 
Summary: TPS: A Theorem Proving System
for Classical Type Theory
Peter B. Andrews 1 , Matthew Bishop 2 , Sunil Issar 3 ,
Dan Nesmith 4 , Frank Pfenning 5 , Hongwei Xi 6
Abstract
This is a description of TPS, a theorem proving system for classical type theory (Church's typed
lcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and
higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a
combination of these modes. An important feature of TPS is the ability to translate between
expansion proofs and natural deduction proofs. Examples of theorems which TPS can prove
completely automatically are given to illustrate certain aspects of TPS's behavior and problems of
theorem proving in higherorder logic. 7
KEY WORDS: higherorder logic, type theory, mating, connection, expansion proof, natural
deduction.
CONTENTS
1 Introduction
2 An Overview of TPS
3 Tactics and Proof Translations
4 Automatic Search
5 An Example
