Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-04-30T14:11:50.812Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis and Transformation of Constrained Horn Clauses for Program Verification

Published online by Cambridge University Press:  15 November 2021

EMANUELE DE ANGELIS Open the ORCID record for EMANUELE DE ANGELIS [Opens in a new window] ,
FABIO FIORAVANTI Open the ORCID record for FABIO FIORAVANTI [Opens in a new window] ,
JOHN P. GALLAGHER Open the ORCID record for JOHN P. GALLAGHER [Opens in a new window] ,
MANUEL V. HERMENEGILDO Open the ORCID record for MANUEL V. HERMENEGILDO [Opens in a new window] ,
ALBERTO PETTOROSSI Open the ORCID record for ALBERTO PETTOROSSI [Opens in a new window]  and
MAURIZIO PROIETTI Open the ORCID record for MAURIZIO PROIETTI [Opens in a new window]
EMANUELE DE ANGELIS
Affiliation:
CNR-IASI, Rome, Italy (e-mail: emanuele.deangelis@iasi.cnr.it)
FABIO FIORAVANTI
Affiliation:
DEC, University ‘G. d’Annunzio’, Chieti-Pescara, Italy (e-mail: fioravanti@unich.it)
JOHN P. GALLAGHER
Affiliation:
Roskilde University, Roskilde, Denmark and IMDEA Software Institute, Madrid, Spain (e-mail: jpg@ruc.dk)
MANUEL V. HERMENEGILDO
Affiliation:
IMDEA Software Institute, Madrid, Spain and Universidad Politécnica de Madrid (UPM), Madrid, Spain (e-mail: manuel.hermenegildo@imdea.org)
ALBERTO PETTOROSSI
Affiliation:
CNR-IASI, Rome, Italy and DICII, University of Rome ‘Tor Vergata’, Rome, Italy (e-mail: pettorossi@info.uniroma2.it)
MAURIZIO PROIETTI
Affiliation:
CNR-IASI, Rome, Italy (e-mail: maurizio.proietti@iasi.cnr.it)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper surveys recent work on applying analysis and transformation techniques that originate in the field of constraint logic programming (CLP) to the problem of verifying software systems. We present specialization-based techniques for translating verification problems for different programming languages, and in general software systems, into satisfiability problems for constrained Horn clauses (CHCs), a term that has become popular in the verification field to refer to CLP programs. Then, we describe static analysis techniques for CHCs that may be used for inferring relevant program properties, such as loop invariants. We also give an overview of some transformation techniques based on specialization and fold/unfold rules, which are useful for improving the effectiveness of CHC satisfiability tools. Finally, we discuss future developments in applying these techniques.

Keywords

Program verificationprogram analysisprogram transformationconstrained Horn clausesconstraint logic programming
Type
Survey Article
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 6 , November 2022 , pp. 974 - 1042
Check for updates
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

*

Research partially funded by Spanish MICINN 2019-108528RB-C21 ProCode project, the Madrid M141047003 N-GREENS and P2018/TCS-4339 BLOQUES-CM programs, and the Tezos Foundation.

References

Albarghouthi, A. 2017. Probabilistic Horn clause verification. In SAS 2017. LNCS 10422. Springer, 1–22.Google Scholar
Albert, E., Arenas, P., Genaim, S. and Puebla, G. 2011. Closed-form upper bounds in static cost analysis. Journal of Automated Reasoning 46, 2, 161–203.Google Scholar
Albert, E., Arenas, P., Genaim, S., Puebla, G. and Zanardini, D. 2007. Cost analysis of Java bytecode. In ESOP 2007. LNCS 4421. Springer, 157–172.Google Scholar
Albert, E., Arenas, P., Genaim, S., Puebla, G. and Zanardini, D. 2008. Removing useless variables in cost analysis of Java bytecode. In ACM SAC - Software Verification Track (SV 2008). ACM Press, 368–375.Google Scholar
Albert, E., Arenas, P. and Gómez-Zamalloa, M. 2018. Systematic testing of actor systems. Software Testing, Verification & Reliability 28, 3, e1661.Google Scholar
Albert, E., Gómez-Zamalloa, M. and Puebla, G. 2010. PET: A partial evaluation-based test case generation tool for Java bytecode. In PEPM 2010. ACM Press, 25–28.Google Scholar
Alberti, F., Ghilardi, S. and Sharygina, N. 2015. Decision procedures for flat array properties. Journal of Automated Reasoning 54, 4, 327–352.CrossRefGoogle Scholar
Amaral, C., Florido, M. and Costa, V. S. 2014. PrologCheck - Property-based testing in Prolog. In 12th FLOPS 2014. LNCS 8475. Springer, 1–17.Google Scholar
Apt, K. R. 1990. Introduction to logic programming. In Handbook of Theoretical Computer Science, J. van Leeuwen, Ed. Elsevier, 493–576.Google Scholar
Apt, K. R. and Bol, R. N. 1994. Logic programming and negation: A survey. Journal of Logic Programming 19, 20, 9–71.CrossRefGoogle Scholar
Bagnara, R., Hill, P. M. and Zaffanella, E. 2008. The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Science of Computer Programming 72, 1–2, 3–21.CrossRefGoogle Scholar
Bancilhon, F., Maier, D., Sagiv, Y. and Ullman, J. 1986. Magic sets and other strange ways to implement logic programs (Extended abstract). In 5th ACM SIGMOD-SIGACT Symposium on Principles of Database Systems, 1985. ACM Press, 1–15.Google Scholar
Banda, G. and Gallagher, J. P. 2009. Analysis of linear hybrid systems in CLP. In LOPSTR 2008. LNCS 5438. Springer, 55–70.Google Scholar
Barbuti, R. and Giacobazzi, R. 1992. A bottom-up polymorphic type inference in logic programming. Science of Computer Programming 19, 281–313.CrossRefGoogle Scholar
Barnett, M., Chang, B.-Y. E., De Line, R., Jacobs, B. and Leino, K. R. M. 2006. Boogie: A modular reusable verifier for object-oriented programs. In Formal Methods for Components and Objects. LNCS 4111. Springer, 364–387.Google Scholar
Barras, B., Boutin, S., Cornes, C., Courant, J., Filliâtre, J.-C., Gimenez, E., Herbelin, H., Huet, G., Munoz, C., Murthy, C., Parent, C., Paulin-Mohring, C., Saibi, A. and Werner, B. 1997. The Coq Proof Assistant Reference Manual: Version 6.1. Tech. Rep. RT-0203. https://hal.inria.fr/inria-00069968 Google Scholar
Barrett, C., Conway, C. L., Deters, M., Hadarean, L., Jovanovic, D., King, T., Reynolds, A. and Tinelli, C. 2011. CVC4. In CAV 2011. LNCS 6806. Springer, 171–177.Google Scholar
