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We propose a method for realising the proofs of Intuitionistic Zermelo-Fraenkel set theory (IZF) by strongly normalising lambda-terms. This method relies on the introduction of a Curry-style type theory extended with specific subtyping principles, which is then used as a low-level language to interpret IZF via a representation of sets as pointed graphs inspired by Aczel's hyperset theory.
As a consequence, we refine a classical result of Myhill and Friedman by showing how a strongly normalising lambda-term that computes a function of type N->N can be extracted from the proof of its existence in IZF.
© 2002-2003 Kurt Gödel Society, Norbert Preining. |
2003-06-04
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