Combining Uniication and Built-in Constraints (extended Abstract)

In less than a decade, Deduction with Constraints (DwC) has opened a new universe in computer science. DwC can be viewed from two perspectives: one related to the automated deduction framework 17, 19], the other to the development and usage of programming languages based on logic 7, 14]. Within the automated deduction framework, constraints on the generic data structure \terms" have become a popular tool because they allow to express and encode strategies and to modularise deduction processes 19]. We call symbolic, constraints over terms 11]. There are plenty of symbolic constraint systems, some examples are uniication (see 16] for a survey), disuniication 10], ordering 5], membership 9, 13] and feature constraints 1]. The most well-known example is equational uniication. Equational uniication is nothing but solving equations between terms when the function symbols of the terms satisfy a certain equational theory. Within programming languages based on logic, the purpose is to develop a class of programming languages, which incorporates the computational properties of a logical theory with the eeciency of constraint solving. In this setting, Constraint Logic Programming (CLP) 7, 8, 15], instance of the Constraint Programming paradigm, is an elegant generalisation of logic programming, aimed at replacing uniication by the concept of constraint solving over a computation domain. Thus, CLP is a class of languages, which merges the computational properties of Horn-clause logic and eecient constraint solving over a given domain. J. Jaaar & J.-L. Lassez proposed in 14] a theoretical semantic, CLP (D), explaining the meaning of a CLP program,