Roland Axelsson, Martin Lange & Rafal Somla (2007):
The Complexity of Model Checking Higher-Order Fixpoint Logic.
Logical Methods in Computer Science 3(2),
doi:10.2168/LMCS-3(2:7)2007.
Thomas Ball, Byron Cook, Vladimir Levin & Sriram K. Rajamani (2004):
SLAM and Static Driver Verifier: Technology Transfer of Formal Methods inside Microsoft.
In: Integrated Formal Methods 2004,
LNCS 2999.
Springer,
pp. 1–20,
doi:10.1007/978-3-540-24756-2_1.
Nikolaj Bjørner, Arie Gurfinkel, Kenneth L. McMillan & Andrey Rybalchenko (2015):
Horn Clause Solvers for Program Verification.
In: Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday,
LNCS 9300.
Springer,
pp. 24–51,
doi:10.1007/978-3-319-23534-9_2.
Christopher H. Broadbent & Naoki Kobayashi (2013):
Saturation-Based Model Checking of Higher-Order Recursion Schemes.
In: CSL 2013,
LIPIcs 23,
pp. 129–148,
doi:10.4230/LIPIcs.CSL.2013.129.
Toby Cathcart Burn, C.-H. Luke Ong & Steven J. Ramsay (2018):
Higher-order constrained horn clauses for verification.
Proc. ACM Program. Lang. 2(POPL),
pp. 11:1–11:28,
doi:10.1145/3158099.
Adrien Champion, Tomoya Chiba, Naoki Kobayashi & Ryosuke Sato (2020):
ICE-Based Refinement Type Discovery for Higher-Order Functional Programs.
J. Autom. Reason. 64(7),
pp. 1393–1418,
doi:10.1007/s10817-020-09571-y.
Edmund M. Clarke, Orna Grumberg & Doron A. Peled (1999):
Model Checking.
The MIT Press.
Byron Cook, Alexey Gotsman, Andreas Podelski, Andrey Rybalchenko & Moshe Y. Vardi (2007):
Proving That Programs Eventually Do Something Good.
In: Proceedings of POPL.
ACM Press,
pp. 265–276,
doi:10.1145/1190216.1190257.
Byron Cook & Eric Koskinen (2013):
Reasoning About Nondeterminism in Programs.
In: Proceedings of PLDI 2013.
ACM Press,
pp. 219–230,
doi:10.1145/2491956.2491969.
Emanuele De Angelis, Fabio Fioravanti, Alberto Pettorossi & Maurizio Proietti (2018):
Solving Horn Clauses on Inductive Data Types Without Induction.
TPLP 18(3-4),
pp. 452–469,
doi:10.1017/S1471068418000157.
Emanuele De Angelis, Fabio Fioravanti, Alberto Pettorossi & Maurizio Proietti (2020):
Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates.
In: Nicolas Peltier & Viorica Sofronie-Stokkermans: Automated Reasoning - 10th International Joint Conference, IJCAR 2020, Paris, France, July 1-4, 2020, Proceedings, Part I,
Lecture Notes in Computer Science 12166.
Springer,
pp. 83–102,
doi:10.1007/978-3-030-51074-9_6.
Giorgio Delzanno & Andreas Podelski (2001):
Constraint-based deductive model checking.
Int. J. Softw. Tools Technol. Transf. 3(3),
pp. 250–270,
doi:10.1007/s100090100049.
P. Ezudheen, Daniel Neider, Deepak D'Souza, Pranav Garg & P. Madhusudan (2018):
Horn-ICE learning for synthesizing invariants and contracts.
Proc. ACM Program. Lang. 2(OOPSLA),
pp. 131:1–131:25,
doi:10.1145/3276501.
Grigory Fedyukovich, Yueling Zhang & Aarti Gupta (2018):
Syntax-Guided Termination Analysis.
In: Computer Aided Verification - 30th International Conference, CAV 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July 14-17, 2018, Proceedings, Part I,
LNCS 10981.
Springer,
pp. 124–143,
doi:10.1007/978-3-319-96145-3_7.
Erich Grädel, Wolfgang Thomas & Thomas Wilke (2002):
Automata, Logics, and Infinite Games: A Guide to Current Research.
LNCS 2500.
Springer,
doi:10.1007/3-540-36387-4.
H. Hojjat & P. Rümmer (2018):
The ELDARICA Horn Solver.
In: 2018 Formal Methods in Computer Aided Design (FMCAD),
pp. 1–7,
doi:10.23919/FMCAD.2018.8603013.
Youkichi Hosoi, Naoki Kobayashi & Takeshi Tsukada (2019):
A Type-Based HFL Model Checking Algorithm.
