dale@LINC.CIS.UPENN.EDU (Dale Miller) (10/23/87)
Implementing Theorem Provers in Logic Programming Dissertation Proposal Amy Felty (felty@linc.cis.upenn.edu) Computer and Information Science University of Pennsylvania Logic programming languages have many characteristics that indicate that they should serve as good implementation languages for theorem provers. For example, they are based on search and unification which are also fundamental to theorem proving. We show how an extended logic programming language can be used to implement theorem provers and other aspects of proof systems for a variety of logics. In this language first-order terms are replaced with simply-typed lambda-terms, and thus unification becomes higher-order unification. Also, implication and universal quantification are allowed in goals. We illustrate that inference rules can be very naturally specified, and that the search operations based on this language correspond to those needed for searching for proofs. We argue on several levels that this extended logic programming language provides a very suitable environment for implementing tactic style theorem provers. Such theorem provers provide extensive capabilities for integrating techniques for automated theorem proving into an interactive proof environment. We are also concerned with representing proofs as objects. We illustrate how such objects can be constructed and manipulated in the logic programming setting. Finally, we propose extensions to tactic style theorem provers in working toward the goal of developing an interactive theorem proving environment that provides a user with many tools and techniques for building and manipulating proofs, and that integrates sophisticated capabilites for automated proof discovery. Many of the theorem provers we present have been implemented in the higher-order logic programming language Lambda Prolog. Date: Friday November 6, 1987 Location: 554 Moore Time: 1:30 PM Committee: Val Breazu-Tannen Robert Constable Jean Gallier (Chair) Andre Scedrov Advisor: Dale Miller