Abstract

CLIP is an implementation of CLP(Intervals) which has been designed to be verifiably correct in the sense that the answers it returns are mathematically correct solutions to the underlying arithmetic constraints. This fundamental design criteria affects many aspects of the implementation from the input and output of decimal constants to the design of the interval arithmetic libraries and the constraint solving algorithms. In particular, to enhance verifiability, CLIP employs the simplest model of constraint solving in which constraints are decomposed into sets of primitive constraints which are then solved using a library of primitive constraint contractors. This approach results in a simple constraint solver whose correctness is relatively straightforward to verify, but the solver is only able to solve relatively simple constraints. In this paper, we present the syntax, semantics, and implementation of CLIP, and we show how to use metalevel techniques to enhance the power of the CLIP constraint solver while preserving the simple structure of the system. In particular, we demonstrate that several of the box-narrowing algorithms from the Newton and Numerica systems can be easily implemented in CLIP. The principal advantages of this approach are (1) the resulting solvers are relatively easy to prove correct, (2) new solvers can be rapidly prototyped since the code is more concise and declarative than for imperative languages, and (3) contractors can be implemented directly from mathematical formulae without having to first prove results about interval arithmetic operators. Finally, the source code for the system is publicly available, which is a clear prerequisite for public, independent verifiability.

Citations