A Formalized procedure for database horizontal fragmentation in isabelle/HOL Proof Assistant

Abstract

We propose a logical procedure for the horizontal fragmentation problem based on predicate abstraction over the entire domain of database relations. The set of minterm predicates is constructed using rewriting rules similar to the well-known semantic tableau algorithm. The procedure start from an initial set of simple predicates, build the set of minterm predicates until rules are no longer required. To ensure this proposition, we give a formal proof of its correctness namely, it’s soundness, completeness and termination with Isabelle proof assistant. The main contribution of this work are: refining the minterm approach by adding a semantic layer to predicates, minimizing the set of minterm predicates by automatically eliminating contradictory ones, detecting and handling subsumptions between them. This leads to the best construction time of the final partitioning schema. Finally, a source code of the procedure is generated automatically by the Isabelle proof assistant.