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Summary: TPS: A Theorem Proving System
for Classical Type Theory
Peter B. Andrews1, Matthew Bishop2, Sunil Issar3,
Dan Nesmith4, Frank Pfenning5, Hongwei Xi6
Abstract
This is a description of TPS, a theorem proving system for classical type theory (Church's typed
-calculus). TPS has been designed to be a general research tool for manipulating wffs of first- and
higher-order 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 higher-order logic.7
KEY WORDS: higher-order 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
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