Barrett, C., Fontaine, P. and Tinelli, C. 2016. The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org Google Scholar
Barrett, C. W. and Tinelli, C. 2018. Satisfiability modulo theories. In Handbook of Model Checking, E. M. Clarke and et al., Eds. Springer, 305–343.CrossRefGoogle Scholar
Barthe, G., Crespo, J. M. and Kunz, C. 2011. Relational verification using product programs. In FM 2011. LNCS 6664. Springer, 200–214.Google Scholar
Basold, H., Komendantskaya, E. and Li, Y. 2019. Coinduction in Uniform: Foundations for corecursive proof search with Horn clauses. In ESOP 2019. LNCS 11423. Springer, 783–813.Google Scholar
Benoy, F. and King, A. 1997. Inferring argument size relationships with CLP(R). In LOPSTR 1996. LNCS 1207. Springer, 204–223.Google Scholar
Benton, N. 2004. Simple relational correctness proofs for static analyses and program transformations. In POPL 2004. ACM Press, 14–25.Google Scholar
Beyene, T. A., Popeea, C. and Rybalchenko, A. 2013. Solving existentially quantified horn clauses. In CAV 2013. LNCS 8044. Springer, 869–882.Google Scholar
Bjørner, N., Gurfinkel, A., McMillan, K. L. and Rybalchenko, A. 2015. Horn clause solvers for program verification. In Fields of Logic and Computation II – Essays dedicated to Yuri Gurevich. LNCS 9300. Springer, 24–51.Google Scholar
Blanchet, B. 2016. Modeling and verifying security protocols with the applied pi calculus and ProVerif. Foundations and Trends in Privacy and Security 1, 1–2, 1–135.Google Scholar
Blazy, S. and Leroy, X. 2009. Mechanized semantics for the Clight subset of the C language. Journal of Automated Reasoning 43, 3, 263–288.CrossRefGoogle Scholar
Borralleras, C., Lucas, S., Oliveras, A., Rodrguez-Carbonell, E. and Rubio, A. 2012. SAT modulo linear arithmetic for solving polynomial constraints. Journal of Automated Reasoning 48, 1, 107–131.CrossRefGoogle Scholar
Bradley, A. R. 2011. SAT-based model checking without unrolling. In VMCAI 2011. LNCS 6538. Springer, 70–87.Google Scholar
Bradley, A. R. and Manna, Z. 2007. The Calculus of Computation. Springer.Google Scholar
Brain, M., D’Silva, V., Griggio, A., Haller, L. and Kroening, D. 2014. Deciding floating-point logic with abstract conflict driven clause learning. Formal Methods in System Design 45, 2, 213–245.CrossRefGoogle Scholar
Brough, D. R. and Hogger, C. J. 1991. Grammar-related transformations of logic programs. New Generation Computing 9, 1, 115–134.Google Scholar
Brummayer, R. and Biere, A. 2009. Boolector: An efficient SMT solver for bit-vectors and arrays. In TACAS 2009. LNCS 5505. Springer, 174–177.Google Scholar
Bueno, F., Deransart, P., Drabent, W., Ferrand, G., Hermenegildo, M., Maluszynski, J. and Puebla, G. 1997. On the role of semantic approximations in validation and diagnosis of constraint logic programs. In 3rd Workshop on Automated Debugging – AADEBUG 1997. Univ. of Linköping Press, Linköping, Sweden, 155–170.Google Scholar
Bulyonkov, M. A. 1984. Polyvariant mixed computation for analyzer programs. Acta Informatica 21, 473–484.CrossRefGoogle Scholar
Bundy, A. 2001. The automation of proof by mathematical induction. In Handbook of Automated Reasoning (I), Robinson, A. and Voronkov, A., Eds. North Holland, 845–911.Google Scholar
Burn, T. C., Ong, C. L. and Ramsay, S. J. 2018. Higher-order constrained Horn clauses for verification. In Proceedings of the ACM on Programming Languages 2, POPL 2018, 11:1–11:28.Google Scholar
Burstall, R. M. and Darlington, J. 1977. A transformation system for developing recursive programs. Journal of the ACM 24, 1, 44–67.CrossRefGoogle Scholar
Casso, I., Morales, J. F., López-Garca, P. and Hermenegildo, M. 2019. An integrated approach to assertion-based random testing in Prolog. In LOPSTR 2019. LNCS 12042. Springer, 159–176.Google Scholar
Champion, A., Chiba, T., Kobayashi, N. and Sato, R. 2020. ICE-based refinement type discovery for higher-order functional programs. Journal of Automated Reasoning 64, 7, 1393–1418.CrossRefGoogle Scholar
Chen, J., Wei, J., Feng, Y., Bastani, O. and Dillig, I. 2019. Relational verification using reinforcement learning. Proceedings of the ACM on Programming Languages 3, OOPSLA, 141:1–141:30.Google Scholar
Churchill, B. R., Padon, O., Sharma, R. and Aiken, A. 2019. Semantic program alignment for equivalence checking. In PLDI 2019. ACM Press, 1027–1040.Google Scholar
Çiçek, E., Barthe, G., Gaboardi, M., Garg, D. and Hoffmann, J. 2017. Relational cost analysis. In POPL 2017. ACM Press, 316–329.Google Scholar
Cimatti, A., Griggio, A., Schaafsma, B. and Sebastiani, R. 2013. The MathSAT5 SMT Solver. In TACAS 2013. LNCS 7795. Springer, 93–107.Google Scholar
Claessen, K. and Hughes, J. 2000. QuickCheck: A lightweight tool for random testing of Haskell programs. In ICFP 2000. ACM Press, 268–279.Google Scholar
Clark, K. L. 1978. Negation as failure. In Logic and Data Bases, Gallaire, H. and Minker, J., Eds. Plenum Press, New York, 293–322.Google Scholar
Clarke, E., Grumberg, O., Jha, S., Lu, Y. and Veith, H. 2003. Counterexample-guided abstraction refinement for symbolic model checking. Journal of the ACM 50, 5, 752–794.Google Scholar
Clarke, E. M., Grumberg, O. and Peled, D. 1999. Model Checking. MIT Press.Google Scholar
Codish, M., Bruynooghe, M., Garca de la Banda, M. and Hermenegildo, M. 1997. Exploiting goal independence in the analysis of logic programs. Journal of Logic Programming 32, 3, 247–261.CrossRefGoogle Scholar
Codish, M., Dams, D. and Yardeni, E. 1994. Bottom-up abstract interpretation of logic programs. Theoretical Computer Science 124, 93–125.Google Scholar
Codish, M. and Demoen, B. 1995. Analyzing logic programs using “PROP”-ositional logic programs and a magic wand. Journal of Logic Programming 25, 3, 249–274.CrossRefGoogle Scholar
Colmerauer, A. 1982. Prolog and infinite trees. In Logic Programming, Clark, K. L. and Tärnlund, S.-Å., Eds. Academic Press, 231–251.Google Scholar
Coppit, D., Le, W., Sullivan, K. J., Khurshid, S. and Yang, J. 2005. Software assurance by bounded exhaustive testing. IEEE Transactions on Software Engineering 31, 4, 328–339.CrossRefGoogle Scholar
