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Model-guided synthesis of inductive lemmas for FOL with least fixpoints

Published:31 October 2022Publication History
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Abstract

Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure first-order logic, do not admit even complete procedures. In this paper, we undertake a novel approach for synthesizing inductive hypotheses to prove validity in this logic. The idea is to utilize several kinds of finite first-order models as counterexamples that capture the non-provability and invalidity of formulas to guide the search for inductive hypotheses. We implement our procedures and evaluate them extensively over theorems involving heap data structures that require inductive proofs and demonstrate the effectiveness of our methodology.

References

  1. Rajeev Alur, Rastislav Bodík, Eric Dallal, Dana Fisman, Pranav Garg, Garvit Juniwal, Hadas Kress-Gazit, P. Madhusudan, Milo M. K. Martin, Mukund Raghothaman, Shambwaditya Saha, Sanjit A. Seshia, Rishabh Singh, Armando Solar-Lezama, Emina Torlak, and Abhishek Udupa. 2015. Syntax-Guided Synthesis. IOS Press, 1– 25. https://doi.org/10.3233/978-1-61499-495-4-1 Google ScholarGoogle ScholarCross RefCross Ref
  2. Rajeev Alur, Rishabh Singh, Dana Fisman, and Armando Solar-Lezama. 2018. Search-Based Program Synthesis. Commun. ACM, 61, 12 (2018), Nov., 84–93. issn:0001-0782 https://doi.org/10.1145/3208071 Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Thomas Ball and Sriram K. Rajamani. 2002. The SLAM Project: Debugging System Software via Static Analysis. 1–3. isbn:1581134509 https://doi.org/10.1145/503272.503274 Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Kshitij Bansal, Sarah M. Loos, Markus N. Rabe, Christian Szegedy, and Stewart Wilcox. 2019. HOList: An Environment for Machine Learning of Higher-Order Theorem Proving. https://doi.org/10.48550/ARXIV.1904.03241 Google ScholarGoogle Scholar
  5. Clark Barrett, Christopher L. Conway, Morgan Deters, Liana Hadarean, Dejan Jovanović, Tim King, Andrew Reynolds, and Cesare Tinelli. 2011. CVC4. In Computer Aided Verification, Ganesh Gopalakrishnan and Shaz Qadeer (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 171–177. isbn:978-3-642-22110-1 https://doi.org/10.1007/978-3-642-22110-1_14 Google ScholarGoogle ScholarCross RefCross Ref
  6. Robert S. Boyer and J. Strother Moore. 1988. A Computational Logic Handbook. Academic Press Professional, Inc., USA. isbn:0121229521 Google ScholarGoogle Scholar
  7. Aaron R. Bradley and Zohar Manna. 2007. The Calculus of Computation: Decision Procedures with Applications to Verification. Springer-Verlag, Berlin, Heidelberg. isbn:3540741127 https://doi.org/10.1007/978-3-540-74113-8 Google ScholarGoogle ScholarCross RefCross Ref
  8. James Brotherston, Dino Distefano, and Rasmus Lerchedahl Petersen. 2011. Automated Cyclic Entailment Proofs in Separation Logic. In Automated Deduction – CADE-23, Nikolaj Bjørner and Viorica Sofronie-Stokkermans (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 131–146. isbn:978-3-642-22438-6 https://doi.org/10.1007/978-3-642-22438-6_12 Google ScholarGoogle ScholarCross RefCross Ref
