Translating a Fragment of Weak Type Theory into Type Theory with Open Terms

  • G. I. Jojgov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3863)


One of the main application areas of interactive proof assistants is the formalization of mathematical texts. This formalization not only allows mathematical texts to be handled electronically, but also to be checked for correctness. Due to the level of detail required in the formalization, formalized texts eliminate ambiguities that may be present in an informally presented mathematical texts.


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  1. 1.
    The Coq Development Team. The Coq Proof Assistant Reference Manual – Version V8 (2004),
  2. 2.
    Geuvers, H., Jojgov, G.: Open Proofs and Open Terms: a Basis for Interactive Logic. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 537–552. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Jojgov, G.I.: Incomplete Proofs and Terms and Their Use in Interactive Theorem Proving. PhD thesis, Eindhoven University of Technology (2004)Google Scholar
  4. 4.
    Kamareddine, F., Nederpelt, R.: A refinement of de Bruijn’s formal language of mathematics. Journal of Logic, Language and Information (2001)Google Scholar
  5. 5.
    Kamareddine, F., Maarek, M., Wells, J.B.: Mathlang: Experience-driven development of a new mathematical language. In: MKM Symposium 2003. Elsevier, Amsterdam (2003)Google Scholar
  6. 6.
    Kamareddine, F., Maarek, M., Wells, J.B.: Flexible encoding of mathematics on the computer. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 160–174. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    McBride, C.: Dependently Typed Functional Programs and their Proofs. PhD thesis, University of Edinburgh (1999)Google Scholar
  8. 8.
    Nederpelt, R.: Weak Type Theory: A formal language for mathematics. Technical report, Eindhoven University of Technology (May 2002)Google Scholar
  9. 9.
    Nederpelt, R.P., Geuvers, J.H., de Vrijer, R.C. (eds.): Selected Papers on Automath. Studies in Logic and Foundations of Mathematics, vol. 133. North Holland, Amsterdam (1994)zbMATHGoogle Scholar
  10. 10.
    Nipkow, T.: Structured Proofs in Isar/HOL. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 259–278. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Paulson, L.: Introduction to Isabelle. Technical report, University of Cambridge (1993)Google Scholar
  12. 12.
    Ranta, A.: Grammatical Framework: A Type-Theoretical Grammar Formalism. Journal of Functional Programming (2003)Google Scholar
  13. 13.
    Rudnicki, P.: An overview of the Mizar project. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs (1992),
  14. 14.
    Thery, L.: Colouring Proofs: A Lightweight Approach to Adding Formal Structure to Proofs. In: Proceedings of User Interfaces for Theorem Provers UITP 2003. ENTCS 103 (2003)Google Scholar
  15. 15.
    Wenzel, M., Nipkow, T., Paulson, L.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  16. 16.
    Wiedijk, F.: Formal Proof Sketches. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 378–393. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • G. I. Jojgov
    • 1
  1. 1.Technische Universiteit EindhovenThe Netherlands

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