A simplification of Girard's paradox

  • Antonius J. C. Hurkens
Conference paper

DOI: 10.1007/BFb0014058

Part of the Lecture Notes in Computer Science book series (LNCS, volume 902)
Cite this paper as:
Hurkens A.J.C. (1995) A simplification of Girard's paradox. In: Dezani-Ciancaglini M., Plotkin G. (eds) Typed Lambda Calculi and Applications. TLCA 1995. Lecture Notes in Computer Science, vol 902. Springer, Berlin, Heidelberg


In 1972 J.-Y. Girard showed that the Burali-Forti paradox can be formalised in the type system U. In 1991 Th. Coquand formalised another paradox in U. The corresponding proof terms (that have no normal form) are large. We present a shorter term of type ⊥ in the Pure Type System λU and analyse its reduction behaviour. The idea is to construct a universe U and two functions such that a certain equality holds. Using this equality, we prove and disprove that a certain object in U is well-founded.


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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Antonius J. C. Hurkens
    • 1
  1. 1.NS HapsThe Netherlands

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