Abstract
We present a possible computational content of the negative translation of classical analysis with the Axiom of Choice. Interestingly, this interpretation uses a refinement of the realizibility semantics of the absurdity proposition, which is not interpreted as the empty type here. We also show how to compute witnesses from proofs in classical analysis, and how to extract algorithms from proofs of ∀∃ statements.
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Berardi, S., Bezem, M., Coquand, T. (1995). A realization of the negative interpretation of the Axiom of Choice. 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/BFb0014044
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DOI: https://doi.org/10.1007/BFb0014044
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