Type inference for datalog with complex type hierarchies

Abstract

Type inference for Datalog can be understood as the problem of mapping programs to a sublanguage for which containment is decidable. To wit, given a program in Datalog, a schema describing the types of extensional relations, and a user-supplied set of facts about the basic types (stating conditions such as disjointness, implication or equivalence), we aim to infer an over-approximation of the semantics of the program, which should be expressible in a suitable sublanguage of Datalog. We argue that Datalog with monadic extensionals is an appropriate choice for that sublanguage of types, and we present an inference algorithm. The inference algorithm is proved sound, and we also show that it infers the tightest possible over-approximation for a large class of Datalog programs. Furthermore, we present a practical containment check for a large subset of our type language. The crux of that containment check is a novel generalisation of Quine's procedure for computing prime implicants. The type system has been implemented in a state-of-the-art industrial database system, and we report on experiments with this implementation.