In: Anthony Widjaja Lin: Programming Languages and Systems - 17th Asian Symposium, APLAS 2019, Nusa Dua, Bali, Indonesia, December 1-4, 2019, Proceedings,
Lecture Notes in Computer Science 11893.
Springer,
pp. 136–155,
doi:10.1007/978-3-030-34175-6_8.
Naoki Iwayama, Naoki Kobayashi, Ryota Suzuki & Takeshi Tsukada (2020):
Predicate Abstraction and CEGAR for νHFL_Z Validity Checking.
In: David Pichardie & Mihaela Sighireanu: Static Analysis - 27th International Symposium, SAS 2020, Virtual Event, November 18-20, 2020, Proceedings,
Lecture Notes in Computer Science 12389.
Springer,
pp. 134–155,
doi:10.1007/978-3-030-65474-0_7.
Joxan Jaffar, Andrew E. Santosa & Razvan Voicu (2006):
A CLP Method for Compositional and Intermittent Predicate Abstraction.
In: Proceedings of VMCAI 2006,
Lecture Notes in Computer Science 3855.
Springer,
pp. 17–32,
doi:10.1007/11609773_2.
Hiroyuki Katsura, Naoki Iwayama, Naoki Kobayashi & Takeshi Tsukada (2020):
A New Refinement Type System for Automated νHFL_Z Validity Checking.
In: Bruno C. d. S. Oliveira: Programming Languages and Systems - 18th Asian Symposium, APLAS 2020, Fukuoka, Japan, November 30 - December 2, 2020, Proceedings,
Lecture Notes in Computer Science 12470.
Springer,
pp. 86–104,
doi:10.1007/978-3-030-64437-6_5.
Naoki Kobayashi (2013):
Model Checking Higher-Order Programs.
J. ACM 60(3),
doi:10.1145/2487241.2487246.
Naoki Kobayashi (2016):
HorSat 2: A Saturation-Based Model Checker for Higher-Order Recursion Schemes.
Available at https://github.com/hopv/horsat2.
Naoki Kobayashi, Grigory Fedyukovich & Aarti Gupta (2020):
Fold/Unfold Transformations for Fixpoint Logic.
In: Armin Biere & David Parker: Tools and Algorithms for the Construction and Analysis of Systems - 26th International Conference, TACAS 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25-30, 2020, Proceedings, Part II,
Lecture Notes in Computer Science 12079.
Springer,
pp. 195–214,
doi:10.1007/978-3-030-45237-7_12.
Naoki Kobayashi, Étienne Lozes & Florian Bruse (2017):
On the relationship between higher-order recursion schemes and higher-order fixpoint logic.
In: POPL 2017,
pp. 246–259,
doi:10.1145/3009837.3009854.
Naoki Kobayashi, Takeshi Nishikawa, Atsushi Igarashi & Hiroshi Unno (2019):
Temporal Verification of Programs via First-Order Fixpoint Logic.
In: Bor-Yuh Evan Chang: Static Analysis - 26th International Symposium, SAS 2019, Porto, Portugal, October 8-11, 2019, Proceedings,
Lecture Notes in Computer Science 11822.
Springer,
pp. 413–436,
doi:10.1007/978-3-030-32304-2_20.
Naoki Kobayashi, Ryosuke Sato & Hiroshi Unno (2011):
Predicate Abstraction and CEGAR for Higher-Order Model Checking.
In: PLDI 2011.
ACM Press,
pp. 222–233,
doi:10.1145/1993498.1993525.
Naoki Kobayashi, Takeshi Tsukada & Keiichi Watanabe (2018):
Higher-Order Program Verification via HFL Model Checking.
In: Amal Ahmed: Programming Languages and Systems - 27th European Symposium on Programming, ESOP 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018, Thessaloniki, Greece, April 14-20, 2018, Proceedings,
Lecture Notes in Computer Science 10801.
Springer,
pp. 711–738,
doi:10.1007/978-3-319-89884-1_25.
Anvesh Komuravelli, Arie Gurfinkel & Sagar Chaki (2016):
SMT-based model checking for recursive programs.
Formal Methods Syst. Des. 48(3),
pp. 175–205,
doi:10.1007/s10703-016-0249-4.
Mayuko Kori, Takeshi Tsukada & Naoki Kobayashi (2021):
A Cyclic Proof System for HFL_N.
In: Christel Baier & Jean Goubault-Larrecq: 29th EACSL Annual Conference on Computer Science Logic, CSL 2021, January 25-28, 2021, Ljubljana, Slovenia (Virtual Conference),
LIPIcs 183.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
pp. 29:1–29:22,
doi:10.4230/LIPIcs.CSL.2021.29.
Dexter Kozen (1983):
Results on the Propositional μ-calculus.
