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Notions of computation and monads
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Modal types as staging specifications for run-time code generation
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A modal analysis of staged computation
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Primitive Recursion for Higher-Order Abstract Syntax
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A modal analysis of staged computation
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Electronic Notes in Theoretical Computer Science (ENTCS)
Completeness and Soundness Results for X with Intersection and Union Types
Fundamenta Informaticae - Intersection Types and Related Systems ITRS
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We reconsider the foundations of modal logic, following Martin-Löf's methodology of distinguishing judgments from propositions. We give constructive meaning explanations for necessity and possibility, which yields a simple and uniform system of natural deduction for intuitionistic modal logic that does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic and find that the lax modality is already expressible using possibility and necessity. Through a computational interpretation of proofs in modal logic we further obtain a new formulation of Moggi's monadic metalanguage.