Tutorial: Using TPS for Higher-Order Theorem Proving and ETPS for Teaching Logic

  • Peter B. Andrews
  • Chad E. Brown
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1831)


TPS is an automated theorem proving system which can be used to prove theorems of first- or higher-order logic automatically, interactively, or in a combination of these modes of operation. Proofs in TPS are presented in natural deduction style. ETPS is a program which was obtained from TPS by deleting all the facilities for proving theorems automatically. ETPS can be used by students to learn how to prove theorems interactively. The objective of the tutorial is to teach participants how to make effective use of TPS and ETPS.


Theorem Prove Type Theory Automate Reasoning Natural Deduction Automate Deduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Andrews, P.B.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Academic Press, London (1986)zbMATHGoogle Scholar
  2. 2.
    Andrews, P.B.: On Connections and Higher-Order Logic. Journal of Automated Reasoning 5, 257–291 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Andrews, P.B., Bishop, M., Issar, S., Nesmith, D., Pfenning, F., Xi, H.: TPS: A Theorem Proving System for Classical Type Theory. Journal of Automated Reasoning 16, 321–353 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bishop, M.: A breadth-first strategy for mating search. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 359–373. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Bishop, M., Andrews, P.B.: Selectively instantiating definitions. In: Kirchner, C., Kirchner, H. (eds.) CADE 1998. LNCS (LNAI), vol. 1421, pp. 365–380. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Church, A.: A Formulation of the Simple Theory of Types. Journal of Symbolic Logic 5, 56–68 (1940)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Goldson, D., Reeves, S., Bornat, R.: A Review of Several Programs for the Teaching of Logic. The Computer Journal 36, 373–386 (1993)CrossRefGoogle Scholar
  8. 8.
    Issar, S.: Path-Focused Duplication: A Search Procedure for General Matings. In: AAAI 1990. Proceedings of the Eighth National Conference on Artificial Intelligence, vol. 1, pp. 221–226. AAAI Press/The MIT Press (1990)Google Scholar
  9. 9.
    Miller, D.A.: A Compact Representation of Proofs. Studia Logica 46(4), 347–370 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pfenning, F., Nesmith, D.: Presenting Intuitive Deductions via Symmetric Simplification. In: Stickel, M.E. (ed.) CADE 1990. LNCS (LNAI), vol. 449, pp. 336–350. Springer, Heidelberg (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Peter B. Andrews
    • 1
  • Chad E. Brown
    • 1
  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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