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Compile-time analysis of nonlinear constraints in CLPR

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Abstract

Solving nonlinear constraints over real numbers is a complex problem. Hence constraint logic programming languages like CLPR or Prolog III solve only linear constraints and delay nonlinear constraints until they become linear. This efficient implementation method has the disadvantage that sometimes computed answers are unsatisfiable or infinite loops occur due to the unsatisfiability of delayed nonlinear constraint These problems could be solved by using a more powerful constraint solver which can deal with nonlinear constraints like in RISC-CLP(Real). Since such powerful constraint solvers are not very efficient, we propose a compromise between these two extremes. We characterize a class of CLPR programs for which all delayed nonlinear constraints become linear at run time. Programs belonging to this class can be safely executed with the efficient CLPR method while the remaining programs need a more powerful constraint solver.

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Authors and Affiliations

  1. Informatik II, RWTH Aachen, D-52056, Aachen, Germany

    Michael Hanus

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  1. Michael Hanus
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Additional information

This paper is an extended and revised version of Ref. 12). The research described in this paper was made during the author’s stay at the Max-planck-Institut für Informatik in Saarbrücken, Germany. It was supported in part by the German Ministry for Research and Technology (BMFT) under grant ITS 9103 and by the ESPRIT Basic Research Working Group 6028 (Construction of Computational Logics). The responsibility for the contents of this publication lies with the author.

Michael Hanus, Prof. Dr.: He received his degrees from the Universities of Dortmund and Saarbrücken. He wrote his dissertation on type systems for logic languages and his habilitation on the integration of functional and logic programming languages. From 1984 to 1994, he held research positions at the University of Dortmund and the Max-Planck-Institut für Informatik in Saarbrücken. Since 1995, he is Professor for Computer Science at the RWTH Aachen. His research interests are in the field of declarative languages. In particular, he is interested in the implementation of logic languages, extensions to logic languages, like types and constraints, the integration of functional and logic languages, and program analysis techniques for logic, functional logic and constraint logic languages.

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Hanus, M. Compile-time analysis of nonlinear constraints in CLPR . New Gener Comput 13, 155–186 (1995). https://doi.org/10.1007/BF03038312

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