In this paper, we show how to integrate linear types with type dependency, by extending the linear\/non-linear calculus of Benton to support type dependency. Next, we give an application of this calculus by giving a proof-theoretic account of imperative programming, which requires extending the calculus with computationally irrelevant quantification, proof irrelevance, and a monad of computations. We show the soundness of our theory by giving a realizability model in the style of Nuprl, which permits us to validate not only the \u03b2-laws for each type, but also the \u03b7-laws. These extensions permit us to decompose Hoare triples into a collection of simpler type-theoretic connectives, yielding a rich equational theory for dependently-typed higherorder imperative programs. Furthermore, both the type theory and its model are relatively simple, even when all of the extensions are considered.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this paper, we show how to integrate linear types with type dependency, by extending the linear\/non-linear calculus of Benton to support type dependency. Next, we give an application of this calculus by giving a proof-theoretic account of imperative programming, which requires extending the calculus with computationally irrelevant quantification, proof irrelevance, and a monad of […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Neelakantan R. 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