Abstract
We present the w constraint combinator that models while loops in Constraint Programming. Embedded in a finite domain constraint solver, it allows programmers to develop non-trivial arithmetical relations using loops, exactly as in an imperative language style. The deduction capabilities of this combinator come from abstract interpretation over the polyhedra abstract domain. This combinator has already demonstrated its utility in constraint-based verification and we argue that it also facilitates the rapid prototyping of arithmetic constraints (e.g. power, gcd or sum).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bagnara, R., Hill, P.M., Ricci, E., Zaffanella, E.: Precise widening operators for convex polyhedra. In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 337–354. Springer, Heidelberg (2003)
Bagnara, R., Ricci, E., Zaffanella, E., Hill, P.M.: Possibly not closed convex polyhedra and the parma polyhedra library. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 213–229. Springer, Heidelberg (2002)
Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Graph properties based filtering. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 59–74. Springer, Heidelberg (2006)
Beldiceanu, N., Carlsson, M., Petit, T.: Deriving filtering algorithms from constraint checkers. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 107–122. Springer, Heidelberg (2004)
Carlsson, M., Ottosson, G., Carlson, B.: An open-ended finite domain constraint solver. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 191–206. Springer, Heidelberg (1997)
Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL 1977. Proc. of Symp. on Principles of Progr. Lang., pp. 238–252. ACM Press, New York (1977)
Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: POPL 1978. Proc. of Symp. on Principles of Progr. Lang., pp. 84–96. ACM Press, New York (1978)
Fruhwirth, T.: Theory and practice of constraint handling rules. Special Issue on Constraint Logic Progr., Journal of Logic Progr. 37(1-3) (1998)
Gotlieb, A., Botella, B., Rueher, M.: A CLP framework for computing structural test data. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 399–413. Springer, Heidelberg (2000)
Holzbaur, C.: OFAI clp(q,r) Manual. Austrian Research Institute for Artificial Intelligence, Vienna, 1.3.3 edition
Marriott, K., Stuckey, P.J.: The 3 r’s of optimizing constraint logic programs: Refinement, removal and reordering. In: POPL 1993. Proc. of Symp. on Principles of Progr. Lang., pp. 334–344. ACM Press, New York (1993)
McCormick, G.P.: Computability of global solutions to factorable nonconvex programs: Part 1 - convex underestimating problems. Math. Progr. 10, 147–175 (1976)
Miné, A.: The octagon abstract domain. Higher-Order and Symbolic Computation Journal 19, 31–100 (2006)
Le Provost, T., Wallace, M.: Domain independent propagation. In: FGCS 1992. Proc. of the Int. Conf. on Fifth Generation Computer Systems, pp. 1004–1011 (1992)
Sankaranarayanan, S., Colòn, M.A., Sipma, H., Manna, Z.: Efficient strongly relational polyhedral analysis. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 115–125. Springer, Heidelberg (2005)
Schimpf, J.: Logical loops. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 224–238. Springer, Heidelberg (2002)
Schulte, C., Tack, G.: Views and iterators for generic constraint implementations. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds.) CSCLP 2005. LNCS (LNAI), vol. 3978, pp. 118–132. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Denmat, T., Gotlieb, A., Ducassé, M. (2007). An Abstract Interpretation Based Combinator for Modelling While Loops in Constraint Programming. In: Bessière, C. (eds) Principles and Practice of Constraint Programming – CP 2007. CP 2007. Lecture Notes in Computer Science, vol 4741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74970-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-74970-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74969-1
Online ISBN: 978-3-540-74970-7
eBook Packages: Computer ScienceComputer Science (R0)