Corsini, M.-M., Musumbu, K., Rauzy, A. and Le Charlier, B. 1994. Efficient bottom-up abstract interpretation of Prolog by means of constraint solving over symbolic finite domains. In PLILP 1993. LNCS 714. Springer, 75–91.Google Scholar
Cousot, P. and Cousot, R. 1977. Abstract interpretation: A unified lattice model for static analysis of programs by construction of approximation of fixpoints. In POPL 1977. ACM Press, 238–252.Google Scholar
Cousot, P. and Cousot, R. 1992. Comparing the Galois connection and widening/ narrowing approaches to abstract interpretation. In PLILP 1992. LNCS 631. Springer, 269–295.Google Scholar
Cousot, P. and Halbwachs, N. 1978. Automatic discovery of linear restraints among variables of a program. In POPL 1978. ACM Press, 84–96.Google Scholar
Craig, S.-J. and Leuschel, M. 2003. A compiler generator for constraint logic programs. In PSI 2003. LNCS 2890. Springer, 148–161.Google Scholar
Craig, W. 1957. Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. The Journal of Symbolic Logic 22, 3, 269–285.CrossRefGoogle Scholar
Cui, B. and Warren, D. S. 2000. A system for tabled constraint logic programming. In Computational Logic 2000. LNCS 1861. Springer, 478–492.Google Scholar
De Angelis, E., Fioravanti, F., Meo, M. C., Pettorossi, A. and Proietti, M. 2019. Semantics and controllability of time-aware business processes. Fundamenta Informaticae 165, 205–244.CrossRefGoogle Scholar
De Angelis, E., Fioravanti, F., Palacios, A., Pettorossi, A. and Proietti, M. 2019. Property-based test case generators for free. In Tests and Proofs - TAP@FM 2019. LNCS 11823. Springer, 186–206.Google Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2014a. Program verification via iterated specialization. Science of Computer Programming 95, Part 2, 149–175.CrossRefGoogle Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2014b. VeriMAP: A tool for verifying programs through transformations. In TACAS 2014. LNCS 8413. Springer, 568–574.Google Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2015. Semantics-based generation of verification conditions by program specialization. In PPDP 2015. ACM Press, 91–102.Google Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2016. Relational verification through Horn clause transformation. In SAS 2016. LNCS 9837. Springer, 147–169.Google Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2017a. Predicate pairing with abstraction for relational verification. In LOPSTR 2017. LNCS 10855. Springer, 289–305.Google Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2017b. Semantics-based generation of verification conditions via program specialization. Science of Computer Programming 147, 78–108.Google Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2018a. Predicate pairing for program verification. Theory and Practice of Logic Programming 18, 2, 126–166.CrossRefGoogle Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2018b. Solving Horn clauses on inductive data types without induction. Theory and Practice of Logic Programming 18, 3–4, 452–469.CrossRefGoogle Scholar
De Angelis, E., Fioravanti, F., Pettorossi, A. and Proietti, M. 2020. Removing algebraic data types from constrained Horn clauses using difference predicates. In IJCAR 2020. Lecture Notes in Artificial Intelligence 12166. Springer, 83–102.Google Scholar
de Moura, L. M. and Bjørner, N. 2008. Z3: An efficient SMT solver. In TACAS 2008. LNCS 4963. Springer, 337–340.Google Scholar
De Schreye, D., Glück, R., Jørgensen, J., Leuschel, M., Martens, B. and Sørensen, M. H. 1999. Conjunctive partial deduction: Foundations, control, algorithms, and experiments. Journal of Logic Programming 41, 2–3, 231–277.CrossRefGoogle Scholar
Debray, S. and Ramakrishnan, R. 1994. Abstract interpretation of logic programs using magic transformations. Journal of Logic Programming 18, 149–176.CrossRefGoogle Scholar
Debray, S. K. and Lin, N. W. 1993. Cost analysis of logic programs. ACM Transactions on Programming Languages and Systems 15, 5, 826–875.CrossRefGoogle Scholar
Debray, S. K., Lin, N.-W. and Hermenegildo, M. 1990. Task granularity analysis in logic programs. In ACM PLDI 1990. ACM Press, 174–188.Google Scholar
Debray, S. K., López-García, P., Hermenegildo, M. and Lin, N.-W. 1997. Lower bound cost estimation for logic programs. In International Symposium on Logic Programming 1997. MIT Press, 291–305.Google Scholar
Delzanno, G. and Podelski, A. 1999. Model checking in CLP. In TACAS 1999. LNCS 1579. Springer, 223–239.Google Scholar
Delzanno, G. and Podelski, A. 2001. Constraint-based deductive model checking. International Journal on Software Tools for Technology Transfer 3, 3, 250–270.CrossRefGoogle Scholar
Demyanova, Y., Rümmer, P. and Zuleger, F. 2017. Systematic predicate abstraction using variable roles. In NASA Formal Methods. Springer Intl. Publishing, 265–281.Google Scholar
Doménech, J. J., Gallagher, J. P. and Genaim, S. 2019. Control-flow refinement by partial evaluation, and its application to termination and cost analysis. Theory and Practice of Logic Programming 19, 5-6, 990–1005.Google Scholar
Donzeau-Gouge, V., Huet, G., Kahn, G. and Lang, B. 1984. Programming environments based on structured editors: The MENTOR experience. In Interactive Programming Environments. McGraw-Hill, 128–140.Google Scholar
Dutertre, B. 2014. Yices 2.2. In CAV 2014. LNCS 8559. Springer, 737–744.Google Scholar
Een, N., Mishchenko, A. and Brayton, R. 2011. Efficient implementation of property directed reachability. In Formal Methods in Computer-Aided Design FMCAD, 125–134.Google Scholar
Enderton, H. 1972. A Mathematical Introduction to Logic. Academic Press, New York.Google Scholar
Esparza, J., Kiefer, S. and Luttenberger, M. 2010. Newtonian program analysis. Journal of the ACM 57, 6, 33.Google Scholar
Etalle, S. and Gabbrielli, M. 1996. Transformations of CLP modules. Theoretical Computer Science 166, 101–146.CrossRefGoogle Scholar
