Proofs as computations in linear logic

Abstract

The notions of uniform proof and of resolution represent the foundations of the proof-theoretic characterization of logic programming. The class of Abstract Logic Programming Languages nicely captures these concepts for a wide spectrum of logical systems. In the logic programming setting, however, the structure of the formulas, e.g. Horn clauses and hereditary Harrop formulas, plays a crucial role in discriminating between programming and theorem proving. In the paper, and in the framework of the proofs as computations interpretation of linear logic, we present an extension of hereditary Harrop formulas and a corresponding logical system which are the foundations of the logic programming language . The starting point of this study is Forum (Miller, Theoret. Comput. Sci. 165 (1) (1996) 201–232), a presentation of higher-order linear logic in terms of uniform proofs. A subset of its formulas have been isolated and proved to be well-suited to encode descriptions of various programming paradigms.