Skip to main content
SpringerLink
Log in
Book cover

HOL Users' Group Workshop

HUG 1993: Higher Order Logic Theorem Proving and Its Applications pp 366–370Cite as

TPS: An interactive and automatic tool for proving theorems of type theory

  • Conference paper
  • First Online:

  • 670 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 780))

Abstract

This is a demonstration of TPS, a theorem proving system for classical type theory (Church's typed λ-calculus). TPS can be used 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.

This material is based upon work supported by the National Science Foundation under grants CCR-9002546 and CCR-9201893.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Peter B. Andrews, “Transforming Matings into Natural Deduction Proofs,” in 5th Conference on Automated Deduction, edited by W. Bibel and R. Kowalski, Les Arcs, France, Lecture Notes in Computer Science 87, Springer-Verlag, 1980, 281–292.

    Google Scholar 

  2. Peter B. Andrews, Theorem Proving via General Matings, Journal of the ACM 28 (1981), 193–214.

    Article  Google Scholar 

  3. Peter B. Andrews, Dale A. Miller, Eve Longini Cohen, Frank Pfenning, “Automating Higher-Order Logic,” in Automated Theorem Proving: After 25 Years, edited by W. W. Bledsoe and D. W. Loveland, Contemporary Mathematics series, vol. 29, American Mathematical Society, 1984, 169–192.

    Google Scholar 

  4. Peter B. Andrews, An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, Academic Press, 1986.

    Google Scholar 

  5. Peter B. Andrews, Frank Pfenning, Sunil Issar, C. P. Klapper, “The TPS Theorem Proving System,” in 8th International Conference on Automated Deduction, edited by Jorg H. Siekmann, Oxford, England, Lecture Notes in Computer Science 230, Springer-Verlag, 1986, 663–664.

    Google Scholar 

  6. Peter B. Andrews, Sunil Issar, Daniel Nesmith, Frank Pfenning, “The TPS Theorem Proving System,” in 9th International Conference on Automated Deduction, edited by Ewing Lusk and Ross Overbeek, Argonne, Illinois, Lecture Notes in Computer Science 310, Springer-Verlag, 1988, 760–761.

    Google Scholar 

  7. Peter B. Andrews, On Connections and Higher-Order Logic, Journal of Automated Reasoning 5 (1989), 257–291.

    Google Scholar 

  8. Peter B. Andrews, Sunil Issar, Dan Nesmith, Frank Pfenning, “The TPS Theorem Proving System,” in 10th International Conference on Automated Deduction, edited by M. E. Stickel, Kaiserslautern, FRG, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, 641–642.

    Google Scholar 

  9. Peter B. Andrews, Sunil Issar, Dan Nesmith, and Frank Pfenning, The TPS Theorem Proving System, Journal of Symbolic Logic 57 (1992), 353–354. (abstract).

    Google Scholar 

  10. Peter B. Andrews, Matthew Bishop, Sunil Issar, Dan Nesmith, Frank Pfenning, Hongwei Xi. TPS: A Theorem Proving System for Classical Type Theory, 1993, unpublished.

    Google Scholar 

  11. Peter B. Andrews, Sunil Issar, Dan Nesmith, Frank Pfenning, Hongwei Xi, Matthew Bishop, TPS3 Facilities Guide for Programmers and Users, 1993. 160+vii pp.

    Google Scholar 

  12. Peter B. Andrews, Sunil Issar, Dan Nesmith, Frank Pfenning, Hongwei Xi, Matthew Bishop, TPS3 Facilities Guide for Users, 1993. 94+v pp.

    Google Scholar 

  13. Wolfgang Bibel, Automated Theorem Proving, Vieweg, Braunschweig, 1987.

    Google Scholar 

  14. Alonzo Church, A Formulation of the Simple Theory of Types, Journal of Symbolic Logic 5 (1940), 56–68.

    Google Scholar 

  15. Doug Goldson and Steve Reeves, Using Programs to Teach Logic to Computer Scientists, Notices of the American Mathematical Society 40 (1993), 143–148.

    Google Scholar 

  16. Michael J. Gordon, Arthur J. Milner, Christopher P. Wadsworth. Edinburgh LCF, Lecture Notes in Computer Science 78, Springer Verlag, 1979.