Fedyukovich, G., Zhang, Y. and Gupta, A. 2018. Syntax-guided termination analysis. In CAV 2018, Part I. LNCS 10981. Springer, 124–143.Google Scholar
Felsing, D., Grebing, S., Klebanov, V., Rümmer, P. and Ulbrich, M. 2014. Automating regression verification. In ASE 2014. ACM Press, 349–360.Google Scholar
Filliâtre, J. C. and Paskevich, A. 2013. Why3 — Where programs meet provers. In ESOP 2013. LNCS 7792. Springer, 125–128.Google Scholar
Fioravanti, F., Pettorossi, A., Proietti, M. and Senni, V. 2013. Controlling polyvariance for specialization-based verification. Fundamenta Informaticae 124, 4, 483–502.CrossRefGoogle Scholar
Fioravanti, F., Pettorossi, A. and Proietti, M. 2001a. Automated strategies for specializing constraint logic programs. In LOPSTR 2000. LNCS 2042. Springer, 125–146.Google Scholar
Fioravanti, F., Pettorossi, A. and Proietti, M. 2001b. Verifying CTL properties of infinite state systems by specializing constraint logic programs. In ACM Workshop VCL 2001. Technical Report DSSE-TR-2001-3. University of Southampton, UK, 85–96.Google Scholar
Fioravanti, F., Pettorossi, A. and Proietti, M. 2004. Transformation rules for locally stratified constraint logic programs. In Program Development in Computational Logic. LNCS 3049. Springer, 292–340.Google Scholar
Fioravanti, F., Pettorossi, A., Proietti, M. and Senni, V. 2012. Improving reachability analysis of infinite state systems by specialization. Fundamenta Informaticae 119, 3-4, 281–300.CrossRefGoogle Scholar
Fioravanti, F., Pettorossi, A., Proietti, M. and Senni, V. 2013a. Generalization strategies for the verification of infinite state systems. Theory and Practice of Logic Programming 13, 2, 175–199.CrossRefGoogle Scholar
Fioravanti, F., Pettorossi, A., Proietti, M. and Senni, V. 2013b. Proving theorems by program transformation. Fundamenta Informaticae 127, 1–4, 115–134.CrossRefGoogle Scholar
Fioravanti, F., Proietti, M. and Senni, V. 2015. Efficient generation of test data structures using constraint logic programming and program transformation. Journal of Logic and Computation 25, 6, 1263–1283.CrossRefGoogle Scholar
Flanagan, C. and Godefroid, P. 2005. Dynamic partial-order reduction for model checking software. In POPL 2005. ACM Press, 110–121.Google Scholar
Fribourg, L. and Olsén, H. 1997. A decompositional approach for computing least fixed-points of Datalog programs with Z-counters. Constraints 2, 3/4, 305–335.Google Scholar
Frühwirth, T. 1998. Theory and practice of constraint handling rules. Journal of Logic Programming 37, 1, 95–138.CrossRefGoogle Scholar
Futamura, Y. 1971. Partial evaluation of computation process – an approach to a compiler-compiler. Systems, Computers, Controls 2(5), 45–50.Google Scholar
Gallagher, J. P. 1993. Tutorial on specialisation of logic programs. In PEPM 1993. ACM Press, 88–98.Google Scholar
Gallagher, J. P., Boulanger, D. and Sağlam, H. 1995. Practical model-based static analysis for definite logic programs. In International Symposium on Logic Programming MIT Press, 351–365.Google Scholar
Gallagher, J. P. and de Waal, D. A. 1994. Fast and precise regular approximation of logic programs. In 11th International Conference on Logic Programming MIT Press, 599–613.Google Scholar
Gallagher, J. P., Hermenegildo, M., Kafle, B., Klemen, M., López-García, P. and Morales, J. F. 2020. From big-step to small-step semantics and back with interpreter specialization. In VPT 2020. Electronic Proceedings in Theoretical Computer Science 320, 50–64.Google Scholar
Gange, G., Navas, J., Schachte, P., Søndergaard, H. and Stuckey, P. 2013. Failure tabled constraint logic programming by interpolation. Theory and Practice of Logic Programming 13, 4–5, 593–607.CrossRefGoogle Scholar
Gange, G., Navas, J. A., Schachte, P., Søndergaard, H. and Stuckey, P. J. 2015. Horn clauses as an intermediate representation for program analysis and transformation. Theory and Practice of Logic Programming 15, 4–5, 526–542.CrossRefGoogle Scholar
García-Contreras, I., Morales, J. F. and Hermenegildo, M. 2020a. Incremental analysis of logic programs with assertions and open predicates. In LOPSTR 2019. LNCS 12042. Springer, 36–56.Google Scholar
García-Contreras, I., Morales, J. F. and Hermenegildo, M. 2020b. Incremental and modular context-sensitive analysis. Theory and Practice of Logic Programming (to appear).CrossRefGoogle Scholar
Garca de la Banda, M. and Hermenegildo, M. 1993. A practical approach to the global analysis of constraint logic programs. In Logic Programming Symposium MIT Press, 437–455.Google Scholar
Garca de la Banda, M., Hermenegildo, M., Bruynooghe, M., Dumortier, V., Janssens, G. and Simoens, W. 1996. Global analysis of constraint logic programs. ACM Transactions on Programming Languages and Systems 18, 5, 564–615.CrossRefGoogle Scholar
Giannotti, F. and Hermenegildo, M. 1991. A technique for recursive invariance detection and selective program specialization. In PLILP 1991. LNCS 528. Springer, 323–335.Google Scholar
Godefroid, P., Klarlund, N. and Sen, K. 2005. DART: Directed automated random testing. In PLDI 2005. ACM Press, 213–223.Google Scholar
Godlin, B. and Strichman, O. 2008. Inference rules for proving the equivalence of recursive procedures. Acta Informatica 45, 6, 403–439.CrossRefGoogle Scholar
Goguen, J. A. and Meseguer, J. 1982. Security policies and security models. In 1982 IEEE Symposium on Security and Privacy. 11–20.CrossRefGoogle Scholar
Gómez-Zamalloa, M., Albert, E. and Puebla, G. 2009. Decompilation of Java bytecode to Prolog by partial evaluation. Information and Software Technology 51, 10, 1409–1427.CrossRefGoogle Scholar
Gómez-Zamalloa, M., Albert, E. and Puebla, G. 2010. Test case generation for object-oriented imperative languages in CLP. Theory and Practice of Logic Programming 10, 4–6, 659–674.CrossRefGoogle Scholar
Gotlieb, A., Botella, B. and Rueher, M. 1998. Automatic test data generation using constraint solving techniques. In ACM Software Testing and Analysis Symposium. ACM Press, 53–62.Google Scholar
Graf, S. and Saïdi, H. 1997. Construction of abstract state graphs with PVS. In CAV 1997. LNCS 1254. Springer, 72–83.Google Scholar
