Article

Symbolic Resource Bound Inference for Functional Programs

Authors:

Ravichandhran Madhavan,

Viktor KuncakAuthors Info & Claims

Proceedings of the 16th International Conference on Computer Aided Verification - Volume 8559

Pages 762 - 778

https://doi.org/10.1007/978-3-319-08867-9_51

Published: 18 July 2014 Publication History

Abstract

We present an approach for inferring symbolic resource bounds for purely functional programs consisting of recursive functions, algebraic data types and nonlinear arithmetic operations. In our approach, the developer specifies the desired shape of the bound as a program expression containing numerical holes which we refer to as templates . For e.g, time ≤ a '—ï height(tree) + b where a , b are unknowns, is a template that specifies a bound on the execution time. We present a scalable algorithm for computing tight bounds for sequential and parallel execution times by solving for the unknowns in the template. We empirically evaluate our approach on several benchmarks that manipulate complex data structures such as binomial heap, lefitist heap, red-black tree and AVL tree. Our implementation is able to infer hard, nonlinear symbolic time bounds for our benchmarks that are beyond the capability of the existing approaches.

References

[1]

Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost analysis of object-oriented bytecode programs. Theor. Comput. Sci.ä413(1), 142—159 (2012)

Digital Library

[2]

Beyene, T.A., Popeea, C., Rybalchenko, A.: Solving existentially quantified horn clauses. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol.ä8044, pp. 869—882. Springer, Heidelberg (2013)

Digital Library

[3]

Beyer, D., Henzinger, T.A., Majumdar, R., Rybalchenko, A.: Invariant synthesis for combined theories. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol.ä4349, pp. 378—394. Springer, Heidelberg (2007)

Digital Library

[4]

Beyer, D., Henzinger, T.A., Majumdar, R., Rybalchenko, A.: Path invariants. In: PLDI (2007)

Digital Library

[5]

Blanc, R.W., Kneuss, E., Kuncak, V., Suter, P.: An overview of the Leon verification system. In: Scala Workshop (2013)

Digital Library

[6]

Blelloch, G.E., Maggs, B.M.: Parallel algorithms. Communications of the ACMä39, 85—97 (1996)

Digital Library

[7]

Colón, M.A., Sankaranarayanan, S., Sipma, H.B.: Linear invariant generation using non-linear constraint solving. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol.ä2725, pp. 420—432. Springer, Heidelberg (2003)

[8]

Cook, B., Gupta, A., Magill, S., Rybalchenko, A., Simsa, J., Singh, S., Vafeiadis, V.: Finding heap-bounds for hardware synthesis. In: FMCAD (2009)

[9]

Cousot, P.: Proving program invariance and termination by parametric abstraction, lagrangian relaxation and semidefinite programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol.ä3385, pp. 1—24. Springer, Heidelberg (2005)

Digital Library

[10]

de Moura, L., BjØrner, N.S.: Z3: An efficient smt solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol.ä4963, pp. 337—340. Springer, Heidelberg (2008)

Digital Library

[11]

Grebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: PLDI (2012)

Digital Library

[12]

Guerraoui, R., Kuncak, V., Losa, G.: Speculative linearizability. In: PLDI (2012)

Digital Library

[13]

Gulwani, S., Jha, S., Tiwari, A., Venkatesan, R.: Synthesis of loop-free programs. In: PLDI (2011)

Digital Library

[14]

Gulwani, S., Mehra, K.K., Chilimbi, T.M.: Speed: Precise and efficient static estimation of program computational complexity. In: POPL (2009)

Digital Library

[15]

Gulwani, S., Srivastava, S., Venkatesan, R.: Program analysis as constraint solving. In: PLDI (2008)

Digital Library

[16]

Jacobs, S., Kuncak, V.: Towards complete reasoning about axiomatic specifications. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol.ä6538, pp. 278—293. Springer, Heidelberg (2011)

Digital Library

[17]

Kaufmann, M., Manolios, P., Moore, J.S. (eds.): Computer-Aided Reasoning: ACL2 Case Studies. Kluwer Academic Publishers (2000)

[18]

Kneuss, E., Kuraj, I., Kuncak, V., Suter, P.: Synthesis modulo recursive functions. In: OOPSLA (2013)

Digital Library

[19]

Leroy, X.: Formal verification of a realistic compiler. Commun. ACMä52(7), 107—115 (2009)

Digital Library

[20]

Madhavan, R., Kuncak, V.: Symbolic resource bound inference. Technical Report EPFL-REPORT-190578, EPFL (2014), http://infoscience.epfl.ch/record/190578

