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Existential witness extraction in classical realizability and via a negative translation

Abstract : We show how to extract existential witnesses from classical proofs using Krivine's classical realizability--where classical proofs are interpreted as lambda_c-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 witness extraction in this framework, by discussing several techniques depending on the shape of the existential formula. In particular, we show that in the Sigma^0_1-case, Krivine's witness extraction method reduces to Friedman's through a well-suited negative translation to intuitionistic second-order arithmetic. Finally we discuss the advantages of using call/cc rather than a negative translation, especially from the point of view of an implementation.
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https://hal.archives-ouvertes.fr/hal-00800560
Contributor : Alexandre Miquel <>
Submitted on : Thursday, March 14, 2013 - 4:29:13 AM
Last modification on : Wednesday, November 20, 2019 - 2:59:50 AM

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  • HAL Id : hal-00800560, version 1

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Alexandre Miquel. Existential witness extraction in classical realizability and via a negative translation. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2011, 7 (2), pp.LMCS-7(2:2). ⟨hal-00800560⟩

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