Correctness and completeness of logic programs

We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we show how to prove completeness and correctness in the presence of SLD-tree pruning, and point out that approximate specifications simplify specifications and proofs. We compare the proof methods to declarative diagnosis (algorithmic debugging), showing that approximate specifications eliminate a major drawback of the latter. We argue that our proof methods reflect natural declarative thinking about programs, and that they can be used, formally or informally, in every-day programming.Comment: 29 pages, 2 figures; with editorial modifications, small corrections and extensions. arXiv admin note: text overlap with arXiv:1411.3015. Overlaps explained in "Related Work" (p. 21

Declarative Debugging of Missing Answers for Maude

Declarative debugging is a semi-automatic technique that starts from an incorrect computation and locates a program fragment responsible for the error by building a tree representing this computation and guiding the user through it to find the error. Membership equational logic (MEL) is an equational logic that in addition to equations allows the statement of membership axioms characterizing the elements of a sort. Rewriting logic is a logic of change that extends MEL by adding rewrite rules, that correspond to transitions between states and can be nondeterministic. In this paper we propose a calculus that allows to infer normal forms and least sorts with the equational part, and sets of reachable terms through rules. We use an abbreviation of the proof trees computed with this calculus to build appropriate debugging trees for missing answers (results that are erroneous because they are incomplete), whose adequacy for debugging is proved. Using these trees we have implemented a declarative debugger for Maude, a high-performance system based on rewriting logic, whose use is illustrated with an example

