The CLP( ℛ ) language and system

TLDR

CLP(ℛ) is a Constraint Logic Programming Scheme instance whose domain consists of uninterpreted functors over real numbers, treating constraints uniformly as input, execution primitives, and output descriptors, and requiring an incremental, prioritized solver architecture. The authors define the CLP(ℛ) programming language, discuss its underlying philosophy and methodology, examine key implementation issues, and present a prototype interpreter. Their system filters constraints through an inference engine, a solver interface, equation and inequality solvers, isolating higher‑priority constraints from lower‑priority ones in a multi‑phase solving pipeline. This multi‑phase constraint solving, supported by associated algorithms, results in a practical CLP(ℛ) system.

Abstract

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.