[21]

Makarios, T.J.M.: The independence of Tarski's Euclidean axiom. Archive of Formal Proofs, Formal proof development (October 2012), http://afp.sf.net/entries/Tarskis_Geometry.shtml,

[22]

Odersky, M., Spoon, L., Venners, B.: Programming in Scala: A comprehensive step-by-step guide. Artima Press (2008)

Digital Library

[23]

Oppen, D.C.: Elementary bounds for presburger arithmetic. In: Proceedings of the Fifth Annual ACM Symposium on Theory of Computing (1973)

Digital Library

[24]

Rybalchenko, A., Sofronie-Stokkermans, V.: Constraint solving for interpolation. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol.ä4349, pp. 346—362. Springer, Heidelberg (2007)

Digital Library

[25]

Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Non-linear loop invariant generation using gröbner bases. In: POPL (2004)

Digital Library

[26]

Solar-Lezama, A., Tancau, L., Bodík, R., Seshia, S.A., Saraswat, V.A.: Combinatorial sketching for finite programs. In: ASPLOS (2006)

Digital Library

[27]

Suter, P., Dotta, M., Kuncak, V.: Decision procedures for algebraic data types with abstractions. In: POPL (2010)

Digital Library

[28]

Suter, P., Köksal, A.S., Kuncak, V.: Satisfiability modulo recursive programs. In: Yahav, E. (ed.) SAS 2011. LNCS, vol.ä6887, pp. 298—315. Springer, Heidelberg (2011)

Digital Library

[29]

Yu, L.: A formal model of IEEE floating point arithmetic. Archive of Formal Proofs, Formal proof development (July 2013), http://afp.sf.net/entries/IEEE_Floating_Point.shtml

Cited By

Wang PWang DChlipala A(2017)TiML: a functional language for practical complexity analysis with invariantsProceedings of the ACM on Programming Languages10.1145/31339031:OOPSLA(1-26)Online publication date: 12-Oct-2017
https://dl.acm.org/doi/10.1145/3133903
Madhavan RKulal SKuncak V(2017)Contract-based resource verification for higher-order functions with memoizationACM SIGPLAN Notices10.1145/3093333.300987452:1(330-343)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009874
Madhavan RKulal SKuncak VCastagna GGordon A(2017)Contract-based resource verification for higher-order functions with memoizationProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009874(330-343)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3009837.3009874
Show More Cited By

Recommendations

Parametric heap usage analysis for functional programs
ISMM '09: Proceedings of the 2009 international symposium on Memory management

This paper presents an analysis that derives a formula describing the worst-case live heap space usage of programs in a functional language with automated memory management (garbage collection). First, the given program is automatically transformed into ...
Functional area lower bound and upper bound on multicomponent selection for interval scheduling

In a realistic register-transfer-level component library, there usually exist several different hardware implementations for one generic function. This gives rise to a large design space of component selection which is interleaved with the scheduling of ...
Incremental precision-preserving symbolic inference for probabilistic programs
PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

We present ISymb an incremental symbolic inference framework for probabilistic programs in situations when some loop-manipulated array data, upon which their probabilistic models are conditioned, undergoes small changes. To tackle the path explosion ...

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

Proceedings of the 16th International Conference on Computer Aided Verification - Volume 8559

July 2014

873 pages

ISBN:9783319088662

Editors:
Armin Biere
Johannes Kepler University Linz, Linz, Austria
,
Roderick Bloem
IAIK, Graz University of Technology, Graz, Austria

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 18 July 2014

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Wang PWang DChlipala A(2017)TiML: a functional language for practical complexity analysis with invariantsProceedings of the ACM on Programming Languages10.1145/31339031:OOPSLA(1-26)Online publication date: 12-Oct-2017
https://dl.acm.org/doi/10.1145/3133903
Madhavan RKulal SKuncak V(2017)Contract-based resource verification for higher-order functions with memoizationACM SIGPLAN Notices10.1145/3093333.300987452:1(330-343)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009874
Madhavan RKulal SKuncak VCastagna GGordon A(2017)Contract-based resource verification for higher-order functions with memoizationProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009874(330-343)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3009837.3009874
Reynolds AKuncak V(2015)Induction for SMT SolversProceedings of the 16th International Conference on Verification, Model Checking, and Abstract Interpretation - Volume 893110.1007/978-3-662-46081-8_5(80-98)Online publication date: 12-Jan-2015
https://dl.acm.org/doi/10.1007/978-3-662-46081-8_5

View Options

View options

Media

Figures

Other

Tables

View Table of Contents