Grebenshchikov, S., Lopes, N. P., Popeea, C. and Rybalchenko, A. 2012. Synthesizing software verifiers from proof rules. In PLDI 2012. ACM Press, 405–416.Google Scholar
Grishchenko, I., Maffei, M. and Schneidewind, C. 2018. Foundations and tools for the static analysis of Ethereum smart contracts. In CAV 2018, Part I. LNCS 10981. Springer, 51–78.Google Scholar
Gulwani, S., Jain, S. and Koskinen, E. 2009. Control-flow refinement and progress invariants for bound analysis. In PLDI 2009. ACM Press, 375–385.Google Scholar
Gupta, G., Bansal, A., Min, R., Simon, L. and Mallya, A. 2007. Coinductive logic programming and its applications. In ICLP 2007. LNCS 4670. Springer, 27–44.Google Scholar
Gurfinkel, A., Kahsai, T., Komuravelli, A. and Navas, J. A. 2015. The SeaHorn verification framework. In CAV 2015. LNCS 9206. Springer, 343–361.Google Scholar
Hamza, J., Voirol, N. and Kunčak, V. 2019. System FR: Formalized foundations for the Stainless verifier. Proceedings of the ACM on Programming Languages 3, OOPSLA, 166:1–166:30.Google Scholar
Heizmann, M., Hoenicke, J. and Podelski, A. 2009. Refinement of trace abstraction. In SAS 2009. LNCS 5673. Springer, 69–85.Google Scholar
Henriksen, K. S. and Gallagher, J. P. 2006. Abstract interpretation of PIC programs through logic programming. In SCAM 2006. IEEE Computer Society, 184–196.Google Scholar
Hermenegildo, M., Bueno, F., Carro, M., López-García, P., Mera, E., Morales, J. F. and Puebla, G. 2012. An overview of Ciao and its design philosophy. Theory and Practice of Logic Programming 12, 1–2, 219–252.CrossRefGoogle Scholar
Hermenegildo, M., Puebla, G. and Bueno, F. 1999. Using global analysis, partial specifications, and an extensible assertion language for program validation and debugging. In The Logic Programming Paradigm: A 25-Year Perspective. Springer, 161–192.Google Scholar
Hermenegildo, M., Puebla, G., Bueno, F. and López-García, P. 2005. Integrated program debugging, verification, and optimization using abstract interpretation (and the Ciao system preprocessor). Science of Computer Programming 58, 1–2, 115–140.Google Scholar
Hermenegildo, M., Puebla, G., Marriott, K. and Stuckey, P. 2000. Incremental analysis of constraint logic programs. ACM TOPLAS 22, 2, 187–223.Google Scholar
Hermenegildo, M., Warren, R. and Debray, S. K. 1992. Global flow analysis as a practical compilation tool. Journal of Logic Programming 13, 4, 349–367.CrossRefGoogle Scholar
Hoare, C. A. R. 1969. An axiomatic basis for computer programming. Communications of the ACM 12, 10, 576–580, 583.CrossRefGoogle Scholar
Hoder, K. and Bjørner, N. 2012. Generalized property directed reachability. In SAT 2012. LNCS 7317. Springer, 157–171.Google Scholar
Hojjat, H. and Rümmer, P. 2018. The ELDARICA Horn solver. In Formal Methods in Computer Aided Design 2018. IEEE, 1–7.Google Scholar
Jacobs, D., Langen, A. and Winsborough, W. 1990. Multiple specialization of logic programs with run-time tests. In International Conference on Logic Programming. MIT Press, 718–731.Google Scholar
Jaffar, J. 1984. Efficient unification over infinite terms. New Gener. Comput. 2, 3, 207–219.CrossRefGoogle Scholar
Jaffar, J. and Lassez, J.-L. 1987. Constraint logic programming. In POPL 1987. ACM Press, 111–119.Google Scholar
Jaffar, J. and Maher, M. 1994. Constraint logic programming: A survey. Journal of Logic Programming 19/20, 503–581.Google Scholar
Jaffar, J., Maher, M., Marriott, K. and Stuckey, P. 1998. The semantics of constraint logic programs. Journal of Logic Programming 37, 1–46.Google Scholar
Jaffar, J., Michaylov, S., Stuckey, P. J. and Yap, R. H. C. 1992. The CLP(R) language and system. ACM Transactions on Programming Languages and Systems 14, 3, 339–395.CrossRefGoogle Scholar
Jaffar, J., Murali, V., Navas, J. A. and Santosa, A. E. 2012. TRACER: A symbolic execution tool for verification. In CAV 2012. LNCS 7358. Springer, 758–766.Google Scholar
Jaffar, J., Santosa, A. and Voicu, R. 2009. An interpolation method for CLP traversal. In CP 2009. LNCS 5732. Springer, 454–469.Google Scholar
Jaffar, J., Santosa, A. E. and Voicu, R. 2004. A CLP proof method for timed automata. In IEEE Real-Time Systems Symposium. IEEE Computer Society, 175–186.Google Scholar
Jeannet, B. and Miné, A. 2009. Apron: A library of numerical abstract domains for static analysis. In CAV 2009. LNCS 5643. Springer, 661–667.Google Scholar
Jhala, R. and Majumdar, R. 2009. Software model checking. ACM Computing Surveys 41, 4, 21:1–21:54.Google Scholar
Jones, N. D., Gomard, C. K. and Sestoft, P. 1993. Partial Evaluation and Automatic Program Generation. Prentice Hall.Google Scholar
Jovanovic, D. and de Moura, L. 2012. Solving non-linear arithmetic. In IJCAR 2012. LNCS 7364. Springer, 339–354.Google Scholar
Kafle, B. and Gallagher, J. P. 2017a. Constraint specialisation in Horn clause verification. Science of Computer Programming 137, 125–140.CrossRefGoogle Scholar
Kafle, B. and Gallagher, J. P. 2017b. Horn clause verification with convex polyhedral abstraction and tree automata-based refinement. Computer Languages, Systems and Structures 47, 2–18.CrossRefGoogle Scholar
Kafle, B., Gallagher, J. P., Gange, G., Schachte, P., Søndergaard, H. and Stuckey, P. J. 2018. An iterative approach to precondition inference using constrained Horn clauses. Theory and Practice of Logic Programming 18, 3–4, 553–570.CrossRefGoogle Scholar
Kafle, B., Gallagher, J. P. and Ganty, P. 2018. Tree dimension in verification of constrained Horn clauses. Theory and Practice of Logic Programming 18, 2, 224–251.CrossRefGoogle Scholar
Kafle, B., Gallagher, J. P. and Morales, J. F. 2016. RAHFT: A tool for verifying Horn clauses using abstract interpretation and finite tree automata. In CAV 2016, Part I. LNCS 9779. Springer, 261–268.Google Scholar
Kahn, G. 1987. Natural semantics. LNCS 247. Springer, 22–39.Google Scholar
Kahsai, T., Rümmer, P., Sanchez, H. and Schäf, M. 2016. JayHorn: A framework for verifying Java programs. In CAV 2016, Part I. LNCS 9779. Springer, 352–358.Google Scholar
