Sorted HiLog: Sorts in higher-order logic data languages

HiLog enhances the modeling capabilities of deductive data bases and logic programming with higher-order and meta-data constructs, complex objects, and schema browsing. Its distinctive feature, a higher-order syntax with a first-order semantics, allows for efficient implementation with speeds comparable to Prolog. In fact, HiLog implementation in XSB [29, 25] together with tabulated query evaluation offers impressive performance with negligible penalty for higher-order syntax, thereby bringing the modeling capabilities of HiLog to practical realization. The lack of sorts in HiLog, however, is somewhat of a problem in database applications, which led to a number of HiLog dialects such as DataHiLog [24]. This paper develops a comprehensive theory of sorts for HiLog. It supports HiLog's flexible higher-order syntax via a polymorphic and recursive sort structure, and it offers an easy and convenient mechanism to control the rules of well-formedness. By varying the sort structure we obtain a full spectrum of languages, ranging from classical predicate logic to the original (non-sorted) HiLog. In between, there is a number of interesting higher-order extensions of Datalog with various degrees of control over the syntax, including second-order predicate calculus with Henkin-style semantics, as described in [10]. We also discuss the benefits of using Sorted HiLog for modeling complex objects and for meta programming. Finally, Sorted HiLog can be easily incorporated into XSB, which makes its practical realization feasible.