Structural Properties of Logic Programs

Miller has shown that disjunctions are not necessary in a large fragment of hereditary Harrop formulae, a class of formulae which properly includes Horn clauses. In this paper we extend this result to include existential quantiications, so that for each program D, there is a program D 0 which is operationally equivalent, but contains no disjunctions or existential quantiications. We may think of this process as deriving a normal form for the program. This process is carried out by pushing the connectives outwards from the body of a clause, and this process leads to a normal form for goals as well. The properties of the search process used to nd uniform proofs of goals (which generalises SLD-resolution) together with the normal form allow successful goals to be converted into program clauses, and so we may add successful goals to the program. The stored form of the goal requires a larger class of formulae, i.e. full rst-order hereditary Harrop formulae, and so this leads to a natural separation into an object level and a meta-level. This separation seems intuitively natural and to correspond to aspects of programming methodology. Finally we discuss some possibilities for amalgamation of the object and meta-level languages.