Relating Classical Realizability and Negative Translation for Existential Witness Extraction
Friedman showed how to turn a classical proof of a \(\Sigma^0_1\) formula into an intuitionistic proof of the same formula, thus giving an effective method to extract witnesses from classical proofs of such formulae. In this paper we show how to achieve the same goal efficiently using Krivine realizability with primitive numerals, and prove that the corresponding program is but the direct-style equivalent (using call-cc) of the CPS-style program underlying Friedman’s method.
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