Kalra, S., Goel, S., Dhawan, M. and Sharma, S. 2018. Zeus: Analyzing safety of smart contracts. In 25th Network and Distributed System Security Symposium The Internet Society, 1–15.Google Scholar
Kanamori, T. 1993. Abstract interpretation based on Alexander templates. Journal of Logic Programming 15, 1&2, 31–54.Google Scholar
Kelly, A., Marriott, K., Søndergaard, H. and Stuckey, P. 1998. A practical object-oriented analysis engine for CLP. Software: Practice and Experience 28, 2, 188–224.Google Scholar
Khedker, U. P. and Karkare, B. 2008. Efficiency, precision, simplicity, and generality in interprocedural data flow analysis: Resurrecting the classical call strings method. In CC 2008. LNCS 4959. Springer, 213–228.Google Scholar
Kimmig, A., Demoen, B., Raedt, L. D., Costa, V. S. and Rocha, R. 2011. On the implementation of the probabilistic logic programming language ProbLog. Theory and Practice of Logic Programming 11, 2–3, 235–262.Google Scholar
Kirkeby, M. H. 2019. Probabilistic output analyses for deterministic programs - reusing existing non-probabilistic analyses. Electronic Proceedings in Theoretical Computer Science 312, 43–57.Google Scholar
Klemen, M., Stulova, N., López-García, P., Morales, J. F. and Hermenegildo, M. 2018. Static performance guarantees for programs with run-time checks. In PPDP 2018. ACM Press, 1–13.Google Scholar
Komuravelli, A., Gurfinkel, A. and Chaki, S. 2016. SMT-based model checking for recursive programs. Formal Methods in System Design 48, 3, 175–205.Google Scholar
Komuravelli, A., Gurfinkel, A., Chaki, S. and Clarke, E. M. 2013. Automatic abstraction in SMT-based unbounded software model checking. In CAV 2013. LNCS 8044. Springer, 846–862.Google Scholar
Kowalski, R. and Kuehner, D. 1971. Linear resolution with selection function. Artificial Intelligence 2, 227–260.CrossRefGoogle Scholar
Lahiri, S. K., McMillan, K. L., Sharma, R. and Hawblitzel, C. 2013. Differential assertion checking. In ESEC/FSE 2013. ACM Press, 345–355.Google Scholar
Le Charlier, B. and Van Hentenryck, P. 1994. Experimental evaluation of a generic abstract interpretation algorithm for Prolog. ACM TOPLAS 16, 1, 35–101.Google Scholar
Leavens, G. T., Baker, A. L. and Ruby, C. 2006. Preliminary design of JML: A behavioral interface specification language for Java. Software Engineering Notes 31, 3, 1–38.Google Scholar
Leino, K. R. M. 2013. Developing verified programs with Dafny. In International Conference on Software Engineering 2013. IEEE Press, 1488–1490.Google Scholar
Leroy, X., Doligez, D., Frisch, A., Garrigue, J., Rémy, D. and Vouillon, J. 2017. The OCaml system, Release 4.06. Documentation and user’s manual, Institut National de Recherche en Informatique et en Automatique, France.Google Scholar
Leuschel, M. and Bruynooghe, M. 2002. Logic program specialisation through partial deduction: Control issues. Theory and Practice of Logic Programming 2, 4&5, 461–515.Google Scholar
Leuschel, M. and De Schreye, D. 1998. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing 16, 3, 283–342.CrossRefGoogle Scholar
Leuschel, M., Elphick, D., Varea, M., Craig, S., and Fontaine, M. 2006. The Ecce and Logen partial evaluators and their web interfaces. In PEPM 2006. ACM Press, 88–94.Google Scholar
Leuschel, M. and Lehmann, H. 2000. Coverability of reset Petri nets and other well-structured transition systems by partial deduction. In CL 2000. Lecture Notes in Artificial Intelligence 1861. Springer, 101–115.Google Scholar
Leuschel, M., Martens, B. and De Schreye, D. 1998. Controlling generalization and polyvariance in partial deduction of normal logic programs. ACM Transactions on Programming Languages and Systems 20, 1, 208–258.CrossRefGoogle Scholar
Leuschel, M. and Massart, T. 2000. Infinite state model checking by abstract interpretation and program specialisation. In LOPSTR 1999. LNCS 1817. Springer, 63–82.Google Scholar
Leuschel, M. and Sørensen, M. H. 1996. Redundant argument filtering of logic programs. In LOPSTR 1996. LNCS 1207. Springer, 83–103.Google Scholar
Leuschel, M. and Vidal, G. 2005. Forward slicing by conjunctive partial deduction and argument filtering. In ESOP 2005. LNCS 3444. Springer, 61–76.Google Scholar
Liang, T., Reynolds, A., Tsiskaridze, N., Tinelli, C., Barrett, C. W. and Deters, M. 2016. An efficient SMT solver for string constraints. Formal Methods in System Design 48, 3, 206–234.CrossRefGoogle Scholar
Liqat, U., Georgiou, K., Kerrison, S., López-García, P., Hermenegildo, M., Gallagher, J. P., and Eder, K. 2016. Inferring parametric energy consumption functions at different software levels: ISA vs. LLVM IR. In FOPARA 2015. LNCS 9964. Springer, 81–100.Google Scholar
Liqat, U., Kerrison, S., Serrano, A., Georgiou, K., López-García, P., Grech, N., Hermenegildo, M. and Eder, K. 2014. Energy consumption analysis of programs based on XMOS ISA-level models. In LOPSTR 2013. LNCS 8901. Springer, 72–90.Google Scholar
Lloyd, J. 1987. Foundations of Logic Programming. Springer. 2nd Extended Edition.CrossRefGoogle Scholar
Lloyd, J. W. and Shepherdson, J. C. 1991. Partial evaluation in logic programming. Journal of Logic Programming 11, 217–242.CrossRefGoogle Scholar
Lopes, N. P. and Monteiro, J. 2016. Automatic equivalence checking of programs with uninterpreted functions and integer arithmetic. International Journal on Software Tools for Technology Transfer 18, 4, 359–374.CrossRefGoogle Scholar
López-García, P., Darmawan, L., Bueno, F. and Hermenegildo, M. 2012. Interval-based resource usage verification: Formalization and prototype. In FOPARA 2011. LNCS 7177. Springer, 54–71.Google Scholar
López-García, P., Darmawan, L., Klemen, M., Liqat, U., Bueno, F. and Hermenegildo, M. 2018. Interval-based resource usage verification by translation into Horn clauses and an application to energy consumption. Theory and Practice of Logic Programming 18, 2, 167–223.Google Scholar
López-García, P., Haemmerlé, R., Klemen, M., Liqat, U. and Hermenegildo, M. 2015. Towards energy consumption verification via static analysis. In HIP3ES Workshop. arXiv:1512.09369.Google Scholar
