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Journal of Logic and Computation 1993 3(3):287-315; doi:10.1093/logcom/3.3.287
© 1993 by Oxford University Press
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Original Articles

A Complete Proof Synthesis Method for the Cube of Type Systems

GILLES DOWEK

INRIA B.P. 105, 78153 Le Chesnay CEDEX, France e-mail: Gilles.Dowek{at}inria.fr

We present a complete proof synthesis method for the eight type systems of Barendregt's cube extended with {eta}-conversion. Because these systems verify the proofs-as-objects paradigm, the proof synthesis method is a one-level process merging unification and resolution. Then we present a variant of this method, which is incomplete but much more efficient. Finally we show how to turn this algorithm into a unification algorithm.

Keywords: Proof synthesis; unification; resolution; Barendregt's cube.


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