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Contextual modal type theory

by: Aleksandar Nanevski, Frank Pfenning, Brigitte Pientka
ACM Trans. Comput. Logic, Vol. 9, No. 3. (2008), pp. 1-49, doi:10.1145/1352582.1352591  Key: citeulike:5447123

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Abstract

The intuitionistic modal logic of necessity is based on the judgmental notion of categorical truth. In this article we investigate the consequences of relativizing these concepts to explicitly specified contexts. We obtain contextual modal logic and its type-theoretic analogue. Contextual modal type theory provides an elegant, uniform foundation for understanding metavariables and explicit substitutions. We sketch some applications in functional programming and logical frameworks.


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