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The Computer Journal 1993 36(4):387-398; doi:10.1093/comjnl/36.4.387
© 1993 by British Computer Society
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On Exploiting the Structure of Martin-Löf's Theory of Types*

A. Ireland §

Department of Artificial Intelligence, University of Edinburgh, Edinburgh EH1 1HN, UK

Program synthesis in Martin-Löf's Theory of Types is a theorem proving activity. We show how the uniform structure of the deductive system may be exploited in the mechanization of this activity. Basic properties of data type constructors are shown to exhibit a general structure in the way in which they are expressed and derived. A proof procedure for negation is developed, based upon uniqueness, closure and cancellation properties. As a consequence our proof procedure may be extended uniformly to incorporate new data types.

Received December 1990.

* A shorter version of this paper appeared in the proceedings of the Seventh Austrian Conference on Artificial Intelligence 1991, Springer-Verlag, Informatik-Fachberichte 287

§ Department of Artificial Intelligence, University of Edinburgh, Edinburgh EH1 1HN, UK


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