  9. Cristiano Calcagno, Philippa Gardner, and Matthew Hague. 2005. From Separation Logic to First-Order Logic. In Foundations of Software Science and Computational Structures, Vladimiro Sassone (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg. 395–409. isbn:978-3-540-31982-5 https://doi.org/10.1007/978-3-540-31982-5_25 Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Duc-Hiep Chu, Joxan Jaffar, and Minh-Thai Trinh. 2015. Automatic Induction Proofs of Data-Structures in Imperative Programs. In Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI ’15). Association for Computing Machinery, New York, NY, USA. 457–466. isbn:9781450334686 https://doi.org/10.1145/2737924.2737984 Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Koen Claessen, Moa Johansson, Dan Rosén, and Nicholas Smallbone. 2013. Automating Inductive Proofs Using Theory Exploration. In Automated Deduction - CADE-24 - 24th International Conference on Automated Deduction, Lake Placid, NY, USA, June 9-14, 2013. Proceedings, Maria Paola Bonacina (Ed.) (Lecture Notes in Computer Science, Vol. 7898). Springer, 392–406. https://doi.org/10.1007/978-3-642-38574-2_27 Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Simon Cruanes. 2017. Superposition with Structural Induction. In Frontiers of Combining Systems, Clare Dixon and Marcelo Finger (Eds.). Springer International Publishing, Cham. 172–188. isbn:978-3-319-66167-4 https://doi.org/10.1007/978-3-319-66167-4_10 Google ScholarGoogle ScholarCross RefCross Ref
  13. Leonardo de Moura and Nikolaj Bjørner. 2008. Z3: An Efficient SMT Solver. In Tools and Algorithms for the Construction and Analysis of Systems, C. R. Ramakrishnan and Jakob Rehof (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 337–340. isbn:978-3-540-78800-3 https://doi.org/10.1007/978-3-540-78800-3_24 Google ScholarGoogle ScholarCross RefCross Ref
  14. David Detlefs, Greg Nelson, and James B. Saxe. 2005. Simplify: A Theorem Prover for Program Checking. J. ACM, 52, 3 (2005), May, 365–473. issn:0004-5411 https://doi.org/10.1145/1066100.1066102 Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. H.B. Enderton. 2001. A Mathematical Introduction to Logic. Elsevier Science Publishers Ltd.. isbn:978-0-12-238452-3 https://doi.org/10.1016/C2009-0-22107-6 Google ScholarGoogle ScholarCross RefCross Ref
  16. Yotam M. Y. Feldman, Oded Padon, Neil Immerman, Mooly Sagiv, and Sharon Shoham. 2017. Bounded Quantifier Instantiation for Checking Inductive Invariants. In Tools and Algorithms for the Construction and Analysis of Systems, Axel Legay and Tiziana Margaria (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 76–95. isbn:978-3-662-54577-5 https://doi.org/10.1007/978-3-662-54577-5_5 Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Pranav Garg, Christof Löding, P. Madhusudan, and Daniel Neider. 2014. ICE: A Robust Framework for Learning Invariants. In Computer Aided Verification, Armin Biere and Roderick Bloem (Eds.). Springer International Publishing, Cham. 69–87. isbn:978-3-319-08867-9 https://doi.org/10.1007/978-3-319-08867-9_5 Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Yeting Ge and Leonardo de Moura. 2009. Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories. In Computer Aided Verification, Ahmed Bouajjani and Oded Maler (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 306–320. isbn:978-3-642-02658-4 https://doi.org/10.1007/978-3-642-02658-4_25 Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Hari Govind V K, Sharon Shoham, and Arie Gurfinkel. 2022. Solving Constrained Horn Clauses modulo Algebraic Data Types and Recursive Functions. Proc. ACM Program. Lang., 6, POPL (2022), Article 60, Jan, 29 pages. https://doi.org/10.1145/3498722 Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Erich Grädel, Phokion G. Kolaitis, Leonid Libkin, Maarten Marx, Joel Spencer, Moshe Y. Vardi, Yde Venema, and Scott Weinstein. 2007. Finite Model Theory and Its Applications. Springer. isbn:978-3-540-00428-8 https://doi.org/10.1007/3-540-68804-8 Google ScholarGoogle ScholarCross RefCross Ref
