Selectively instantiating definitions

  • Matthew Bishop
  • Peter B. Andrews
Conference paper

DOI: 10.1007/BFb0054272

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1421)
Cite this paper as:
Bishop M., Andrews P.B. (1998) Selectively instantiating definitions. In: Kirchner C., Kirchner H. (eds) Automated Deduction — CADE-15. CADE 1998. Lecture Notes in Computer Science, vol 1421. Springer, Berlin, Heidelberg

Abstract

When searching for proofs of theorems which contain definitions, it is a significant problem to decide which instances of the definitions to instantiate. We describe a method called dual instantiation, which is a partial solution to the problem in the context of the connection method; the same solution may also be adaptable to other search procedures. Dual instantiation has been implemented in TPS, a theorem prover for classical type theory, and we provide some examples of theorems that have been proven using this method. Dual instantiation has the desirable properties that the search for a proof cannot possibly fail due to insufficient instantiation of definitions, and that the natural deduction proof which results from a successful search will contain no unnecessary instantiations of definitions. Furthermore, the time taken by a proof search using dual instantiation is in general comparable to the time taken by a search in which exactly the required instances of each definition have been instantiated. We also describe how this technique can be applied to the problem of instantiating set variables.

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Matthew Bishop
    • 1
  • Peter B. Andrews
    • 1
  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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