Executing Specifications Using Synthesis and Constraint Solving

  • Viktor Kuncak
  • Etienne Kneuss
  • Philippe Suter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8174)

Abstract

Specifications are key to improving software reliability as well as documenting precisely the intended behavior of software. Writing specifications is still perceived as expensive. Of course, writing implementations is at least as expensive, but is hardly questioned because there is currently no real alternative. Our goal is to give specifications a more balanced role compared to implementations, enabling the developers to compile, execute, optimize, and verify against each other mixed code fragments containing both specifications and implementations. To make specification constructs executable we combine deductive synthesis with run-time constraint solving, in both cases leveraging modern SMT solvers. Our tool decomposes specifications into simpler fragments using a cost-driven deductive synthesis framework. It compiles as many fragments as possible into conventional functional code; it executes the remaining fragments by invoking our constraint solver that extends an SMT solver to handle recursive functions. Using this approach we were able to execute constraints that describe the desired properties of integers, sets, maps and algebraic data types.

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References

  1. 1.
    Ait-Kaci, H.: Warren’s Abstract Machine: A Tutorial Reconstruction. MIT Press (1991)Google Scholar
  2. 2.
    Antoy, S.: Definitional trees. In: ALP, pp. 143–157 (1992)Google Scholar
  3. 3.
    Antoy, S., Hanus, M.: Functional logic programming. CACM 53(4), 74–85 (2010)CrossRefGoogle Scholar
  4. 4.
    Asarin, E., Maler, O., Pnueli, A.: Symbolic controller synthesis for discrete and timed systems. In: Hybrid Systems II, pp. 1–20 (1995)Google Scholar
  5. 5.
    Back, R.-J., von Wright, J.: In: Refinement Calculus, Springer (1998)Google Scholar
  6. 6.
    Barnett, M., Chang, B.-Y.E., DeLine, R., Jacobs, B., Leino, K.R.M.: Boogie: A modular reusable verifier for object-oriented programs. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2005. LNCS, vol. 4111, pp. 364–387. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Advances in Computers 58 (2003)Google Scholar
  8. 8.
    Bierman, G.M., Gordon, A.D., Hritcu, C., Langworthy, D.E.: Semantic subtyping with an SMT solver. In: ICFP, pp. 105–116 (2010)Google Scholar
  9. 9.
    Blanc, R.W., Kneuss, E., Kuncak, V., Suter, P.: An overview of the Leon verification system: Verification by translation to recursive functions. In: Scala Workshop (2013)Google Scholar
  10. 10.
    Bodden, E., Lam, P., Hendren, L.J.: Partially evaluating finite-state runtime monitors ahead of time. ACM Trans. Program. Lang. Syst. 34(2), 7 (2012)CrossRefGoogle Scholar
  11. 11.
    Braßel, B., Hanus, M., Müller, M.: High-level database programming in Curry. In: Hudak, P., Warren, D.S. (eds.) PADL 2008. LNCS, vol. 4902, pp. 316–332. Springer, Heidelberg (2008)Google Scholar
  12. 12.
    Bruynooghe, M., Schreye, D.D., Krekels, B.: Compiling control. The Journal of Logic Programming 6(12), 135–162 (1989)CrossRefMATHGoogle Scholar
  13. 13.
    Butler, M., Grundy, J., Langbacka, T., Ruksenas, R., von Wright, J.: The refinement calculator: Proof support for program refinement. In: Formal Methods Pacific (1997)Google Scholar
  14. 14.
    Chen, W., Warren, D.S.: Tabled evaluation with delaying for general logic programs. J. ACM 43(1), 20–74 (1996)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press and McGraw-Hill (2001)Google Scholar
  16. 16.
    de Moura, L., Bjørner, N.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    de Moura, L., Bjørner, N.: Generalized, efficient array decision procedures. In: Formal Methods in Computer-Aided Design (November 2009)Google Scholar
  18. 18.
    Demsky, B., Rinard, M.C.: Automatic detection and repair of errors in data structures. In: OOPSLA, pp. 78–95 (2003)Google Scholar
  19. 19.
    Demsky, B., Rinard, M.C.: Data structure repair using goal-directed reasoning. In: ICSE, pp. 176–185 (2005)Google Scholar
  20. 20.
    Dutertre, B., de Moura, L.: The Yices SMT solver (2006), http://yices.csl.sri.com/tool-paper.pdf
  21. 21.
    Elkarablieh, B., Khurshid, S.: Juzi: a tool for repairing complex data structures. In: ICSE, pp. 855–858 (2008)Google Scholar
  22. 22.
    Elkarablieh, B., Khurshid, S., Vu, D., McKinley, K.S.: Starc: static analysis for efficient repair of complex data. In: OOPSLA, pp. 387–404 (2007)Google Scholar
  23. 23.
    von Essen, C., Jobstmann, B.: Program repair without regret. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 896–911. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  24. 24.
