The design of languages to tackle constraint satisfaction problems has a long history. Only more recently the reverse problem of introducing constraints as primitive constructs in programming languages has been addressed. A main task that the designers and implementers of such languages face is to use and adapt the concepts and algorithms from the extensive studies on constraints done in areas such as Mathematical Programming, Symbolic Computation, Artificial Intelligence, Program Verification and Computational Geometry. In this paper, we illustrate this task in a simple and yet important domain: linear arithmetic constraints. We show how one can design a querying system for sets of linear constraints by using basic concepts from logic programming and symbolic computation, as well as algorithms from linear programming and computational geometry. We conclude by reporting briefly on how notions of negation and canonical representation used in linear constraints can be generalized to account for cases in term algebras, symbolic computation, affine geometry, and elsewhere.
用于解决约束满足问题的语言设计历史悠久。直到最近,才解决了将约束作为编程语言中的原始构造引入的相反问题。这种语言的设计者和实现者面临的主要任务是,通过对数学编程,符号计算,人工智能,程序验证和计算几何学等领域的约束进行广泛研究,来使用和适应这些概念和算法。在本文中,我们在一个简单但重要的领域中说明了这一任务:线性算术约束。我们展示了如何使用逻辑编程和符号计算的基本概念,以及线性编程和计算几何的算法,来设计一套线性约束查询系统。最后,我们简要报告一下如何将线性约束中使用的否定和规范表示的概念概括起来,以解决术语代数,符号计算,仿射几何以及其他方面的情况。 P>
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