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tps: A theorem proving system for classical type theory
 Journal of Automated Reasoning
, 1996
"... This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). 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 comb ..."
Abstract

Cited by 71 (6 self)
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This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). 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
On Sets, Types, Fixed Points, and Checkerboards
 In Pierangelo Miglioli, Ugo Moscato, Daniele Mundici, and Mario Ornaghi, editors, Theorem Proving with Analytic
, 1996
"... Most current research on automated theorem proving is concerned with proving theorems of firstorder logic. We discuss two examples which illustrate the advantages of using higherorder logic in certain contexts. For some purposes type theory is a much more convenient vehicle for formalizing mathema ..."
Abstract

Cited by 8 (2 self)
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Most current research on automated theorem proving is concerned with proving theorems of firstorder logic. We discuss two examples which illustrate the advantages of using higherorder logic in certain contexts. For some purposes type theory is a much more convenient vehicle for formalizing mathematics than axiomatic set theory. Even theorems of firstorder logic can sometimes be proven more expeditiously in higherorder logic than in firstorder logic. We also note the need to develop automatic theoremproving methods which may produce proofs which do not have the subformula property. 1. Introduction In some ways it appears that the field of automated deduction is ahead of its time. We have increasingly good methods for proving theorems, but the hardware available is still not adequate for many of the problems to which we would like to apply our techniques. However, this will change. Radically new computers based on exotic technologies such as DNA computing, quantum computing, and ...