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The system of intuitionistic modal logic IEL^- was proposed by S. Artemov and T. Protopopescu as the intuitionistic version of belief logic. We construct the modal lambda calculus which is Curry-Howard isomorphic to IEL^- as the type-theoretical representation of applicative computation widely known in functional programming. We also provide a categorical interpretation of this modal lambda calculus considering coalgebras associated with a monoidal functor on a cartesian closed category.arXiv:2005.01135v3 fatcat:7f3qvt33dzgmtdl4rcztcv7me4