  21. Márton Hajdú, Petra Hozzová, Laura Kovács, Johannes Schoisswohl, and Andrei Voronkov. 2020. Induction with Generalization in Superposition Reasoning. In Intelligent Computer Mathematics - 13th International Conference, CICM 2020, Bertinoro, Italy, July 26-31, 2020, Proceedings, Christoph Benzmüller and Bruce R. Miller (Eds.) (Lecture Notes in Computer Science, Vol. 12236). Springer, 123–137. https://doi.org/10.1007/978-3-030-53518-6_8 Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Wilfrid Hodges. 1997. A Shorter Model Theory. Cambridge University Press, USA. isbn:0521587131 Google ScholarGoogle Scholar
  23. Bart Jacobs, Jan Smans, Pieter Philippaerts, Frédéric Vogels, Willem Penninckx, and Frank Piessens. 2011. VeriFast: A Powerful, Sound, Predictable, Fast Verifier for C and Java. In NASA Formal Methods, Mihaela Bobaru, Klaus Havelund, Gerard J. Holzmann, and Rajeev Joshi (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 41–55. isbn:978-3-642-20398-5 https://doi.org/10.1007/978-3-642-20398-5_4 Google ScholarGoogle ScholarCross RefCross Ref
  24. Moa Johansson. 2019. Lemma Discovery for Induction - A Survey. In Intelligent Computer Mathematics - 12th International Conference, CICM 2019, Prague, Czech Republic, July 8-12, 2019, Proceedings, Cezary Kaliszyk, Edwin C. Brady, Andrea Kohlhase, and Claudio Sacerdoti Coen (Eds.) (Lecture Notes in Computer Science, Vol. 11617). Springer, 125–139. https://doi.org/10.1007/978-3-030-23250-4_9 Google ScholarGoogle ScholarCross RefCross Ref
  25. Matt Kaufmann and J. S. Moore. 1997. An Industrial Strength Theorem Prover for a Logic Based on Common Lisp. IEEE Trans. Softw. Eng., 23, 4 (1997), April, 203–213. issn:0098-5589 https://doi.org/10.1109/32.588534 Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Matt Kaufmann, J. Strother Moore, and Panagiotis Manolios. 2000. Computer-Aided Reasoning: An Approach. Springer New York, NY. isbn:978-1-4615-4449-4 https://doi.org/10.1007/978-1-4615-4449-4 Google ScholarGoogle ScholarCross RefCross Ref
  27. Jason R. Koenig, Oded Padon, Neil Immerman, and Alex Aiken. 2020. First-Order Quantified Separators. In Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2020). Association for Computing Machinery, New York, NY, USA. 703–717. isbn:9781450376136 https://doi.org/10.1145/3385412.3386018 Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Laura Kovács, Simon Robillard, and Andrei Voronkov. 2017. Coming to Terms with Quantified Reasoning. In Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL ’17). ACM, New York, NY, USA. 260–270. isbn:978-1-4503-4660-3 https://doi.org/10.1145/3009837.3009887 Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Paul Krogmeier and P. Madhusudan. 2022. Learning Formulas in Finite Variable Logics. Proc. ACM Program. Lang., 6, POPL (2022), Article 10, Jan, 28 pages. https://doi.org/10.1145/3498671 Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Quang Loc Le, Makoto Tatsuta, Jun Sun, and Wei-Ngan Chin. 2017. A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic. In Computer Aided Verification, Rupak Majumdar and Viktor Kunčak (Eds.). Springer International Publishing, Cham. 495–517. isbn:978-3-319-63390-9 https://doi.org/10.1007/978-3-319-63390-9_26 Google ScholarGoogle ScholarCross RefCross Ref