A Survey of Algorithmic Debugging

"© ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Computing Surveys, {50, 4, 2017} https://dl.acm.org/doi/10.1145/3106740"[EN] Algorithmic debugging is a technique proposed in 1982 by E. Y. Shapiro in the context of logic programming. This survey shows how the initial ideas have been developed to become a widespread debugging schema ftting many diferent programming paradigms and with applications out of the program debugging feld. We describe the general framework and the main issues related to the implementations in diferent programming paradigms and discuss several proposed improvements and optimizations. We also review the main algorithmic debugger tools that have been implemented so far and compare their features. From this comparison, we elaborate a summary of desirable characteristics that should be considered when implementing future algorithmic debuggers.This work has been partially supported by the EU (FEDER) and the Spanish Ministerio de Economia y Competitividad under grant TIN2013-44742-C4-1-R, TIN2016-76843-C4-1-R, StrongSoft (TIN2012-39391-C04-04), and TRACES (TIN2015-67522-C3-3-R) by the Generalitat Valenciana under grant PROMETEO-II/2015/013 (SmartLogic) and by the Comunidad de Madrid project N-Greens Software-CM (S2013/ICE-2731).Caballero, R.; Riesco, A.; Silva, J. (2017). A Survey of Algorithmic Debugging. ACM Computing Surveys. 50(4):1-35. https://doi.org/10.1145/3106740S135504Abramson, D., Foster, I., Michalakes, J., & Sosič, R. (1996). Relative debugging. Communications of the ACM, 39(11), 69-77. doi:10.1145/240455.240475K. R. Apt H. A. Blair and A. Walker. 1988. Towards a theory of declarative knowledge. In Foundations of Deductive Databases and Logic Programming J. Minker (Ed.). Morgan Kaufmann Publishers Inc. San Francisco CA 89--148. 10.1016/B978-0-934613-40-8.50006-3 K. R. Apt H. A. Blair and A. Walker. 1988. Towards a theory of declarative knowledge. In Foundations of Deductive Databases and Logic Programming J. Minker (Ed.). Morgan Kaufmann Publishers Inc. San Francisco CA 89--148. 10.1016/B978-0-934613-40-8.50006-3Arora, T., Ramakrishnan, R., Roth, W. G., Seshadri, P., & Srivastava, D. (1993). Explaining program execution in deductive systems. Lecture Notes in Computer Science, 101-119. doi:10.1007/3-540-57530-8_7E. Av-Ron. 1984. Top-Down Diagnosis of Prolog Programs. Ph.D. Dissertation. Weizmann Institute. E. Av-Ron. 1984. Top-Down Diagnosis of Prolog Programs. Ph.D. Dissertation. Weizmann Institute.A. Beaulieu. 2005. Learning SQL. O’Reilly Farnham UK. A. Beaulieu. 2005. Learning SQL. O’Reilly Farnham UK.D. Binks. 1995. Declarative Debugging in Gödel. Ph.D. Dissertation. University of Bristol. D. Binks. 1995. Declarative Debugging in Gödel. Ph.D. Dissertation. University of Bristol.B. Braßel and H. Siegel. 2008. Debugging Lazy Functional Programs by Asking the Oracle. Springer-Verlag Berlin 183--200. DOI:http://dx.doi.org/10.1007/978-3-540-85373-2_11 10.1007/978-3-540-85373-2_11 B. Braßel and H. Siegel. 2008. Debugging Lazy Functional Programs by Asking the Oracle. Springer-Verlag Berlin 183--200. DOI:http://dx.doi.org/10.1007/978-3-540-85373-2_11 10.1007/978-3-540-85373-2_11Caballero, R. (2005). A declarative debugger of incorrect answers for constraint functional-logic programs. Proceedings of the 2005 ACM SIGPLAN workshop on Curry and functional logic programming - WCFLP ’05. doi:10.1145/1085099.1085102Caballero, R., García-Ruiz, Y., & Sáenz-Pérez, F. (2012). Declarative Debugging of Wrong and Missing Answers for SQL Views. Lecture Notes in Computer Science, 73-87. doi:10.1007/978-3-642-29822-6_9Caballero, R., García-Ruiz, Y., & Sáenz-Pérez, F. (2015). Debugging of wrong and missing answers for datalog programs with constraint handling rules. Proceedings of the 17th International Symposium on Principles and Practice of Declarative Programming - PPDP ’15. doi:10.1145/2790449.2790522Caballero, R., Martin-Martin, E., Riesco, A., & Tamarit, S. (2015). A zoom-declarative debugger for sequential Erlang programs. Science of Computer Programming, 110, 104-118. doi:10.1016/j.scico.2015.06.011Caballero, R., & Rodríguez-Artalejo, M. (2002). A Declarative Debugging System for Lazy Functional Logic Programs. Electronic Notes in Theoretical Computer Science, 64, 113-175. doi:10.1016/s1571-0661(04)80349-9Ceri, S., Gottlob, G., & Tanca, L. (1989). What you always wanted to know about Datalog (and never dared to ask). IEEE Transactions on Knowledge and Data Engineering, 1(1), 146-166. doi:10.1109/69.43410Chen, M., Mao, S., & Liu, Y. (2014). Big Data: A Survey. Mobile Networks and Applications, 19(2), 171-209. doi:10.1007/s11036-013-0489-0Chitil, O., & Davie, T. (2008). Comprehending finite maps for algorithmic debugging of higher-order functional programs. Proceedings of the 10th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP ’08. doi:10.1145/1389449.1389475Chitil, O., Faddegon, M., & Runciman, C. (2016). A Lightweight Hat. Proceedings of the 28th Symposium on the Implementation and Application of Functional Programming Languages - IFL 2016. doi:10.1145/3064899.3064904O. Chitil C. Runciman and M. Wallace. 2001. Freja Hat and Hood—A Comparative Evaluation of Three Systems for Tracing and Debugging Lazy Functional Programs. Springer Berlin 176--193. O. Chitil C. Runciman and M. Wallace. 2001. Freja Hat and Hood—A Comparative Evaluation of Three Systems for Tracing and Debugging Lazy Functional Programs. Springer Berlin 176--193.O. Chitil C. Runciman and Malcolm Wallace. 2003. Transforming Haskell for Tracing. Springer-Verlag Berlin 165--181. DOI:http://dx.doi.org/10.1007/3-540-44854-3_11 10.1007/3-540-44854-3_11 O. Chitil C. Runciman and Malcolm Wallace. 2003. Transforming Haskell for Tracing. Springer-Verlag Berlin 165--181. DOI:http://dx.doi.org/10.1007/3-540-44854-3_11 10.1007/3-540-44854-3_11Minh Ngoc Dinh, Abramson, D., & Chao Jin. (2014). Scalable Relative Debugging. IEEE Transactions on Parallel and Distributed Systems, 25(3), 740-749. doi:10.1109/tpds.2013.86Faddegon, M., & Chitil, O. (2015). Algorithmic debugging of real-world haskell programs: deriving dependencies from the cost centre stack. ACM SIGPLAN Notices, 50(6), 33-42. doi:10.1145/2813885.2737985Faddegon, M., & Chitil, O. (2016). Lightweight computation tree tracing for lazy functional languages. Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation - PLDI 2016. doi:10.1145/2908080.2908104Ferrand, G. (1987). Error diagnosis in logic programming an adaptation of E.Y. Shapiro’s method. The Journal of Logic Programming, 4(3), 177-198. doi:10.1016/0743-1066(87)90001-xFritzson, P., Shahmehri, N., Kamkar, M., & Gyimothy, T. (1992). Generalized algorithmic debugging and testing. ACM Letters on Programming Languages and Systems, 1(4), 303-322. doi:10.1145/161494.161498Fromherz, M. P. J. (s. f.). Towards declarative debugging of concurrent constraint programs. Lecture Notes in Computer Science, 88-100. doi:10.1007/bfb0019403Harman, M., & Hierons, R. (2001). An overview of program slicing. Software Focus, 2(3), 85-92. doi:10.1002/swf.41F. Henderson T. Conway Z. Somogyi D. Jeffery P. Schachte S. Taylor C. Speirs T. Dowd R. Becket M. Brown and P. Wang. 2014. The Mercury Language Reference Manual (Version 14.01.1). The University of Melbourne. F. Henderson T. Conway Z. Somogyi D. Jeffery P. Schachte S. Taylor C. Speirs T. Dowd R. Becket M. Brown and P. Wang. 2014. The Mercury Language Reference Manual (Version 14.01.1). The University of Melbourne.C. Hermanns and H. Kuchen. 2013. Hybrid Debugging of Java Programs. Springer-Verlag Berlin 91--107. DOI:http://dx.doi.org/10.1007/978-3-642-36177-7_6 10.1007/978-3-642-36177-7_6 C. Hermanns and H. Kuchen. 2013. Hybrid Debugging of Java Programs. Springer-Verlag Berlin 91--107. DOI:http://dx.doi.org/10.1007/978-3-642-36177-7_6 10.1007/978-3-642-36177-7_6Hirunkitti, V., & Hogger, C. J. (s. f.). A generalised query minimisation for program debugging. Lecture Notes in Computer Science, 153-170. doi:10.1007/bfb0019407Hughes, J. (2010). Software Testing with QuickCheck. Lecture Notes in Computer Science, 183-223. doi:10.1007/978-3-642-17685-2_6G. Hutton. 2016. Programming in Haskell. Cambridge University Press Cambridge UK. G. Hutton. 2016. Programming in Haskell. Cambridge University Press Cambridge UK.Insa, D., & Silva, J. (2010). 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Information 8 Software Technology 58 (2015) 95--109. DOI:http://dx.doi.org/10.1016/j.infsof.2014.10.001 10.1016/j.infsof.2014.10.001 D. Insa and J. Silva. 2015a. Automatic transformation of iterative loops into recursive methods. Information 8 Software Technology 58 (2015) 95--109. DOI:http://dx.doi.org/10.1016/j.infsof.2014.10.001 10.1016/j.infsof.2014.10.001Insa, D., & Silva, J. (2015). A Generalized Model for Algorithmic Debugging. Lecture Notes in Computer Science, 261-276. doi:10.1007/978-3-319-27436-2_16Insa, D., Silva, J., & Riesco, A. (2013). Speeding Up Algorithmic Debugging Using Balanced Execution Trees. Lecture Notes in Computer Science, 133-151. doi:10.1007/978-3-642-38916-0_8Insa, D., Silva, J., & Tomás, C. (2013). Enhancing Declarative Debugging with Loop Expansion and Tree Compression. Lecture Notes in Computer Science, 71-88. doi:10.1007/978-3-642-38197-3_6K. Jensen and N. Wirth. 1974. PASCAL User Manual and Report. Springer-Verlag Berlin. 10.1007/978-3-662-21554-8 K. 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Developer-Centric Automated Debugging

