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The CLP( ℛ ) programming language is defined, its underlying philosophy and programming methodology are discussed, important implementation issues are explored in detail, and finally, a prototype interpreter is described. CLP( ℛ ) is designed to be an instance of the Constraint Logic Programming Scheme, a family of rule-based constraint programming languages defined by Jaffar and Lassez. The domain of computation ℛ of this particular instance is the algebraic structure consisting of uninterpreted functors over real numbers. An important property of CLP( ℛ )is that the constraints are treated uniformly in the sense that they are used to specify the input parameters to a program, they are the only primitives used in the execution of a program, and they are used to describe the output of a program. Implementation of a CLP language, and of CLP( ℛ ) in particular, raises new problems in the design of a constraint-solver. For example, the constraint solver must be incremental in the sense that solving additional constraints must not entail the resolving of old constraints. In our system, constraints are filtered through an inference engine, an engine/solver interface, an equation solver and an inequality solver. This sequence of modules reflects a classification and prioritization of the classes of constraints. Modules solving higher priority constraints are isolated from the complexities of modules solving lower priority constraints. This multiple-phase solving of constraints, together with a set of associated algorithms, gives rise to a practical system.

Abstract. We consider the problem of exploring the search tree of a CLP goal in pursuit of a target property. Essential to such a process is a method of tabling to prevent duplicate exploration. Typically, only actually traversed goals are memoed in the table. In this paper we present a method where, upon the successful traversal of a subgoal, a generalization of the subgoal is memoed. This enlarges the record of already traversed goals, thus providing more pruning in the subsequent search process. The key feature is that the abstraction computed is guaranteed not to give rise to a spurious path that might violate the target property.A driving application area is the use of CLP to model the behavior of other programs. We demonstrate the performance of our method on a benchmark of program verfication problems.

The notion of Cartesian closure on a set of unifiers has been used to define approximations of the least models of logic programs. Such approximations, often called types, are not known to be recursive. In this paper, we use Cartesian closure to define a similar, but more accurate, approximation. The main result proves that our approximation is not only recursive, but that it can be finitely represented in the form of a cyclic term graph. This explicit representation can be used as a starting point for logic program analyzers.