Article

Amortized resource analysis with polymorphic recursion and partial big-step operational semantics

Authors:

Martin HofmannAuthors Info & Claims

APLAS'10: Proceedings of the 8th Asian conference on Programming languages and systems

Pages 172 - 187

Published: 28 November 2010 Publication History

Abstract

This paper studies the problem of statically determining upper bounds on the resource consumption of first-order functional programs. A previous work approached the problem with an automatic type-based amortized analysis for polynomial resource bounds. The analysis is parametric in the resource and can be instantiated to heap space, stack space, or clock cycles. Experiments with a prototype implementation have shown that programs are analyzed efficiently and that the computed bounds exactly match the measured worst-case resource behavior for many functions. This paper describes the inference algorithm that is used in the implementation of the system. It can deal with resource-polymorphic recursion which is required in the type derivation of many functions. The computation of the bounds is fully automatic if a maximal degree of the polynomials is given. The soundness of the inference is proved with respect to a novel operational semantics for partial evaluations to show that the inferred bounds hold for terminating as well as non-terminating computations. A corollary is that run-time bounds also establish the termination of programs.

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Cited By

Wang PFu HGoharshady AChatterjee KQin XShi WMcKinley KFisher K(2019)Cost analysis of nondeterministic probabilistic programsProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314581(204-220)Online publication date: 8-Jun-2019
https://dl.acm.org/doi/10.1145/3314221.3314581
Wang DHoffmann J(2019)Type-guided worst-case input generationProceedings of the ACM on Programming Languages10.1145/32903263:POPL(1-30)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1145/3290326
Ngo VCarbonneaux QHoffmann J(2018)Bounded expectations: resource analysis for probabilistic programsACM SIGPLAN Notices10.1145/3296979.319239453:4(496-512)Online publication date: 11-Jun-2018
https://dl.acm.org/doi/10.1145/3296979.3192394
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Index Terms

Amortized resource analysis with polymorphic recursion and partial big-step operational semantics
1. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning
      1. Program analysis
    2. Program semantics

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Guide Proceedings

APLAS'10: Proceedings of the 8th Asian conference on Programming languages and systems

November 2010

456 pages

ISBN:364217163X

Editor:
Kazunori Ueda
Dept. of Computer Science and Engineering, Waseda University, Tokyo, Japan

Sponsors

AAFS: Asian Association for Foundation of Software
Shanghai Jiao Tong University: Shanghai Jiao Tong University

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 28 November 2010

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Cited By

Wang PFu HGoharshady AChatterjee KQin XShi WMcKinley KFisher K(2019)Cost analysis of nondeterministic probabilistic programsProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314581(204-220)Online publication date: 8-Jun-2019
https://dl.acm.org/doi/10.1145/3314221.3314581
Wang DHoffmann J(2019)Type-guided worst-case input generationProceedings of the ACM on Programming Languages10.1145/32903263:POPL(1-30)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1145/3290326
Ngo VCarbonneaux QHoffmann J(2018)Bounded expectations: resource analysis for probabilistic programsACM SIGPLAN Notices10.1145/3296979.319239453:4(496-512)Online publication date: 11-Jun-2018
https://dl.acm.org/doi/10.1145/3296979.3192394
Ngo VCarbonneaux QHoffmann JFoster JGrossman D(2018)Bounded expectations: resource analysis for probabilistic programsProceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3192366.3192394(496-512)Online publication date: 11-Jun-2018
https://dl.acm.org/doi/10.1145/3192366.3192394
Hoffmann JDas AWeng S(2017)Towards automatic resource bound analysis for OCamlACM SIGPLAN Notices10.1145/3093333.300984252:1(359-373)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009842
Hoffmann JDas AWeng SCastagna GGordon A(2017)Towards automatic resource bound analysis for OCamlProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009842(359-373)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3009837.3009842
Hoffmann JShao Z(2015)Automatic Static Cost Analysis for Parallel ProgramsProceedings of the 24th European Symposium on Programming on Programming Languages and Systems - Volume 903210.1007/978-3-662-46669-8_6(132-157)Online publication date: 11-Apr-2015
https://dl.acm.org/doi/10.1007/978-3-662-46669-8_6
Hoffmann JAehlig KHofmann M(2012)Multivariate amortized resource analysisACM Transactions on Programming Languages and Systems10.1145/2362389.236239334:3(1-62)Online publication date: 5-Nov-2012
https://dl.acm.org/doi/10.1145/2362389.2362393
Hoffmann JAehlig KHofmann M(2012)Resource aware MLProceedings of the 24th international conference on Computer Aided Verification10.1007/978-3-642-31424-7_64(781-786)Online publication date: 7-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31424-7_64
Hoffmann JAehlig KHofmann MBall TSagiv M(2011)Multivariate amortized resource analysisProceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages10.1145/1926385.1926427(357-370)Online publication date: 26-Jan-2011
https://dl.acm.org/doi/10.1145/1926385.1926427
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