López-García, P., Klemen, M., Liqat, U. and Hermenegildo, M. 2016. A general framework for static profiling of parametric resource usage. Theory and Practice of Logic Programming 16, 5–6, 849–865.CrossRefGoogle Scholar
Madhusudan, P., Parlato, G. and Qiu, X. 2011. Decidable logics combining heap structures and data. In POPL 2011. ACM Press, 611–622.Google Scholar
Marriott, K. and Søndergaard, H. 1988. Bottom-up abstract interpretation of logic programs. In Conference and Symposium on Logic Programming. MIT Press, 733–748.Google Scholar
Martens, B. and Gallagher, J. P. 1995. Ensuring global termination of partial deduction while allowing flexible polyvariance. In ICLP 1995. MIT Press, 597–611.Google Scholar
Matiyasevich, J. V. 1970. Enumerable sets are diophantine. Doklady Akademii Nauk SSSR 191, 279–282. In English: Soviet Mathematics–Doklady, 11 (1970), 354–357.Google Scholar
McMillan, K. L. 2013. Logic as the lingua franca of software verification. Invited talk at the VMCAI 2013, Rome, Italy. Slides at https://studylib.net/doc/9889611/ Google Scholar
McMillan, K. L. and Rybalchenko, A. 2013. Solving constrained Horn clauses using interpolation. MSR Tech. Rep. 2013-6, Microsoft Research, Redmond, WA, USA.Google Scholar
Mendelson, E. 1997. Introduction to Mathematical Logic. Chapman&Hall. 4th Edition.Google Scholar
Méndez-Lojo, M., Navas, J. and Hermenegildo, M. 2007. A flexible (C)LP-based approach to the analysis of object-oriented programs. In LOPSTR 2007. LNCS 4915. Springer, 154–168.Google Scholar
Mesnard, F., Payet, É. and Vidal, G. 2020. Concolic testing in CLP. Theory Pract. Log. Program. 20, 5, 671–686.CrossRefGoogle Scholar
Meudec, C. 2001. ATGen: Automatic test data generation using constraint logic programming and symbolic execution. Software Testing, Verification & Reliability 11, 2, 81–96.CrossRefGoogle Scholar
Meyer, B. 1988. Object-oriented Software Construction. Prentice Hall.Google Scholar
Monniaux, D. 2000. Abstract interpretation of probabilistic semantics. In SAS 2000. LNCS 1824. Springer, 322–339.Google Scholar
Mordvinov, D. and Fedyukovich, G. 2017. Synchronizing constrained Horn clauses. In LPAR-21. EPiC Series in Computing, vol. 46. EasyChair, 338–355.Google Scholar
Mordvinov, D. and Fedyukovich, G. 2019. Property directed inference of relational invariants. In Formal Methods in Computer Aided Design 2019. IEEE, 152–160.Google Scholar
Muthukumar, K. and Hermenegildo, M. 1990. Deriving a fixpoint computation algorithm for top-down abstract interpretation of logic programs. Techn. Rep. ACT-DC-153-90, MCC, Austin, TX 78759.Google Scholar
Muthukumar, K. and Hermenegildo, M. 1992. Compile-time derivation of variable dependency using abstract interpretation. Journal of Logic Programming 13, 2/3, 315–347.Google Scholar
Navas, J., Méndez-Lojo, M. and Hermenegildo, M. 2008. Safe upper-bounds inference of energy consumption for Java bytecode applications. In NASA Langley Formal Methods Workshop, 29–32.Google Scholar
Navas, J., Méndez-Lojo, M. and Hermenegildo, M. 2009. User-definable resource usage bounds analysis for Java bytecode. In BYTECODE 2009 Workshop. Electronic Notes in Theoretical Computer Science 253, 5. Elsevier, 65–82.Google Scholar
Navas, J., Mera, E., López-García, P. and Hermenegildo, M. 2007. User-definable resource bounds analysis for logic programs. In ICLP 2007. LNCS 4670. Springer, 348–363.Google Scholar
Nelson, G. and Oppen, D. C. 1979. Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems 1, 2, 245–257.CrossRefGoogle Scholar
Nielson, H. R. and Nielson, F. 1992. Semantics With Applications - A Formal Introduction . Wiley Professional Computing. Wiley.Google Scholar
Nilsson, U. 1995. Abstract interpretation: A kind of magic. Theoretical Computer Science 142, 1, 125–139.CrossRefGoogle Scholar
Nipkow, T., Wenzel, M. and Paulson, L. C. 2002. Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Springer.CrossRefGoogle Scholar
Ochoa, C., Puebla, G. and Hermenegildo, M. 2006. Removing superfluous versions in polyvariant specialization of Prolog programs. In LOPSTR 2005. LNCS 3901. Springer, 80–97.Google Scholar
Peralta, J. C. and Gallagher, J. P. 2003. Convex hull abstractions in specialization of CLP programs. In LOPSTR 2002. LNCS 2664. Springer, 90–108.Google Scholar
Peralta, J. C., Gallagher, J. P. and Saglam, H. 1998. Analysis of imperative programs through analysis of constraint logic programs. In SAS 1998. LNCS 1503. Springer, 246–261.Google Scholar
Pérez-Carrasco, V., Klemen, M., López-García, P., Morales, J. F. and Hermenegildo, M. 2020. Cost analysis of smart contracts via parametric resource analysis. In SAS 2020. LNCS 12389. Springer.CrossRefGoogle Scholar
Pettorossi, A. and Proietti, M. 1994. Transformation of logic programs: Foundations and techniques. Journal of Logic Programming 19–20, 261–320.CrossRefGoogle Scholar
Plotkin, G. 1981. A structural approach to operational semantics. Technical report DAIMI FN-19, Computer Science Department, Aarhus University, Denmark.Google Scholar
Proietti, M. and Pettorossi, A. 1993. The loop absorption and the generalization strategies for the development of logic programs and partial deduction. Journal of Logic Programming 16, 1–2, 123–161.CrossRefGoogle Scholar
Proietti, M. and Pettorossi, A. 1995. Unfolding-definition-folding, in this order, for avoiding unnecessary variables in logic programs. Theoretical Computer Science 142, 1, 89–124.CrossRefGoogle Scholar
Puebla, G., Albert, E. and Hermenegildo, M. 2006. Abstract interpretation with specialized definitions. In SAS 2006. LNCS 4134. Springer, 107–126.Google Scholar
Puebla, G., Bueno, F. and Hermenegildo, M. 2000. Combined static and dynamic assertion-based debugging of constraint logic programs. In LOPSTR 1999. LNCS 1817. Springer, 273–292.Google Scholar
Puebla, G. and Hermenegildo, M. 1996. Optimized algorithms for the incremental analysis of logic programs. In SAS 1996. LNCS 1145. Springer, 270–284.Google Scholar
