Abstract
We introduce a new theory of algebraic datatypes where selector symbols can be shared between multiple constructors, thereby reducing the number of terms considered by current SMT-based solving approaches. We show that the satisfiability problem for the traditional theory of algebraic datatypes can be reduced to problems where selectors are mapped to shared symbols based on a transformation provided in this paper. The use of shared selectors addresses a key bottleneck for an SMT-based enumerative approach to the Syntax-Guided Synthesis (SyGuS) problem. Our experimental evaluation of an implementation of the new theory in the SMT solver cvc4 on syntax-guided synthesis and other domains provides evidence that the use of shared selectors improves state-of-the-art SMT-based approaches for constraints over algebraic datatypes.
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- 1.
The two references differ on how they make selectors (which are naturally partial functions) total. We follow the SMT-LIB 2 standard here.
- 2.
Such tests are effective by well-known results about the theory of equality [6].
- 3.
For a thorough description of this approach, see [24].
- 4.
The data and details on how to reproduce our results are available at https://cvc4.cs.stanford.edu/papers/IJCAR2018-shsel/.
References
Alur, R., Bodík, R., Juniwal, G., Martin, M.M.K., Raghothaman, M., Seshia, S.A., Singh, R., Solar-Lezama, A., Torlak, E., Udupa, A.: Syntax-guided synthesis. In: FMCAD, pp. 1–8. IEEE (2013)
Alur, R., Černý, P., Radhakrishna, A.: Synthesis through unification. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9207, pp. 163–179. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21668-3_10
Alur, R., Fisman, D., Singh, R., Solar-Lezama, A.: SyGuS-comp 2017: results and analysis. In: Fisman, D., Jacobs, S. (eds.) Proceedings Sixth Workshop on Synthesis (SYNT). EPTCS, vol. 260, pp. 97–115 (2017)
Alur, R., Fisman, D., Singh, R., Solar-Lezama, A.: SyGuS-comp 2017: Results and analysis. CoRR, abs/1711.11438 (2017)
Alur, R., Radhakrishna, A., Udupa, A.: Scaling enumerative program synthesis via divide and conquer. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 319–336. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_18
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, New York (1998)
Barrett, C., Conway, C.L., Deters, M., Hadarean, L., Jovanović, D., King, T., Reynolds, A., Tinelli, C.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171–177. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_14
Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB) (2016). www.SMT-LIB.org
Barrett, C., Fontaine, P., Tinelli, C.: The SMT-LIB Standard: Version 2.6. Technical report, Department of Computer Science, The University of Iowa (2017)
Barrett, C., Shikanian, I., Tinelli, C.: An abstract decision procedure for a theory of inductive data types. JSAT 3(1–2), 21–46 (2007)
Barrett, C., Tinelli, C.: Satisfiability modulo theories. In: Clarke, E., Henzinger, T., Veith, H., Bloem, R. (eds.) Handbook of Model Checking, pp. 305–343. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-10575-8_11
Blanc, R., Kuncak, V., Kneuss, E., Suter, P.: An overview of the Leon verification system: verification by translation to recursive functions. In: Proceedings of the 4th Workshop on Scala, pp. 1:1–1:10. ACM (2013)
Blanchette, J.C., Hölzl, J., Lochbihler, A., Panny, L., Popescu, A., Traytel, D.: Truly modular (co)datatypes for Isabelle/HOL. In: Klein, G., Gamboa, R. (eds.) ITP 2014. LNCS, vol. 8558, pp. 93–110. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08970-6_7
Böhme, S., Nipkow, T.: Sledgehammer: judgement day. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS (LNAI), vol. 6173, pp. 107–121. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14203-1_9
Cruanes, S.: Satisfiability modulo bounded checking. In: de Moura, L. (ed.) CADE 2017. LNCS (LNAI), vol. 10395, pp. 114–129. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63046-5_8
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). https://doi.org/10.1007/978-3-540-78800-3_24
Gulwani, S.: Automating string processing in spreadsheets using input-output examples. In: POPL, pp. 317–330. ACM (2011)
Gulwani, S.: Programming by examples: applications, algorithms, and ambiguity resolution. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 9–14. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40229-1_2
Kovács, L., Robillard, S., Voronkov, A.: Coming to terms with quantified reasoning. In: POPL, pp. 260–270. ACM (2017)
Leino, K.R.M.: Developing verified programs with Dafny. Ada Lett. 32(3), 9–10 (2012)
Nipkow, T., Wenzel, M., Paulson, L.C. (eds.): Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45949-9
Reynolds, A., Blanchette, J.C.: A decision procedure for (co)datatypes in SMT solvers. J. Autom. Reason. 58(3), 341–362 (2017)
Reynolds, A., Blanchette, J.C., Cruanes, S., Tinelli, C.: Model finding for recursive functions in SMT. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 133–151. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40229-1_10
Reynolds, A., Kuncak, V., Tinelli, C., Barrett, C., Deters, M.: Refutation-based synthesis in SMT. Form. Methods Syst. Des. (2017)
Reynolds, A., Tinelli, C.: SyGuS techniques in the core of an SMT solver. arXiv preprint arXiv:1711.10641 (2017)
Reynolds, A., Viswanathan, A., Barbosa, H., Tinelli, C., Barrett, C.: Datatypes with shared selectors. Technical report, The University of Iowa (2018). http://cvc4.cs.stanford.edu/papers/IJCAR2018-shsel/
Solar-Lezama, A., Tancau, L., Bodík, R., Seshia, S.A., Saraswat, V.A.: Combinatorial sketching for finite programs. In: ASPLOS, pp. 404–415. ACM (2006)
Stump, A., Sutcliffe, G., Tinelli, C.: StarExec: a cross-community infrastructure for logic solving. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS (LNAI), vol. 8562, pp. 367–373. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08587-6_28
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Reynolds, A., Viswanathan, A., Barbosa, H., Tinelli, C., Barrett, C. (2018). Datatypes with Shared Selectors. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds) Automated Reasoning. IJCAR 2018. Lecture Notes in Computer Science(), vol 10900. Springer, Cham. https://doi.org/10.1007/978-3-319-94205-6_39
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