A canonical form for generalized linear constraints

The integration of the constraint solving paradigm in programming languages raises a number of new issues. Foremost is the need for a useful canonical form for the representation of constraints. In the context of an extended class of linear arithmetic constraints we develop a natural canonical representation and we design polynomial time algorithms for deciding solvability and generating the canonical form. Important issues encountered include negative constraints, the elimination of redundancy and parallelism. The canonical form allows us to decide by means of a simple syntactic check the equivalence of two sets of constraints and provides the starting point for a symbolic computation system. It has, moreover, other applications and we show in particular that it yields a completeness theorem for constraint propagation and is an appropriate tool to be used in connection with constraint based programming languages. © 1992.