research-article

Open access

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

Authors:

Adithya Murali,

Eion Blanchard,

Christof Löding,

P. MadhusudanAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 6, Issue OOPSLA2

Article No.: 191, Pages 1873 - 1902

https://doi.org/10.1145/3563354

Published: 31 October 2022 Publication History

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

[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

Digital 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

Digital 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

[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

[6]

Robert S. Boyer and J. Strother Moore. 1988. A Computational Logic Handbook. Academic Press Professional, Inc., USA. isbn:0121229521

[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

[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

[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

Digital 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

Digital 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

Digital 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

[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

[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

Digital 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

[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

Digital 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

Digital 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

Digital 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

Digital 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

[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

Digital Library

[22]

Wilfrid Hodges. 1997. A Shorter Model Theory. Cambridge University Press, USA. isbn:0521587131

[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

[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

[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

Digital 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

[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

Digital 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

Digital 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

Digital 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

[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

Digital 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

[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

Digital 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

Digital 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

[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

Digital 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

Digital 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

[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

[40]

Charles Gregory Nelson. 1980. Techniques for Program Verification. Ph. D. Dissertation. Stanford University. Stanford, CA, USA. AAI8011683

[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

Digital 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

Digital 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

Digital 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

Digital 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

Digital 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

[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

[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

Digital 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

[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

Digital 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

[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

[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

Digital 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

Digital 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

Digital 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

[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

Digital 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

[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

Digital 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

Digital Library

Cited By

Elad NShoham S(2025)Axe ’Em: Eliminating Spurious States with Induction AxiomsProceedings of the ACM on Programming Languages10.1145/37048539:POPL(479-508)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704853
Kurashige CJi RGiridharan ABarbone MNoor DItzhaky SJhala RPolikarpova N(2024)CCLemma: E-Graph Guided Lemma Discovery for Inductive Equational ProofsProceedings of the ACM on Programming Languages10.1145/36746538:ICFP(818-844)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674653
Murali ARivera CMadhusudan P(2024)Predictable Verification using Intrinsic DefinitionsProceedings of the ACM on Programming Languages10.1145/36564508:PLDI(1804-1829)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656450
Show More Cited By

Index Terms

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

Recommendations

Synthesizing axiomatizations using logic learning

Axioms and inference rules form the foundation of deductive systems and are crucial in the study of reasoning with logics over structures. Historically, axiomatizations have been discovered manually with much expertise and effort. In this paper we show ...
Grounded fixpoints
AAAI'15: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence

Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced ...
Polymorphic lemmas and definitions in $\lambda$Prolog and Twelf

$\lambda$Prolog is known to be well-suited for expressing and implementing logics and inference systems. We show that lemmas and definitions in such logics can be implemented with a great economy of expression. We encode a higher-order logic using an ...

Comments

Information & Contributors

Information

Published In

cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 6, Issue OOPSLA2

October 2022

1932 pages

EISSN:2475-1421

DOI:10.1145/3554307

Editor:
Philip Wadler
University of Edinburgh, UK

Issue’s Table of Contents

Copyright © 2022 Owner/Author.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 October 2022

Published in PACMPL Volume 6, Issue OOPSLA2

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Badges

Artifacts Available / v1.1

Author Tags

Qualifiers

Research-article

Funding Sources

Discovery Partners Institute
Amazon

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
397
Total Downloads

Downloads (Last 12 months)184
Downloads (Last 6 weeks)14

Reflects downloads up to 12 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Elad NShoham S(2025)Axe ’Em: Eliminating Spurious States with Induction AxiomsProceedings of the ACM on Programming Languages10.1145/37048539:POPL(479-508)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704853
Kurashige CJi RGiridharan ABarbone MNoor DItzhaky SJhala RPolikarpova N(2024)CCLemma: E-Graph Guided Lemma Discovery for Inductive Equational ProofsProceedings of the ACM on Programming Languages10.1145/36746538:ICFP(818-844)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674653
Murali ARivera CMadhusudan P(2024)Predictable Verification using Intrinsic DefinitionsProceedings of the ACM on Programming Languages10.1145/36564508:PLDI(1804-1829)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656450
Elad NPadon OShoham S(2024)An Infinite Needle in a Finite Haystack: Finding Infinite Counter-Models in Deductive VerificationProceedings of the ACM on Programming Languages10.1145/36328758:POPL(970-1000)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632875
Sun YJi RFang JJiang XChen MXiong Y(2024)Proving Functional Program Equivalence via Directed Lemma SynthesisFormal Methods10.1007/978-3-031-71162-6_28(538-557)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71162-6_28
Frenkel EChajed TPadon OShoham S(2024)Efficient Implementation of an Abstract Domain of Quantified First-Order FormulasComputer Aided Verification10.1007/978-3-031-65630-9_5(86-108)Online publication date: 24-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-65630-9_5
Murali APeña LJhala RMadhusudan P(2023)Complete First-Order Reasoning for Properties of Functional ProgramsProceedings of the ACM on Programming Languages10.1145/36228357:OOPSLA2(1063-1092)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622835
Murali APeña LLöding CMadhusudan P(2023)A First-order Logic with FramesACM Transactions on Programming Languages and Systems10.1145/358305745:2(1-44)Online publication date: 15-May-2023
https://dl.acm.org/doi/10.1145/3583057

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents