Arrays are ubiquitous in the context of software verication. However, eective reasoning over arrays is still rare in CP, as local reasoning is dramatically ill-conditioned for constraints over arrays. In this paper, we propose an approach com- bining both global symbolic reasoning and local consistency ltering in order to solve constraint systems involving arrays (with accesses, updates and size constraints) and nite-domain constraints over their elements and indexes. Our approach, named fdcc, is based on a combination of a congruence closure algorithm for the standard theory of arrays and a CP solver over nite domains. The tricky part of the work lies in the bi- directional communication mechanism between both solvers. We identify the signicant information to share, and design ways to master the communication overhead. Exper- iments on random instances show that fdcc solves more formulas than any portfolio combination of the two solvers taken in isolation, while overhead is kept reasonable.
A method for combining decision procedures for several theories into a single decision procedure for their combination is described, and a simplifier based on this method is discussed. The simplifier finds a normal form for any expression formed from individual variables, the usual Boolean connectives, the equality predicate =, the conditional function if-then-else, the integers, the arithmetic functions and predicates +, -, and ≤, the Lisp functions and predicates car, cdr, cons, and atom, the functions store and select for storing into and selecting from arrays, and uninterpreted function symbols. If the expression is a theorem it is simplified to the constant true, so the simplifier can be used as a decision procedure for the quantifier-free theory containing these functions and predicates. The simplifier is currently used in the Stanford Pascal Verifier.