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A Higher-order Interpretation of Deductive Tableau

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44047

Ayari,  Abdelwaheb
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44075

Basin,  David A.
Programming Logics, MPI for Informatics, Max Planck Society;

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Ayari, A., & Basin, D. A. (2001). A Higher-order Interpretation of Deductive Tableau. Journal of Symbolic Computation, 31(5), 487-520.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-31D6-A
Abstract
The Deductive Tableau of Manna and Waldinger is a formal system with an associated methodology for synthesizing functional programs by existence proofs 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 used 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 implementing the Deductive Tableau system in standard theorem provers that support the kinds of higher-order reasoning listed above. We demonstrate this, as well as a new development methodology, within a conservative extension of higher-order logic in the Isabelle system. We report too on a case-study in synthesizing sorting programs.