Selectively instantiating definitions

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.

This material is based upon work supported by the National Science Foundation under grant CCR-9624683. This work was supported in part by Intel Corporation through an equipment grant.