  31. K. Rustan M. Leino. 2012. Automating Induction with an SMT Solver. In Proceedings of the 13th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI’12). Springer-Verlag, Berlin, Heidelberg. 315–331. isbn:9783642279393 https://doi.org/10.1007/978-3-642-27940-9_21 Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Leonid Libkin. 2004. Elements of Finite Model Theory. Springer Berlin, Heidelberg. isbn:978-3-662-07003-1 https://doi.org/10.1007/978-3-662-07003-1 Google ScholarGoogle ScholarCross RefCross Ref
  33. Christof Löding, P. Madhusudan, and Lucas Peña. 2018. Foundations for natural proofs and quantifier instantiation. PACMPL, 2, POPL (2018), 10:1–10:30. https://doi.org/10.1145/3158098 Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. P. Madhusudan, Xiaokang Qiu, and Andrei Ştefănescu. 2012. Recursive Proofs for Inductive Tree Data-structures. In Proceedings of the 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’12). ACM, New York, NY, USA. 123–136. isbn:978-1-4503-1083-3 https://doi.org/10.1145/2103656.2103673 Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. A. I. Mal’tsev. 1962. Axiomatizable classes of locally free algebras of certain types. Sibirsk. Mat. Zh., 3 (1962), 729–743. http://mi.mathnet.ru/eng/smj/v3/i5/p729 Google ScholarGoogle Scholar
  36. Adithya Murali, Lucas Peña, Eion Blanchard, Christof Löding, and P. Madhusudan. 2022. Artifact for OOPSLA 2022 Article Model-Guided Synthesis of Inductive Lemmas for FOL with Least Fixpoints. https://doi.org/10.1145/3554331 Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Adithya Murali, Lucas Peña, Christof Löding, and P. Madhusudan. 2020. A First-Order Logic with Frames. In Programming Languages and Systems, Peter Müller (Ed.). Springer International Publishing, Cham. 515–543. isbn:978-3-030-44914-8 https://doi.org/10.1007/978-3-030-44914-8_19 Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Kedar S. Namjoshi and Robert P. Kurshan. 2000. Syntactic Program Transformations for Automatic Abstraction. In Computer Aided Verification, E. Allen Emerson and Aravinda Prasad Sistla (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 435–449. isbn:978-3-540-45047-4 https://doi.org/10.1007/10722167_33 Google ScholarGoogle ScholarCross RefCross Ref
  39. Daniel Neider, Pranav Garg, P. Madhusudan, Shambwaditya Saha, and Daejun Park. 2018. Invariant Synthesis for Incomplete Verification Engines. In Tools and Algorithms for the Construction and Analysis of Systems, Dirk Beyer and Marieke Huisman (Eds.). Springer International Publishing, Cham. 232–250. isbn:978-3-319-89960-2 https://doi.org/10.1007/978-3-319-89960-2_13 Google ScholarGoogle ScholarCross RefCross Ref
  40. Charles Gregory Nelson. 1980. Techniques for Program Verification. Ph. D. Dissertation. Stanford University. Stanford, CA, USA. AAI8011683 Google ScholarGoogle Scholar
  41. Greg Nelson and Derek C. Oppen. 1979. Simplification by Cooperating Decision Procedures. ACM Trans. Program. Lang. Syst., 1, 2 (1979), Oct, 245–257. issn:0164-0925 https://doi.org/10.1145/357073.357079 Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. Huu Hai Nguyen and Wei-Ngan Chin. 2008. Enhancing Program Verification with Lemmas. In Proceedings of the 20th International Conference on Computer Aided Verification (CAV ’08). Springer-Verlag, Berlin, Heidelberg. 