Automating Inductive Speciication Proofs in Nuprl

We present an automatic method which combines logical proof search and rippling heuristics to prove speciications. The key idea is to instantiate meta-variables in the proof with a simultaneous match based on rippling/reverse rippling heuristic. Underlying our rippling strategy is the rippling distance strategy which introduces a new powerful approach to rippling, as it avoids termination problems of other rippling strategies. Moreover, we are able to synthesize conditional substitutions for meta-variables in the proof. The strength of our approach is illustrated by discussing the speciication of the integer square root and automatically synthesizing the corresponding algorithm. The described procedure is integrated as a tactic into the NuPRL system. This work has been carried out during the stay of the rst author in the NuPRL group. It has been made possible through a fellowship of the Daimler Benz Foundation and the support of Robert Constable who provided the additional nancial means and an intellectual challenging and encouraging environment for this work.