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Type-based amortized resource analysis with integers and arrays*

Published online by Cambridge University Press:  29 October 2015

JAN HOFFMANN
Affiliation:
Department of Computer Science, Yale University, 51 Prospect St., New Haven, CT 06511, USA (e-mail: jan.hoffmann@yale.edu, zhong.shao@yale.edu)
ZHONG SHAO
Affiliation:
Department of Computer Science, Yale University, 51 Prospect St., New Haven, CT 06511, USA (e-mail: jan.hoffmann@yale.edu, zhong.shao@yale.edu)
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Abstract

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Proving bounds on the resource consumption of a program by statically analyzing its source code is an important and well-studied problem. Automatic approaches for numeric programs with side effects usually apply abstract interpretation-based invariant generation to derive bounds on loops and recursion depths of function calls. This article presents an alternative approach to resource-bound analysis for numeric and heap-manipulating programs that uses type-based amortized resource analysis. As a first step towards the analysis of imperative code, the technique is developed for a first-order ML-like language with unsigned integers and arrays. The analysis automatically derives bounds that are multivariate polynomials in the numbers and the lengths of the arrays in the input. Experiments with example programs demonstrate two main advantages of amortized analysis over current abstract interpretation–based techniques. For one thing, amortized analysis can handle programs with non-linear intermediate values like f((n + m)2). For another thing, amortized analysis is compositional and works naturally for compound programs like f(g(x)).

Type
Articles
Copyright
Copyright © Cambridge University Press 2015 

Footnotes

*

This research is based on work supported in part by NSF grants 1319671 and 1065451, and DARPA grants FA8750-10-2-0254 and FA8750-12-2-0293. Any opinions, findings, and conclusions contained in this document are those of the authors and do not reflect the views of these agencies.

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