Puebla, G. and Hermenegildo, M. 1999. Abstract multiple specialization and its application to program parallelization. Journal of Logic Programming 41, 2&3, 279–316.Google Scholar
Puebla, G., Hermenegildo, M. and Gallagher, J. P. 1999. An integration of partial evaluation in a generic abstract interpretation framework. In ACM SIGPLAN PEPM 1999. BRISC Series NS-99-1. University of Aarhus, Denmark, 75–85.Google Scholar
Reps, T. W., Horwitz, S. and Sagiv, S. 1995. Precise interprocedural dataflow analysis via graph reachability. In POPL 1995. ACM Press, 49–61.Google Scholar
Reynolds, A. and Kunčak, V. 2015. Induction for SMT solvers. In VMCAI 2015. LNCS 8931. Springer, 80–98.Google Scholar
Rohmer, J., Lescoeur, R. and Kerisit, J. 1986. The Alexander method - A technique for the processing of recursive axioms in deductive databases. New Generation Computing 4, 3, 273–285.CrossRefGoogle Scholar
Rosu, G. and Serbanuta, T. 2010. An overview of the K semantic framework. Journal of Logic and Algebraic Programming 79, 6, 397–434.CrossRefGoogle Scholar
Roychoudhury, A., Kumar, K. N., Ramakrishnan, C. R., and Ramakrishnan, I. V. 2002. Beyond Tamaki-Sato style unfold/fold transformations for normal logic programs. International Journal on Foundations of Computer Science 13, 3, 387–403.CrossRefGoogle Scholar
Roychoudhury, A., Kumar, K. N., Ramakrishnan, C. R., Ramakrishnan, I. V. and Smolka, S. A. 2000. Verification of parameterized systems using logic program transformations. In TACAS 2000. LNCS 1785. Springer, 172–187.Google Scholar
Rümmer, P. 2020. Competition Report: CHC-COMP-20. Tech. Rep. Available at https://chc-comp.github.io/report.pdf CrossRefGoogle Scholar
Sahlin, D. 1993. Mixtus: An automatic partial evaluator for full Prolog. New Generation Computing 12, 7–51.CrossRefGoogle Scholar
Sato, T. and Kameya, Y. 1997. PRISM: A language for symbolic-statistical modeling. In 15th IJCAI 1997. Morgan Kaufmann, 1330–1339.Google Scholar
Schneidewind, C., Grishchenko, I., Scherer, M. and Maffei, M. 2020. eThor: Practical and provably sound static analysis of Ethereum smart contracts. In CCS 2020: ACM Conference on Computer and Communications Security. ACM Press, 621–640.Google Scholar
Schrijver, A. 1998. Theory of Linear and Integer Programming. John Wiley & Sons.Google Scholar
Seki, H. 1991. Unfold/fold transformation of stratified programs. Theoretical Computer Science 86, 107–139.CrossRefGoogle Scholar
Seki, H. 2012. Proving properties of co-logic programs by unfold/fold transformations. In LOPSTR 2011. LNCS 7225. Springer, 205–220.Google Scholar
Senni, V. and Fioravanti, F. 2012. Generation of test data structures using constraint logic programming. In Tests and Proofs. LNCS 7305. Springer, 115–131.Google Scholar
Serrano, A., López-García, P. and Hermenegildo, M. 2014. Resource usage analysis of logic programs via abstract interpretation using sized types. Theory and Practice of Logic Programming 14, 4–5, 739–754.CrossRefGoogle Scholar
Sharir, M. and Pnueli, A. 1981. Two approaches to interprocedural data flow analysis. In Program Flow Analysis: Theory and Applications. Prentice-Hall, Chapter 7, 189–233.Google Scholar
Shemer, R., Gurfinkel, A., Shoham, S. and Vizel, Y. 2019. Property directed self composition. In CAV 2019, Part I. LNCS 11561. Springer, 161–179.Google Scholar
Shoenfield, J. R. 1967. Mathematical Logic. Addison-Wesley Publishing Company.Google Scholar
Spoto, F., Mesnard, F. and Payet, É. 2010. A termination analyzer for Java bytecode based on path-length. ACM Transactions on Programming Languages and Systems 32, 3, 8:1–8:70.Google Scholar
Suter, P., Köksal, A. S. and Kunčak, V. 2011. Satisfiability modulo recursive programs. In SAS 2011. LNCS 6887. Springer, 298–315.Google Scholar
Tamaki, H. and Sato, T. 1984. Unfold/fold transformation of logic programs. In ICLP 1984, S.-Å. Tärnlund, Ed. University, Uppsala, Uppsala, Sweden, 127–138.Google Scholar
Tärnlund, S. 1977. Horn clause computability. BIT 17, 2, 215–226.CrossRefGoogle Scholar
Tarski, A. 1955. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5, 285–309.CrossRefGoogle Scholar
Thakur, M. and Nandivada, V. K. 2020. Mix your contexts well: Opportunities unleashed by recent advances in scaling context-sensitivity. In Conference on Compiler Construction. ACM Press, 27–38.Google Scholar
Tsankov, P., Dan, A. M., Drachsler-Cohen, D., Gervais, A., Bünzli, F. and Vechev, M. T. 2018. Securify: Practical security analysis of smart contracts. In ACM Conference on Computer and Communications Security. ACM Press, 67–82.Google Scholar
Unno, H., Torii, S. and Sakamoto, H. 2017. Automating induction for solving Horn clauses. In CAV 2017, Part II. LNCS 10427. Springer, 571–591.Google Scholar
Verschaetse, K. and De Schreye, D. 1992. Derivation of linear size relations by abstract interpretation. In PLILP 1992. LNCS 631. Springer, 296–310.Google Scholar
Wadler, P. L. 1990. Deforestation: Transforming programs to eliminate trees. Theoretical Computer Science 73, 231–248.CrossRefGoogle Scholar
Wang, W. and Jiao, L. 2016. Trace abstraction refinement for solving Horn clauses. The Computer Journal 59, 8, 1236–1251.CrossRefGoogle Scholar
Warren, D. S. 1992. Memoing for logic programs. Communications of the ACM 35, 3, 93–111.CrossRefGoogle Scholar
Warren, R., Hermenegildo, M. and Debray, S. K. 1988. On the practicality of global flow analysis of logic programs. In Conference and Symposium on Logic Programming. MIT Press, 684–699.Google Scholar
Wybraniec-Skardowska, U. 2019. On certain axiomatizations of arithmetic of natural and integer numbers. Axioms 8, 3. doi: 10.3390/axioms8030103.CrossRefGoogle Scholar
Zaks, A. and Pnueli, A. 2008. CoVaC: Compiler validation by program analysis of the cross-product. In International Symposium on Formal Methods. LNCS 5014. Springer, 35–51.Google Scholar
Zhou, Q., Heath, D. and Harris, W. 2019. Relational verification via invariant-guided synchronization. In HCVS/PERR@ETAPS 2019. Electronic Proceedings in Theoretical Computer Science 296, 28–41.Google Scholar