Relating Classical Realizability and Negative Translation for Existential Witness Extraction
نویسنده
چکیده
Friedman showed how to turn a classical proof of a Σ 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.
منابع مشابه
Existential witness extraction in classical realizability and via a negative translation
We show how to extract existential witnesses from classical proofs using Krivine’s classical realizability—where classical proofs are interpreted as λ-terms with the call/cc control operator. We first recall the basic framework of classical realizability (in classical second-order arithmetic) and show how to extend it with primitive numerals for faster computations. Then we show how to perform ...
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