Abstract
In the previous version of the constraint logic programming language RISC-CLP(Real), the domain Real of real numbers was the intended domain of computation. In this paper, we extend it to the domain Tree Real of finite symbolic trees with real numbers as leaves, that is the integration of the domain of reals with the domain of finite Herbrand trees. In the extended language, a system of constraints over the new domain is decided by first decomposing equations into a tree-solved form produced by an adapted unification algorithm. Then, polynomial real constraints are decided by the partial cylindrical algebraic decomposition method and a solution to the original system is constructed.
In the frame of the ACCLAIM project sponsored by European Community ESPRIT BRA 7195 Austrian Science Foundation P9374-PHY.
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References
A. Aggoun, M. Dincbas, A. Herold, H. Simonis, and P. Van Hentenryck. The CHIP System. Technical Report TR-LP-24, European Computer Industry Research Centre (ECRC), Munich, Germany, June 1987.
B. Buchberger. An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal. PhD thesis, Universitat Innsbruck, Institut fur Mathematik, 1965. German.
B. Buchberger. Groebner bases: An algorithmic method in polynomial ideal theory. In N. K. Bose, editor, Recent Trends in Multidimensional Systems Theory, chapter 6. D. Riedel Publ. Comp., 1983.
G. E. Collins. Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In Lecture Notes In Computer Science, pages 134–183. Springer-Verlag, Berlin, 1975. Vol. 33.
G. E. Collins and H. Hong. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation, 12(3):299–328, September 1991.
A. Colmerauer. An introduction to Prolog III. Communications of the ACM, 33(7):69–90, July 1990.
Alain Colmerauer. Final specifications for PROLOG-III. Technical Report P1219(1106), ESPRIT, February 1988.
William Havens, Susan Sidebottom, Greg Sidebottom, John Jones, and Russel Ovans. Echidna: a constraint logic programming shell. In Proceedings of the 1992 Pacific Rim International Conference on Artificial Intelligence, volume I, pages 165–171, Seoul, Korea, 1992.
N. Heintze, J. Jaffar, S. Michaylov, P. Stuckey, and R. Yap, The CLP(R) Programmer's Manual Version 1.1, November 1991.
H. Hong. Improvements in CAD-based Quantifier Elimination. PhD thesis, The Ohio State University, 1990.
H. Hong. Comparison of several decision algorithms for the existential theory of the reals. Technical Report 91-41.0, Research Institute for Symbolic Computation, Johannes Kepler University A-4040 Linz, Austria, 1991. Submitted to Journal of Symbolic Computation.
H. Hong. Non-linear real constraints in constraint logic programming. In International Conference on Algebraic and Logic Programming (LNCS 632), pages 201–212, 1992.
Hoon Hong. Quantifier elimination for formulas constrainted by quadratic equations via slope resultants. The Computer Journal, Special issue on Quantifier Elimination, 1993.
J. Jaffar and S. Michaylov. Methodology and implementation of a CLP system. In J.-L. Lassez, editor, Proceedings 4th ICLP, pages 196–218, Cambridge, MA, May 1987. The MIT Press.
J. Jaffar, S. Michaylov, and Roland H. C. Yap. A methodology for managing hard constraints in clp systems. In Proceedings of the ACM-SIGPLAN Conference on Programming Language Design and Implementation, pages 306–316, Toronto, June 1991.
Joxan Jaffar and Jean-Louis Lassez. Constraint logic programming. In Proceedings of the 14th ACM Symposium on Principles of Programming Languages, Munich, Germany, pages 111-119. ACM, January 1987.
Joxan Jaffar, Spiro Michaylov, Peter Stuckey, and Roland H. C. Yap. The CLP(R) Language and System. Research Report RC 16292, IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598, November 1990.
Jean-Pierre Jouannaud and Claude Kirchner. Solving equations in abstract algebras: A rule-based survey of unification. In J.-L. Lassez and G. Plotkin, editors, Computational Logic. Essays in honour of Alan Robinson, chapter 8, pages 257–321. MIT Press, Cambridge, (MA) USA, 1991.
D.A. Kohler. Projection of Convex Polyhedral Sets. PhD thesis, University of California, Berkeley, 1967.
E. Monfroy. Specification of Geometrical Constraints. Technical Report ECRC-92-31, ECRC, Munich, Germany, 1992. presented at AAGR 92, Linz, Austria.
Jean Michel Nataf. Algorithm of simplification of nonlinear equations systems. SIGSAM Bulletin, 26(3):9–16, April 1992.
William Older and Andrè Vellino. Constraint arithmetic on real intervals. In Frèdèric Benhamou and Alain Colmerauer, editors, Constraint Logic Programming: Selected Research. The MIT Press, Cambridge, 1992.
K. Sakai and A. Aiba. CAL: A Theoretical Background of Constraint Logic Programming and its Applications. Journal of Symbolic Computation, 8:589–603, 1989.
A. Tarski. A Decision Method for Elementary Algebra and Geometry. Univ. of California Press, Berkeley, second edition, 1951.
Clifford Walinsky. Clp(σ *): Constraint logic programming with regular sets. In Logic Programming: Proceedings 6 th International Conference, Jerusalem, Israel, pages 181–196. MIT Press, June 1989.
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Caprotti, O. (1993). Extending RISC-CLP(Real) to handle symbolic functions. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1993. Lecture Notes in Computer Science, vol 722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013181
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DOI: https://doi.org/10.1007/BFb0013181
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