Abstract
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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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. https://doi.org/10.1007/BFb0014058
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DOI: https://doi.org/10.1007/BFb0014058
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