Journal of Automated Reasoning

, Volume 16, Issue 3, pp 321–353 | Cite as

TPS: A theorem-proving system for classical type theory

  • Peter B. Andrews
  • Matthew Bishop
  • Sunil Issar
  • Dan Nesmith
  • Frank Pfenning
  • Hongwei Xi
Research Article


This is description of TPS, a theorem-proving system for classical type theory (Church's typed λ-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 that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higher-order logic.

AMS Subject Classification

03-04 68T15 03B35 03B15 03B10 

Key words

higher-order logic type theory mating connection expansion proof natural deduction 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Peter B. Andrews
    • 1
  • Matthew Bishop
    • 1
  • Sunil Issar
    • 2
  • Dan Nesmith
  • Frank Pfenning
    • 3
  • Hongwei Xi
    • 1
  1. 1.Mathematics DepartmentCarnegie Mellon UniversityPittsburghUSA
  2. 2.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA
  3. 3.Department of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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