Software debugging is an expensive activity that is responsible for a significant part of software maintenance cost. In particular, locating faulty code (i.e., fault localization) is one of the most challenging parts of software debugging. In the past years, researchers have proposed many techniques that aim at fully automating the task of fault localization. Although these techniques have been shown to be effective in reducing the amount of code developers need to inspect to locate faults, there is growing evidence that they provide developers with limited help in realistic debugging scenarios. I believe that a practical automated debugging technique should have human developers at the center of the debugging process rather than trying to completely replace them. In this dissertation, I present three of my techniques that support developer-centric automated debugging. First, I present ENLIGHTEN, an interactive, feedback-driven fault localization technique. ENLIGHTEN supports and automates developers’ debugging workflow as follows. It 1) uses traditional statistical fault localization (SFL) to formulate an initial hypothesis of where the fault may be; 2) identifies a relevant subset of execution that can help support or refute the formulated hypothesis; 3) presents the developer with a query about the identified execution subset in the form of a correctness question about the input-output relation of the partial execution; 4) refines its hypothesis of the fault by using the developer’s feedback; and 5) repeats these steps until the fault is found. Second, I discuss my work on improving the accuracy of dynamic dependence analysis, which is a powerful tool for developers to investigate program behavior in an interactive debugging setting and a foundation that many automated debugging techniques leverage to model dynamic execution semantics. I present my finding that existing dynamic dependence analysis techniques could miss the cause-effect relations between faults and the observed failures if the faulty program states propagate via incorrect computation of memory addresses. To address this limitation, I define the concept of potential memory-address dependence, which explicitly represents this type of causal relations, and describe an algorithm that computes it. Third, I present TESSERACT, a technique that improves the scalability of dynamic dependency analysis in the context of interactive debugging. Many existing dependency-based debugging techniques are shown to work well on short executions, but fail to scale to larger ones. TESSERACT has the potential to address this limitation by utilizing a record-and-replay system to efficiently recreate the failing execution, break it down into small time slices, and analyze these slices in a parallelized, on-demand fashion.Ph.D