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Modal Type Theory Based on the Intuitionistic Modal Logic \(\mathbf{IEL}^{-}\)

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Logical Foundations of Computer Science (LFCS 2020)

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Abstract

The modal intuitionistic epistemic logic \(\mathbf{IEL}^{-}\) was proposed by Artemov and Protopopescu as the intuitionistic version of belief logic. We construct the modal lambda calculus which is Curry-Howard isomorphic to \(\mathbf{IEL}^{-}\) as the type-theoretical representation of applicative computation widely known in functional programming.

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Notes

  1. 1.

    In Haskell, type class is a general interface for some special group of datatypes.

References

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Acknowledgment

The author is grateful to Neel Krishnaswami, Vladimir Krupski, Valerii Plisko, and Vladimir Vasyukov for consulting and advice.

The author thanks anonymous peer-reviewers for valuable and considerable comments and remarks that improved the paper significantly.

The research described in this paper was supported by Russian Foundation for Basic Research (grant 16-03-00364).

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Correspondence to Daniel Rogozin .

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Rogozin, D. (2020). Modal Type Theory Based on the Intuitionistic Modal Logic \(\mathbf{IEL}^{-}\). In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2020. Lecture Notes in Computer Science(), vol 11972. Springer, Cham. https://doi.org/10.1007/978-3-030-36755-8_15

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