Theoretical Computer Science 27,
pp. 333–354,
doi:10.1016/0304-3975(82)90125-6.
Takuya Kuwahara, Ryosuke Sato, Hiroshi Unno & Naoki Kobayashi (2015):
Predicate Abstraction and CEGAR for Disproving Termination of Higher-Order Functional Programs.
In: Proceedings of CAV 2015,
LNCS 9207.
Springer,
pp. 287–303,
doi:10.1007/978-3-319-21668-3_17.
Takuya Kuwahara, Tachio Terauchi, Hiroshi Unno & Naoki Kobayashi (2014):
Automatic Termination Verification for Higher-Order Functional Programs.
In: Proceedings of ESOP 2014,
LNCS 8410.
Springer,
pp. 392–411,
doi:10.1007/978-3-642-54833-8_21.
Akihiro Murase, Tachio Terauchi, Naoki Kobayashi, Ryosuke Sato & Hiroshi Unno (2016):
Temporal verification of higher-order functional programs.
In: Rastislav Bodík & Rupak Majumdar: Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2016, St. Petersburg, FL, USA, January 20 - 22, 2016.
ACM,
pp. 57–68,
doi:10.1145/2837614.2837667.
C.-H. Luke Ong (2006):
On Model-Checking Trees Generated by Higher-Order Recursion Schemes.
In: LICS 2006.
IEEE Computer Society Press,
pp. 81–90,
doi:10.1109/LICS.2006.38.
C.-H. Luke Ong & Dominik Wagner (2019):
HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories.
In: 34th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2019, Vancouver, BC, Canada, June 24-27, 2019.
IEEE,
pp. 1–14,
doi:10.1109/LICS.2019.8785784.
Julio C. Peralta, John P. Gallagher & Hüseyin Saglam (1998):
Analysis of Imperative Programs through Analysis of Constraint Logic Programs.
In: Proceedings of SAS '98,
Lecture Notes in Computer Science 1503.
Springer,
pp. 246–261,
doi:10.1007/3-540-49727-7_15.
Andreas Podelski & Andrey Rybalchenko (2004):
Transition Invariants.
In: 19th IEEE Symposium on Logic in Computer Science (LICS 2004), 14-17 July 2004, Turku, Finland, Proceedings,
pp. 32–41,
doi:10.1109/LICS.2004.1319598.
Patrick M. Rondon, Ming Kawaguchi & Ranjit Jhala (2008):
Liquid types.
In: PLDI 2008,
pp. 159–169,
doi:10.1145/1375581.1375602.
Yuki Satake, Hiroshi Unno & Hinata Yanagi (2020):
Probabilistic Inference for Predicate Constraint Satisfaction.
In: The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, February 7-12, 2020.
AAAI Press,
pp. 1644–1651,
doi:10.1609/aaai.v34i02.5526.
Takeshi Tsukada (2020):
On Computability of Logical Approaches to Branching-Time Property Verification of Programs.
In: Holger Hermanns, Lijun Zhang, Naoki Kobayashi & Dale Miller: LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science, Saarbrücken, Germany, July 8-11, 2020.
ACM,
pp. 886–899,
doi:10.1145/3373718.3394766.
Hiroshi Unno & Naoki Kobayashi (2009):
Dependent type inference with interpolants.
In: Proceedings of the 11th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, September 7-9, 2009, Coimbra, Portugal.
ACM,
pp. 277–288,
doi:10.1145/1599410.1599445.
Hiroshi Unno, Tachio Terauchi & Naoki Kobayashi (2013):
Automating relatively complete verification of higher-order functional programs.
In: Roberto Giacobazzi & Radhia Cousot: The 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL '13, Rome, Italy - January 23 - 25, 2013.
ACM,
pp. 75–86,
doi:10.1145/2429069.2429081.
M. Viswanathan & R. Viswanathan (2004):
A Higher Order Modal Fixed Point Logic.
In: CONCUR,
LNCS 3170.
Springer,
pp. 512–528,
doi:10.1007/978-3-540-28644-8_33.
Keiichi Watanabe, Takeshi Tsukada, Hiroki Oshikawa & Naoki Kobayashi (2019):
Reduction from branching-time property verification of higher-order programs to HFL validity checking.
In: Manuel V. Hermenegildo & Atsushi Igarashi: Proceedings of the 2019 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, PEPM@POPL 2019, Cascais, Portugal, January 14-15, 2019.
ACM,
pp. 22–34,
doi:10.1145/3294032.3294077.
Hongwei Xi & Frank Pfenning (1999):
Dependent Types in Practical Programming.
In: Proceedings of POPL,
pp. 214–227,
doi:10.1145/292540.292560.