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On Correspondence between Selective CPS Transformation and Selective Double Negation Translation

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  • Hyeonseung Im

    (Department of Computer Science and Engineering, Interdisciplinary Graduate Program in Medical Bigdata Convergence, Kangwon National University, Chuncheon-si, Gangwon-do 24341, Korea)

Abstract

A double negation translation (DNT) embeds classical logic into intuitionistic logic. Such translations correspond to continuation passing style (CPS) transformations in programming languages via the Curry-Howard isomorphism. A selective CPS transformation uses a type and effect system to selectively translate only nontrivial expressions possibly with computational effects into CPS functions. In this paper, we review the conventional call-by-value (CBV) CPS transformation and its corresponding DNT, and provide a logical account of a CBV selective CPS transformation by defining a selective DNT via the Curry-Howard isomorphism. By using an annotated proof system derived from the corresponding type and effect system, our selective DNT translates classical proofs into equivalent intuitionistic proofs, which are smaller than those obtained by the usual DNTs. We believe that our work can serve as a reference point for further study on the Curry-Howard isomorphism between CPS transformations and DNTs.

Suggested Citation

  • Hyeonseung Im, 2021. "On Correspondence between Selective CPS Transformation and Selective Double Negation Translation," Mathematics, MDPI, vol. 9(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:385-:d:499638
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