355–369. isbn:9783540705437 https://doi.org/10.1007/978-3-540-70545-1_34 Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. Grant Passmore, Simon Cruanes, Denis Ignatovich, Dave Aitken, Matt Bray, Elijah Kagan, Kostya Kanishev, Ewen Maclean, and Nicola Mometto. 2020. The Imandra Automated Reasoning System (System Description). In Automated Reasoning, Nicolas Peltier and Viorica Sofronie-Stokkermans (Eds.). Springer International Publishing, Cham. 464–471. isbn:978-3-030-51054-1 https://doi.org/10.1007/978-3-030-51054-1_30 Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Edgar Pek, Xiaokang Qiu, and P. Madhusudan. 2014. Natural Proofs for Data Structure Manipulation in C Using Separation Logic. In Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI ’14). ACM, New York, NY, USA. 440–451. isbn:978-1-4503-2784-8 https://doi.org/10.1145/2594291.2594325 Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Xiaokang Qiu, Pranav Garg, Andrei Ştefănescu, and P. Madhusudan. 2013. Natural Proofs for Structure, Data, and Separation. In Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI ’13). ACM, New York, NY, USA. 231–242. isbn:978-1-4503-2014-6 https://doi.org/10.1145/2491956.2462169 Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. Andrew Reynolds. 2017. Conflicts, Models and Heuristics for Quantifier Instantiation in SMT. In Vampire 2016. Proceedings of the 3rd Vampire Workshop, Laura Kovacs and Andrei Voronkov (Eds.) (EPiC Series in Computing, Vol. 44). EasyChair, 1–15. issn:2398-7340 https://doi.org/10.29007/jmd3 Google ScholarGoogle ScholarCross RefCross Ref
  47. Andrew Reynolds, Haniel Barbosa, Andres Nötzli, Clark Barrett, and Cesare Tinelli. 2019. cvc4sy: Smart and Fast Term Enumeration for Syntax-Guided Synthesis. In Computer Aided Verification, Isil Dillig and Serdar Tasiran (Eds.). Springer International Publishing, Cham. 74–83. isbn:978-3-030-25543-5 https://doi.org/10.1007/978-3-030-25543-5_5 Google ScholarGoogle ScholarCross RefCross Ref
  48. Andrew Reynolds and Viktor Kuncak. 2015. Induction for SMT Solvers. In Verification, Model Checking, and Abstract Interpretation, Deepak D’Souza, Akash Lal, and Kim Guldstrand Larsen (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 80–98. isbn:978-3-662-46081-8 https://doi.org/10.1007/978-3-662-46081-8_5 Google ScholarGoogle ScholarDigital LibraryDigital Library
  49. John C. Reynolds. 2002. Separation Logic: A Logic for Shared Mutable Data Structures. In Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science (LICS ’02). IEEE Press, 55–74. https://doi.org/10.1109/LICS.2002.1029817 Google ScholarGoogle ScholarCross RefCross Ref
  50. Philipp Rümmer. 2012. E-Matching with Free Variables. In Logic for Programming, Artificial Intelligence, and Reasoning, Nikolaj Bjørner and Andrei Voronkov (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 359–374. isbn:978-3-642-28717-6 https://doi.org/10.1007/978-3-642-28717-6_28 Google ScholarGoogle ScholarDigital LibraryDigital Library
  51. Mihaela Sighireanu, Juan A. Navarro Pérez, Andrey Rybalchenko, Nikos Gorogiannis, Radu Iosif, Andrew Reynolds, Cristina Serban, Jens Katelaan, Christoph Matheja, Thomas Noll, Florian Zuleger, Wei-Ngan Chin, Quang Loc Le, Quang-Trung Ta, Ton-Chanh Le, Thanh-Toan Nguyen, Siau-Cheng Khoo, Michal Cyprian, Adam Rogalewicz, Tomas Vojnar, Constantin Enea, Ondrej Lengal, Chong Gao, and Zhilin Wu. 2019. SL-COMP: Competition of Solvers for Separation Logic. In Tools and Algorithms for the Construction and Analysis of Systems, Dirk Beyer, Marieke Huisman, Fabrice Kordon, and Bernhard Steffen (Eds.). Springer International Publishing, Cham. 116–132. isbn:978-3-030-17502-3 https://doi.org/10.1007/978-3-030-17502-3_8 Google ScholarGoogle ScholarCross RefCross Ref
