Abstract

Many features of current logic programming languages are not captured by conventional semantics. Their fundamentally non-ground character, and the uniform way in which such languages have been extended to typed domains, subject to constraints, suggest that a categorical treatment of constraint domains, of programming syntax and of semantics may be closer in spirit to what declarative programming is really about, than conventional settheoretic semantics. We generalize the notion of a (many-sorted) logic program and of a resolution proof, by defining them both over a (not necessarily free) -category C , a category with products enriched with a mechanism for canonically manipulating n-ary relations [8]. Computing over this domain includes computing over the Herbrand Universe, and over equationally presented constraint domains as special cases. We give a categorical treatment of the fixpoint semantics of Kowalski and van Emden, which establishes completeness in a very general setting. 1 In...

Citations