    Google Scholar 

  17. Gerard P. Huet, A Unification Algorithm for Typed λ-Calculus, Theoretical Computer Science 1 (1975), 27–57.

    Article  Google Scholar 

  18. Sunil Issar, “Path-Focused Duplication: A Search Procedure for General Matings,” in AAAI-90. Proceedings of the Eighth National Conference on Artificial Intelligence, AAAI Press/The MIT Press, 1990, 221–226.

    Google Scholar 

  19. Sunil Issar. Operational Issues in Automated Theorem Proving Using Matings, Ph.D. Thesis, Carnegie Mellon University, 1991. 147 pp.

    Google Scholar 

  20. Sunil Issar, Peter B. Andrews, Frank Pfenning, Dan Nesmith, GRADER Manual, 1991. 23+ipp.

    Google Scholar 

  21. Sunil Issar, Dan Nesmith, Peter B. Andrews, Frank Pfenning, TPS3 Programmer's Guide, 1992. 99+iii pp.

    Google Scholar 

  22. Dale A. Miller, Eve Longini Cohen, Peter B. Andrews, “A Look at TPS,” in 6th Conference on Automated Deduction, edited by Donald W. Loveland, New York, USA, Lecture Notes in Computer Science 138, Springer-Verlag, 1982, 50–69.

    Google Scholar 

  23. Dale A. Miller. Proofs in Higher-Order Logic, Ph.D. Thesis, Carnegie Mellon University, 1983. 81 pp.

    Google Scholar 

  24. Dale A. Miller, “Expansion Tree Proofs and Their Conversion to Natural Deduction Proofs,” in 7th International Conference on Automated Deduction, edited by R. E. Shostak, Napa, California, USA, Lecture Notes in Computer Science 170, Springer-Verlag, 1984, 375–393.

    Google Scholar 

  25. Dale A. Miller, A Compact Representation of Proofs, Studia Logica 46 (1987), 347–370.

    Google Scholar 

  26. Dan Nesmith, Peter B. Andrews, Sunil Issar, Frank Pfenning, TPS User's Manual, 1991. 35+ii pp.

    Google Scholar 

  27. Frank Pfenning, “Analytic and Non-analytic Proofs,” in 7th International Conference on Automated Deduction, edited by R. E. Shostak, Napa, California, USA, Lecture Notes in Computer Science 170, Springer-Verlag, 1984, 394–413.

    Google Scholar 

  28. Frank Pfenning. Proof Transformations in Higher-Order Logic, Ph.D. Thesis, Carnegie Mellon University, 1987. 156 pp.

    Google Scholar 

  29. Frank Pfenning and Dan Nesmith, “Presenting Intuitive Deductions via Symmetric Simplification,” in 10th International Conference on Automated Deduction, edited by M. E. Stickel, Kaiserslautern, FRG, Lecture Notes in Artificial Intelligence 449, Springer-Verlag, 1990, 336–350.

    Google Scholar 

  30. Frank Pfenning, Sunil Issar, Dan Nesmith, Peter B.Andrews, ETPS User's Manual, 1992. 48+ii pp.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    Peter B. Andrews, Matthew Bishop, Sunil Issar, Frank Pfenning & Hongwei Xi

  2. University of the Saarland, D-W-6600, Saarbrucken, Germany

    Dan Nesmith

Authors
  1. Peter B. Andrews
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthew Bishop
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sunil Issar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dan Nesmith
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Frank Pfenning
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hongwei Xi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jeffrey J. Joyce Carl-Johan H. Seger

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Andrews, P.B., Bishop, M., Issar, S., Nesmith, D., Pfenning, F., Xi, H. (1994). TPS: An interactive and automatic tool for proving theorems of type theory. In: Joyce, J.J., Seger, CJ.H. (eds) Higher Order Logic Theorem Proving and Its Applications. HUG 1993. Lecture Notes in Computer Science, vol 780. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57826-9_148

Download citation

  • DOI: https://doi.org/10.1007/3-540-57826-9_148

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57826-0

  • Online ISBN: 978-3-540-48346-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation