 
Summary: System Description: TPS:
A Theorem Proving System for Type Theory
Peter B. Andrews 1 , Matthew Bishop 2 , and Chad E. Brown 1
1 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh
PA 15213, USA. Peter.Andrews@cmu.edu, cebrown@andrew.cmu.edu
2 Department of Computer Science, King's College London, Strand,
London WC2R 2LS, England. bishopm@dcs.kcl.ac.uk
1 Introduction
This is a brief update on the Tps automated theorem proving system for clas
sical type theory, which was described in [3]. Manuals and information about
obtaining Tps can be found at http://gtps.math.cmu.edu/tps.html.
In Section 2 we discuss some examples of theorems which Tps can now prove
automatically, and in Section 3 we discuss an example which illustrates one of
the many challenges of theorem proving in higherorder logic. We rst provide a
brief summary of the key features of Tps .
Tps uses Church's type theory [8] (typed calculus) as its logical language.
Ws are displayed on the screen and in printed proofs in the notation of this
system of symbolic logic.
One can use Tps in automatic, semiautomatic, or interactive mode to con
struct proofs in natural deduction style, and a mixture of these modes of oper
