Two applications of equational theories to database theory
Databases and equational theorem proving are well developed and seemingly unrelated areas of Computer Science Research. We provide two natural links between these fields and demonstrate how equational theorem proving can provide useful and tools for a variety of database tasks.
Our first application is a novel way of formulating functional and inclusion dependencies (the most common database constraints) using equations. The central computational problem of dependency implication is directly reduced to equational reasoning. Mathematical techniques from universal algebra provide new proof procedures and better lower bounds for dependency implication. The use of REVE, a general purpose transformer of equations into term rewriting systems, is illustrated on nontrivial sets of functional and inclusion dependencies.
Our second application demonstrates that the uniform word problem for lattices is equivalent to implication of dependencies expressing transitive closure, together with functional dependencies. This natural generalization of functional dependencies, which is not expressible using conventional database theory formulations, has a natural inference system and an efficient decision procedure.
KeywordsWord Problem Equational Theory Transitive Closure Horn Clause Proof Procedure
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