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.

References

[1]

Hofmann, M., Jost, S.: Static Prediction of Heap Space Usage for First-Order Functional Programs. In: 30th ACM Symp. on Principles of Prog. Langs. (POPL 2003), pp. 185-197 (2003).

Digital Library

[2]

Tarjan, R.E.: Amortized Computational Complexity. SIAM J. Algebraic Discrete Methods 6(2), 306-318 (1985).

Digital Library

[3]

Hofmann, M., Jost, S.: Type-Based Amortised Heap-Space Analysis. In: Sestoft, P. (ed.) ESOP 2006. LNCS, vol. 3924, pp. 22-37. Springer, Heidelberg (2006).

Digital Library

[4]

Hofmann, M., Rodriguez, D.: Efficient Type-Checking for Amortised Heap-Space Analysis. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 317-331. Springer, Heidelberg (2009).

Digital Library

[5]

Jost, S., Loidl, H.W., Hammond, K., Scaife, N., Hofmann, M.: Carbon Credits for Resource-Bounded Computations using Amortised Analysis. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 354-369. Springer, Heidelberg (2009).

Digital Library

[6]

Campbell, B.: Amortised Memory Analysis using the Depth of Data Structures. In: Castagna, G. (ed.) ESOP 2009. LNCS, vol. 5502, pp. 190-204. Springer, Heidelberg (2009).

Digital Library

[7]

Jost, S., Hammond, K., Loidl, H.W., Hofmann, M.: Static Determination of Quantitative Resource Usage for Higher-Order Programs. In: 37th ACM Symp. on Principles of Prog. Langs. (POPL 2010), pp. 223-236 (2010).

Digital Library

[8]

Atkey, R.: Amortised Resource Analysis with Separation Logic. In: Gordon, A.D. (ed.) Programming Languages and Systems. LNCS, vol. 6012, pp. 85-103. Springer, Heidelberg (2010).

Digital Library

[9]

Hoffmann, J., Hofmann, M.: Amortized Resource Analysis with Polynomial Potential. In: Gordon, A.D. (ed.) Programming Languages and Systems. LNCS, vol. 6012, pp. 287-306. Springer, Heidelberg (2010).

Digital Library

[10]

Cousot, P., Cousot, R.: Inductive Definitions, Semantics and Abstract Interpretations. In: 19th ACM Symp. on Principles of Prog. Langs. (POPL 1992), pp. 83-94 (1992).

Digital Library

[11]

Leroy, X.: Coinductive Big-Step Operational Semantics. In: Sestoft, P. (ed.) ESOP 2006. LNCS, vol. 3924, pp. 54-68. Springer, Heidelberg (2006).

Digital Library

[12]

Grobauer, B.: Cost Recurrences for DML Programs. In: 6th Intl. Conf. on Funct. Prog. (ICFP 2001), pp. 253-264 (2001).

Digital Library

[13]

Flajolet, P., Salvy, B., Zimmermann, P.: Automatic Average-case Analysis of Algorithms. Theoret. Comput. Sci. 79(1), 37-109 (1991).

Digital Library

[14]

Crary, K., Weirich, S.: Resource Bound Certification. In: 27th ACM Symp. on Principles of Prog. Langs. (POPL 2000), pp. 184-198 (2000).

Digital Library

[15]

Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost Analysis of Java Bytecode. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 157-172. Springer, Heidelberg (2007).

Digital Library

[16]

Albert, E., Arenas, P., Genaim, S., Puebla, G.: Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 221-237. Springer, Heidelberg (2008).

Digital Library

[17]

Benzinger, R.: Automated Higher-Order Complexity Analysis. Theor. Comput. Sci. 318(1- 2), 79-103 (2004).

Digital Library

[18]

Gulwani, S., Mehra, K.K., Chilimbi, T.M.: SPEED: Precise and Efficient Static Estimation of Program Computational Complexity. In: 36th ACM Symp. on Principles of Prog. Langs. (POPL 2009), pp. 127-139 (2009).

Digital Library

[19]

Gulavani, B.S., Gulwani, S.: A Numerical Abstract Domain Based on Expression Abstraction and Max Operator with Application in Timing Analysis. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 370-384. Springer, Heidelberg (2008).

Digital Library

[20]

Gulwani, S., Zuleger, F.: The Reachability-Bound Problem. In: Conf. on Prog. Lang. Design and Impl. (PLDI 2010), pp. 292-304 (2010).

Digital Library

[21]

Beringer, L., Hofmann, M., Momigliano, A., Shkaravska, O.: Automatic Certification of Heap Consumption. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 347-362. Springer, Heidelberg (2005).

[22]

Hughes, J., Pareto, L., Sabry, A.: Proving the Correctness of Reactive Systems Using Sized Types. In: Symp. Princ. of Prog. Langs. (POPL 1996), pp. 410-423 (1996).

Digital Library

[23]

Hughes, J., Pareto, L.: Recursion and Dynamic Data-structures in Bounded Space: Towards Embedded ML Programming. In: 4th Intl. Conf. on Funct. Prog. (ICFP 1999), pp. 70-81 (1999).

Digital Library

[24]

Chin, W.N., Khoo, S.C.: Calculating Sized Types. High.-Ord. and Symb. Comp. High.-Ord. and Symb. Comp. 14(2-3), 261-300 (2001).

Digital Library

[25]

Shkaravska, O., van Kesteren, R., van Eekelen, M.C.: Polynomial Size Analysis of First-Order Functions. In: Della Rocca, S.R. (ed.) TLCA 2007. LNCS, vol. 4583, pp. 351-365. Springer, Heidelberg (2007).

Digital Library

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

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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
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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
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