Abstract
A system which extracts a dataflow graph from sets of arithmetic constraints is described. This information is used to simplify constraints and to extract positive information from negations of constraints. The context for this work is a Prolog implementation where intervals are used to represent the underlying arithmetic variables. The system uses simple information about the existence of solutions of primitive constraints to derive the dataflow graph. This makes the system easily extensible to new primitives and domains. A practical implementation over both real and integer arithmetic is described and an extended example of its application given.
Similar content being viewed by others
References
D. Chan. (1988). Constructive negation based on the completed dataBase. Fifth International Conference and Symposium on Logic Programming, pp. 111–125.
J. G. Cleary. (1987). Logical arithmetic. Future Computing Systems 2(2): 125–149.
J. G. Cleary. (1993a). Informal introduction to Starlog. Research Report, 93/10, Dept. Computer Science, University of Waikato, October.
J. G. Cleary. (1993b). Proving the Existence of Solutions in Logical Arithmetic. NATO Advanced Study Institute: Constraint Programming, P¨arnu, Estonia, August, pp. 52–63.
N. Dershowitz & J-P. Jouannaud. (1994). Rewrite systems. In J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, volume B, pp. 243–320, Elsevier, Amsterdam.
ECRC (1993). ECLIPSE—ECRC common logic programming system—Users manual. ECRC GmbH, Munich, Germany.
M. Mantyla. (1988). An Introduction to Solid Modeling. Computer Science Press, Rockville, Maryland.
P. J. Stuckey. (1991) Constructive negation for constraint logic programming. Proc. 6th Annual Symposium on Logic in Computer Science, Amsterdam, pp. 328–339.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cleary, J.G. Constructive Negation of Arithmetic Constraints Using Dataflow Graphs. Constraints 2, 131–162 (1997). https://doi.org/10.1023/A:1009753625663
Issue Date:
DOI: https://doi.org/10.1023/A:1009753625663