Synthesis of positive logic programs for checking a class of definitions with infinite quantification

Abstract

We describe a method based on unfold/fold transformations that synthesizes positive logicprograms P(r)with the purpose of checking mechanically definitions of the form D(r) =∀X(r(X) ⇔QYR(X, Y))where ris the relation defined by the formula QYR(X, Y), Xis a set of variables to be instantiated at runtime by ground terms, QYis a set of quantifiedvariables on infinite domains (Qis the quantifier) and R(X, Y)a quantifier-free formulain the language of a first-order logic theory. This work constitutes a first step towards theconstruction of a new type of assertion checkers with the ability of handling restrictedforms of infinite quantification.