    Flener, P., Partridge, D.: Inductive programming. Autom. Softw. Eng. 8(2), 131–137 (2001)CrossRefGoogle Scholar
  25. 25.
    Gallagher, J., Peralta, J.: Regular tree languages as an abstract domain in program specialisation. Higher-Order and Symbolic Computation 14(2-3), 143–172 (2001)CrossRefMATHGoogle Scholar
  26. 26.
    Gligoric, M., Gvero, T., Jagannath, V., Khurshid, S., Kuncak, V., Marinov, D.: Test generation through programming in UDITA. In: International Conference on Software Engineering (ICSE) (2010)Google Scholar
  27. 27.
    Gulwani, S., Jha, S., Tiwari, A., Venkatesan, R.: Synthesis of loop-free programs. In: PLDI, pp. 62–73 (2011)Google Scholar
  28. 28.
    Hanus, M.: Type-oriented construction of web user interfaces. In: PPDP, pp. 27–38 (2006)Google Scholar
  29. 29.
    Hanus, M., Kluß, C.: Declarative programming of user interfaces. In: Gill, A., Swift, T. (eds.) PADL 2009. LNCS, vol. 5418, pp. 16–30. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  30. 30.
    Hofmann, M.: IgorII - an analytical inductive functional programming system (tool demo). In: PEPM, pp. 29–32 (2010)Google Scholar
  31. 31.
    Jackson, D.: Alloy: a lightweight object modelling notation. ACM Trans. Softw. Eng. Methodol. 11(2), 256–290 (2002)CrossRefGoogle Scholar
  32. 32.
    Jacobs, S., Kuncak, V., Suter, P.: Reductions for synthesis procedures. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 88–107. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  33. 33.
    Jobstmann, B., Bloem, R.: Optimizations for LTL synthesis. In: FMCAD (2006)Google Scholar
  34. 34.
    Jobstmann, B., Galler, S., Weiglhofer, M., Bloem, R.: Anzu: A tool for property synthesis. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 258–262. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  35. 35.
    Kahsai, T., Tinelli, C.: PKIND: A parallel k-induction based model checker. In: 10th Int. Workshop Parallel and Distributed Methods in verifiCation, PDMC 2011 (2011)Google Scholar
  36. 36.
    Kitzelmann, E., Schmid, U.: Inductive synthesis of functional programs: An explanation based generalization approach. JMLR 7, 429–454 (2006)MathSciNetMATHGoogle Scholar
  37. 37.
    Kneuss, E., Kuncak, V., Kuraj, I., Suter, P.: On integrating deductive synthesis and verification systems. Technical Report EPFL-REPORT-186043, EPFL (2013)Google Scholar
  38. 38.
    Köksal, A.S., Kuncak, V., Suter, P.: Scala to the power of Z3: Integrating SMT and programming. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 400–406. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  39. 39.
    Köksal, A., Kuncak, V., Suter, P.: Constraints as control. In: ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL (2012)Google Scholar
  40. 40.
    Kuncak, V., Mayer, M., Piskac, R., Suter, P.: Complete functional synthesis. In: ACM SIGPLAN Conf. Programming Language Design and Implementation, PLDI (2010)Google Scholar
  41. 41.
    Kuncak, V., Mayer, M., Piskac, R., Suter, P.: Functional synthesis for linear arithmetic and sets. Software Tools for Technology Transfer (STTT), TBD (TBD) (2012)Google Scholar
  42. 42.
    Kuncak, V., Mayer, M., Piskac, R., Suter, P.: Software synthesis procedures. Communications of the ACM (2012)Google Scholar
  43. 43.
    Leino, K.R.M.: This is Boogie 2. Manuscript KRML 178, working draft (June 24, 2008)Google Scholar
  44. 44.
    Malik, M.Z., Siddiqui, J.H., Khurshid, S.: Constraint-based program debugging using data structure repair. ICST, 190–199 (2011)Google Scholar
  45. 45.
    Manna, Z., Waldinger, R.: A deductive approach to program synthesis. ACM Trans. Program. Lang. Syst. 2(1), 90–121 (1980)CrossRefMATHGoogle Scholar
  46. 46.
    Manna, Z., Waldinger, R.J.: Toward automatic program synthesis. Commun. ACM 14(3), 151–165 (1971)CrossRefMATHGoogle Scholar
  47. 47.
    Michael Hanus, E.: Curry: An integrated functional logic language vers. 0.8.2 (2006), http://www.curry-language.org
  48. 48.
    Milicevic, A., Rayside, D., Yessenov, K., Jackson, D.: Unifying execution of imperative and declarative code. In: ICSE, pp. 511–520 (2011)Google Scholar
  49. 49.
    Muggleton, S., Raedt, L.D.: Inductive logic programming: Theory and methods. J. Log. Program. 19(20), 629–679 (1994)CrossRefGoogle Scholar
  50. 50.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  51. 51.
    Odersky, M.: Contracts for Scala. In: Barringer, H., et al. (eds.) RV 2010. LNCS, vol. 6418, pp. 51–57. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  52. 52.
    Okasaki, C.: Purely Functional Data Structures. Cambridge University Press (1998)Google Scholar
  53. 53.
    Pei, Y., Wei, Y., Furia, C.A., Nordio, M., Meyer, B.: Evidence-based automated program fixing. CoRR, abs/1102.1059 (2011)Google Scholar
  54. 54.
    Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of reactive(1) designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364–380. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  55. 55.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL 1989: Proceedings of the 16th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 179–190. ACM, New York (1989)CrossRefGoogle Scholar
  56. 56.
    Polikarpova, N., Furia, C.A., West, S.: To run what no one has run before. In: Int. Conf. Runtime Verification (2013)Google Scholar
  57. 57.
    Samimi, H., Aung, E.D., Millstein, T.: Falling back on executable specifications. In: D’Hondt, T. (ed.) ECOOP 2010. LNCS, vol. 6183, pp. 552–576. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  58. 58.
    Schrijvers, T., Stuckey, P.J., Wadler, P.: Monadic constraint programming. J. Funct. Program. 19(6), 663–697 (2009)MathSciNetCrossRefMATHGoogle Scholar
  59. 59.
    Senni, V., Fioravanti, F.: Generation of test data structures using constraint logic programming. In: Brucker, A.D., Julliand, J. (eds.) TAP 2012. LNCS, vol. 7305, pp. 115–131. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  60. 60.
    Singh, R., Gulwani, S.: Synthesizing number transformations from input-output examples. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 634–651. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  61. 61.
    Smith, D.R.: Generating programs plus proofs by refinement. In: Meyer, B., Woodcock, J. (eds.) VSTTE 2005. LNCS, vol. 4171, pp. 182–188. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  62. 62.
    Solar-Lezama, A., Arnold, G., Tancau, L., Bodík, R., Saraswat, V.A., Seshia, S.A.: Sketching stencils. In: PLDI, pp. 167–178 (2007)Google Scholar
  63. 63.
    Solar-Lezama, A., Jones, C.G., Bodík, R.: Sketching concurrent data structures. In: PLDI (2008)Google Scholar
  64. 64.
    Solar-Lezama, A., Tancau, L., Bodík, R., Seshia, S.A., Saraswat, V.A.: Combinatorial sketching for finite programs. In: ASPLOS (2006)Google Scholar
  65. 65.
    Srivastava, S., Gulwani, S., Foster, J.: From program verification to program synthesis. In: POPL (2010)Google Scholar
  66. 66.
    Summers, P.D.: A methodology for LISP program construction from examples. JACM 24(1), 161–175 (1977)MathSciNetCrossRefMATHGoogle Scholar
  67. 67.
    Suter, P.: Programming with Specifications. PhD thesis, EPFL (December 2012)Google Scholar
  68. 68.
    Suter, P., Dotta, M., Kuncak, V.: Decision procedures for algebraic data types with abstractions. In: ACM POPL (2010)Google Scholar
  69. 69.
    Suter, P., Köksal, A.S., Kuncak, V.: Satisfiability modulo recursive programs. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 298–315. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  70. 70.
    Torlak, E., Jackson, D.: Kodkod: A relational model finder. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 632–647. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  71. 71.
    Udupa, A., Raghavan, A., Deshmukh, J., Mador-Haim, S., Martin, M., Alur, R.: Transit: Specifying protocols with concolic snippets. In: ACM Conference on Programming Language Design and Implementation (2013)Google Scholar
  72. 72.
    Van Roy, P.: Logic programming in Oz with Mozart. In: ICLP (1999)Google Scholar
  73. 73.
    Vechev, M., Yahav, E., Yorsh, G.: Inferring synchronization under limited observability. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 139–154. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  74. 74.
    Wei, Y., Furia, C.A., Kazmin, N., Meyer, B.: Inferring better contracts. In: ICSE (2011)Google Scholar
  75. 75.
    Wei, Y., Pei, Y., Furia, C.A., Silva, L.S., Buchholz, S., Meyer, B., Zeller, A.: Automated fixing of programs with contracts. In: Proceedings of the 19th International Symposium on Software Testing and Analysis, ISSTA 2010, pp. 61–72 (2010)Google Scholar
  76. 76.
    Wirth, N.: Program development by stepwise refinement. Commun. ACM 26(1), 70–74 (1983) (reprint)Google Scholar
  77. 77.
    Nokhbeh Zaeem, R., Khurshid, S.: Contract-based data structure repair using alloy. In: D’Hondt, T. (ed.) ECOOP 2010. LNCS, vol. 6183, pp. 577–598. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  78. 78.
    Zaeem, R.N., Malik, M.Z., Khurshid, S.: Repair abstractions for more efficient data structure repair. In: Int. Conf. Runtime Verification (2013)Google Scholar
  79. 79.
    Zee, K., Kuncak, V., Taylor, M., Rinard, M.: Runtime checking for program verification. In: Sokolsky, O., Taşıran, S. (eds.) RV 2007. LNCS, vol. 4839, pp. 202–213. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Viktor Kuncak
    • 1
  • Etienne Kneuss
    • 1
  • Philippe Suter
    • 1
    • 2
  1. 1.École Polytechnique Fédérale de Lausanne (EPFL)Switzerland
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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