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The paradox of trees in type theory

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Abstract

We show how to represent a paradox similar to Russell's paradox in Type Theory withW-types and a type of all types, and how to use this in order to represent a fixed-point operator in such a theory. It is still open whether such a construction is possible without theW-type.

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References

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This research was partly supported by ESPIRIT Basic Research Action “Logical Frameworks”.

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Coquand, T. The paradox of trees in type theory. BIT 32, 10–14 (1992). https://doi.org/10.1007/BF01995104

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  • DOI: https://doi.org/10.1007/BF01995104

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