A Prolog Technology Theorem Prover: A New Exposition and Implementation in Prolog

A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full rst-order predicate calculus. It di ers from Prolog in its use of uni cation with the occurs check for soundness, depthrst iterative-deepening search instead of unbounded depthrst search to make the search strategy complete, and the model elimination reduction rule that is added to Prolog inferences to make the inference system complete. This paper describes a new Prolog-based implementation of PTTP. It uses three compile-time transformations to translate formulas into Prolog clauses that directly execute, with the support of a few run-time predicates, the model elimination procedure with depthrst iterative-deepening search and uni cation with the occurs check. Its high performance exceeds that of Prolog-based PTTP interpreters, and it is more concise and readable than the earlier Lisp-based compiler, which makes it superior for expository purposes. Examples of inputs and outputs of the compile-time transformations provide an easy and quite precise way to explain how PTTP works. This Prolog-based version makes it easier to incorporate PTTP theorem-proving ideas into Prolog programs. Some suggestions are made on extensions to Prolog that could be used to improve PTTP's performance. This research was supported by the National Science Foundation under Grant CCR-8611116. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the o cial policies, either expressed or implied, of the National Science Foundation or the United States government.