Automatic generation of simplified weakest preconditions for integrity constraint verification

Given a constraint c assumed to hold on a database B and an update u to be performed on B, we address the following question: will c still hold after u is performed? When B is a relational database, we define a confluent terminating rewriting system which, starting from c and u, automatically derives a simplified weakest precondition wp(c, u) such that, whenever B satisfies wp(c, u), then the updated database u(B) will satisfy c, and moreover wp(c, u) is simplified in the sense that its computation depends only upon the instances of c that may be modified by the update. We then extend the definition of a simplified wp(c, u) to the case of deductive databases; we prove it using fixpoint induction.