Convex Hull Abstractions in Specialization of CLP Programs
We introduce an abstract domain consisting of atomic formulas constrained by linear arithmetic constraints (or convex hulls). This domain is used in an algorithm for specialization of constraint logic programs. The algorithm incorporates in a single phase both top-down goal directed propagation and bottom-up answer propagation, and uses a widening on the convex hull domain to ensure termination. We give examples to show the precision gained by this approach over other methods in the literature for specializing constraint logic programs. The specialization method can also be used for ordinary logic programs containing arithmetic, as well as constraint logic programs. Assignments, inequalities and equalities with arithmetic expressions can be interpreted as constraints during specialization, thus increasing the amount of specialization that can be achieved.
KeywordsConvex Hull Logic Program Partial Evaluation Atomic Formula Abstract Interpretation
Unable to display preview. Download preview PDF.
- 1.Krysztof R. Apt and Ernst-Rüdiger Olderog. Verification of Sequential and Concurrent Programs. Springer-Verlag, 1991.Google Scholar
- 2.F. Benoy and A. King. Inferring argument size relations in CLP(R). In Proceedings of the 6th International Workshop on Logic Program Synthesis and Transformation, pages 204–223, Sweden, 1996. Springer-Verlag, LNCS 1207.Google Scholar
- 3.Edmund M. Clarke, Orna Grumberg, and Doron Peled. Model Checking. The MIT Press, 2000.Google Scholar
- 4.P. Cousot and N. Halbwachs. Automatic discovery of linear restraints among variables of a program. In Proceedings of the Conference Record of the 5th ACM Symposium on Principles of Programming Languages, pages 84–97, Albuquerque, New Mexico, 1978. Also in “http://www.di.ens.fr/~cousot/COUSOTpapers/POPL78.shtml”.
- 6.Fabio Fioravanti, Alberto Pettorossi, and Maurizio Proietti. Automated strategies for specialising constraint logic programs. In Kung-Kiu Lau, editor, 10th International Workshop on Logic-based Program Synthesis and Transformation, pages 125–146. Springer-Verlag, LNCS 2042, 2000.CrossRefGoogle Scholar
- 7.Fabio Fioravanti, Alberto Pettorossi, and Maurizio Proietti. Verifying CTL properties of infinite state systems by specializing constraint logic programs. Technical Report DSSE-TR-2001-3, Department of Electronics and Computer Science, University of Southampton, 2001. Proceedings of the Second International Workshop on Verification and Computational Logic (VCL’01).Google Scholar
- 8.J. Gallagher. Specialisation of logic programs: A tutorial. In Proceedings PEPM’93, ACM SIGPLAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation, pages 88–98, Copenhagen, June 1993. ACM Press.Google Scholar
- 10.J. Gallagher and D.A. de Waal. Deletion of redundant unary type predicates from logic programs. In K.K. Lau and T. Clement, editors, Logic Program Synthesis and Transformation, Workshops in Computing, pages 151–167. Springer-Verlag, 1993.Google Scholar
- 11.John P. Gallagher and L. Lafave. Regular approximation of computation paths in logic and functional languages. In O. Danvy, R. Gluck, and P. Thiemman, editors, Partial Evaluation, pages 115–136. Springer-Verlag, LNCS 1110, 1996.Google Scholar
- 15.N. Jones, C.K. Gomard, and P. Sestoft. Partial Evaluation and Automatic Software Generation. Prentice Hall, 1993.Google Scholar
- 17.M. Leuschel. Program specialisation and abstract interpretation reconciled. In Joxan Jaffar, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming JICSLP’98, pages 220–234, Manchester, UK, June 1998. MIT Press.Google Scholar
- 18.M. Leuschel and S. Gruner. Abstract partial deduction using regular types and its application to model checking. In A. Pettorossi, editor, (Pre)Proceedings of LOPSTR-2001 11th International Workshop on Logic-based Program Synthesis and Transformation (LOPSTR-2001), Paphos, Cyprus, December 2001.Google Scholar
- 22.Torben Æ. Mogensen. Partially static structures in a self-applicable partial evaluator. In D. Bjørner, A.P. Ershov, and N.D. Jones, editors, Partial Evaluation and Mixed Computation, pages 325–347. North-Holland, 1988.Google Scholar
- 24.G. Puebla, M. Hermenegildo, and J. P. Gallagher. An integration of partial evaluation in a generic abstract interpretation framework. In Olivier Danvy, editor, Proceedings of the ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation (PEPM’99), Technical report BRICS-NS-99-1, University of Aarhus, pages 75–84, San Antonio, Texas, January 1999.Google Scholar
- 25.J. C. Reynolds. Transformational systems and the algebraic structure of atomic formulas. Machine Intelligence, pages 135–151, 1970.Google Scholar
- 26.Huseyin Sağlam and John P. Gallagher. Constrained regular approximations of logic programs. In N. Fuchs, editor, LOPSTR’97, pages 282–299. Springer-Verlag, LNCS 1463, 1997.Google Scholar
- 27.Danny De Schreye, Robert Glück, Jesper Jørgensen, Michael Leuschel, Bern Martens, and Morten Heine Sørensen. Conjunctive partial deduction: Foundations, control, algorithms, and experiments. The Journal of Logic Programming, 41(2–3):231–277, 1999. Erratum appeared in JLP 43(3): 265(2000).zbMATHCrossRefGoogle Scholar