Abstract
We propose a method for realising the proofs of Intuitionistic Zermelo-Fraenkel set theory (IZF) by strongly normalising λ-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 λ-term that computes a function of type ℕ→ℕ can be extracted from the proof of its existence in IZF.
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Miquel, A. (2003). A Strongly Normalising Curry-Howard Correspondence for IZF Set Theory. In: Baaz, M., Makowsky, J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45220-1_35
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DOI: https://doi.org/10.1007/978-3-540-45220-1_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40801-7
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