A higher-order interpretation of Deductive Tableau

The Deductive Tableau of Manna and Waldinger is a formal system with an ass ociated methodology for synthesizing functional programs by existence proof s in classical first-order theories. We reinterpret the formal system in a setting that is higher-order in two respects: higher-order logic is used to formalize a theory of functional programs and higher-order resolution is u sed to synthesize programs during proof. Their synthesis methodology can be applied in our setting as well as new methodologies that take advantage of these higher-order features. The reinterpretation gives us a framework for directly formalizing and impl ementing the Deductive Tableau system in standard theorem provers that supp ort the kinds of higher-order reasoning listed above. We demonstrate this, as well as a new develop ment methodology, within a conservative extension of higher-order logic in the ISABELLE system. We report too on a case-study in synthesizing sorting programs. (C) 2001 Academic Press.