our work is that it deals directly with polymorphic higher-order functions without requiring source-level transformations that could alter resource usage. We thus obtain safe and accurate compile-time bounds. Our work is generic in that it deals with a variety of quantitative resources. We illustrate our approach with reference to dynamic memory allocations/deallocations, stack usage, and worst-case execution time, using metrics taken from a real implementation on a simple micro-controller platform that is used in safety-critical automotive applications.

A Type System for Complexity Flow Analysis

“…In particular, a static analysis based on our approach could be made by compiling a source program into an abstract program with respect to resource consumption. Here, we follow ideas suggested in [20] and [23]. Then, the complexity of a source program could be obtained from a type inference algorithms.…”

“…Jost, Hammond, Loidl & Hofmann [23] work on automatic amortized cost analysis using type systems, which is related to the study of non-size increasing systems. Hughes, Pareto & Sabry [24] propose sized types in order to determine bound on data structure sizes.…”

Denotational cost semantics for functional languages with inductive types

“…Jost et al [2010] describe a formalism that automatically infers linear resource bounds for higher-order programs, provided that the input program does in fact have a linear resource cost. Hoffmann and Hofmann [2010] and Hoffmann et al [2012] extend this work to handle polynomial bounds, though for first-order programs only, and Hoffmann and Shao [2015] extend it to parallel programs.…”

The reachability-bound problem

“…In contrast, we infer bounds. [22] uses linear programming to infer bounds for functional programs, but they are restricted to computing only linear bounds.…”