Intelligent backtracking in CLP(R)

CLP(R) is a constraint logic programming language in which constraints can be expressed in the domain of real numbers. Computation in this specialized domain gives access to information useful in intelligent backtracking. In this paper, we present an efficient constraint satisfaction algorithm for linear constraints in the real number domain and show that our algorithm directly generates minimal sets of conflicting constraints when failures occur. We demonstrate how information gleaned during constraint satisfaction can be integrated with unification failure analysis. The resulting intelligent backtracking method works in the context of a two-sorted domain, where variables can be bound to either structured terms or real number expressions. We discuss the implementation of backtracking and show examples where the benefit of pruning the search tree outweighs the overhead of failure analysis.