  52. Armando Solar Lezama. 2008. Program Synthesis By Sketching. Ph. D. Dissertation. EECS Department, University of California, Berkeley. http://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-177.html Google ScholarGoogle Scholar
  53. Armando Solar-Lezama, Gilad Arnold, Liviu Tancau, Rastislav Bodík, Vijay A. Saraswat, and Sanjit A. Seshia. 2007. Sketching stencils. In Proceedings of the ACM SIGPLAN 2007 Conference on Programming Language Design and Implementation, San Diego, California, USA, June 10-13, 2007, Jeanne Ferrante and Kathryn S. McKinley (Eds.). ACM, 167–178. https://doi.org/10.1145/1250734.1250754 Google ScholarGoogle ScholarDigital LibraryDigital Library
  54. William Sonnex, Sophia Drossopoulou, and Susan Eisenbach. 2012. Zeno: An Automated Prover for Properties of Recursive Data Structures. In Tools and Algorithms for the Construction and Analysis of Systems, Cormac Flanagan and Barbara König (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 407–421. isbn:978-3-642-28756-5 https://doi.org/10.1007/978-3-642-28756-5_28 Google ScholarGoogle ScholarDigital LibraryDigital Library
  55. Philippe Suter, Mirco Dotta, and Viktor Kunćak. 2010. Decision Procedures for Algebraic Data Types with Abstractions. In Proceedings of the 37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL ’10). ACM, New York, NY, USA. 199–210. isbn:978-1-60558-479-9 https://doi.org/10.1145/1706299.1706325 Google ScholarGoogle ScholarDigital LibraryDigital Library
  56. Quang-Trung Ta, Ton Chanh Le, Siau-Cheng Khoo, and Wei-Ngan Chin. 2016. Automated Mutual Explicit Induction Proof in Separation Logic. In FM 2016: Formal Methods, John Fitzgerald, Constance Heitmeyer, Stefania Gnesi, and Anna Philippou (Eds.). Springer International Publishing, Cham. 659–676. https://doi.org/10.1007/978-3-319-48989-6_40 Google ScholarGoogle ScholarCross RefCross Ref
  57. Quang-Trung Ta, Ton Chanh Le, Siau-Cheng Khoo, and Wei-Ngan Chin. 2017. Automated Lemma Synthesis in Symbolic-Heap Separation Logic. Proc. ACM Program. Lang., 2, POPL (2017), Article 9, Dec, 29 pages. https://doi.org/10.1145/3158097 Google ScholarGoogle ScholarDigital LibraryDigital Library
  58. Alfred Tarski. 1955. A lattice-theoretical fixpoint theorem and its applications.. Pacific J. Math., 5, 2 (1955), 285 – 309. https://projecteuclid.org/euclid.pjm/1103044538 Google ScholarGoogle ScholarCross RefCross Ref
  59. Weikun Yang, Grigory Fedyukovich, and Aarti Gupta. 2019. Lemma Synthesis for Automating Induction over Algebraic Data Types. In Principles and Practice of Constraint Programming, Thomas Schiex and Simon de Givry (Eds.). Springer International Publishing, Cham. 600–617. isbn:978-3-030-30048-7 https://doi.org/10.1007/978-3-030-30048-7_35 Google ScholarGoogle ScholarDigital LibraryDigital Library
  60. Hongce Zhang, Aarti Gupta, and Sharad Malik. 2021. Syntax-Guided Synthesis for Lemma Generation in Hardware Model Checking. In Verification, Model Checking, and Abstract Interpretation - 22nd International Conference, VMCAI 2021, Copenhagen, Denmark, January 17-19, 2021, Proceedings, Fritz Henglein, Sharon Shoham, and Yakir Vizel (Eds.) (Lecture Notes in Computer Science, Vol. 12597). Springer, 325–349. https://doi.org/10.1007/978-3-030-67067-2_15 Google ScholarGoogle ScholarDigital LibraryDigital Library

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