Extensional Higher-Order Datalog ?

We define a higher-order extension of Datalog based on the Horn fragment of higher-order logic introduced in [Wad91]. Programs of Higher-Order Datalog can be understood declaratively as formulas in extensional higher-order logic, in which (for example) a unary predicate of unary predicates is a set of sets of data objects. The language retains all the basic principles of first-order logic programming. In particular, programs in this extended Datalog always have a minimum Herbrand model which can be computed in a bottom-up way. We present the syntax and semantics of our extended Datalog, state the main result cited above, and describe an implementation of this new language.