Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A brief account: Implementation and applications of a Pascal program verifier (Position Statement)
ACM '78 Proceedings of the 1978 annual conference - Volume 2
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We define the notion of the ''congruence closure'' of a relation on a graph and give a simple algorithm for computing it. We then give decision procedures for the quantifier-free theory of equality and the quantifier-free theory of LISP list structure, both based on this algorithm. The procedures are fast enough to be practical in mechanical theorem proving: each procedure determines the satisfiability of a conjunction of length n of literals in time O($n^2$). We also show that if the axiomatization of the theory of list structure is changed slightly, the problem of determining the satisfiability of a conjunction of literals becomes NP-complete. We have implemented the decision procedures in our simplifier for the Stanford Pascal Verifier.