Implementing Constraint Propagation by Composition of Reductions

Constraint propagation is a general algorithmic approach for pruning the search space of a constraint satisfaction problem. In a uniform way, K. R. Apt [1] has defined computation as an iteration of reduction functions over a domain. In [2], he has also demonstrated the need for integrating static properties of reduction functions (commutativity and semi-commutativity) to design specialized algorithms such as AC3 and DAC. We introduce here a set of operators for modeling compositions of reduction functions in an iteration framework. Two of the major goals are to tackle parallel computations, and to manage dynamic behaviors such as slow convergences in numerical computations. An object-oriented software architecture is described using the Unified Modeling Language.