The Logic Programming Paradigm in Numerical Computation

Although CLP(R) is a promising application of the logic programming paradigm to numerical computation, it has not addressed what has long been known as \the pitfalls of numerical] computation" 12]. These show that rounding errors induce a severe correctness problem wherever oating-point computation is used. Independently of logic programming, constraint processing has been applied to problems in terms of real-valued variables. By using the techniques of interval arithmetic, constraint processing can be regarded as a computer-generated proof that a certain real-valued solution lies in a narrow interval. In this paper we propose a method for interfacing this technique with CLP(R). This is done via a real-valued analogy of Apt's proof-theoretic framework for constraint processing.