From Realizability to Induction via Dependent Intersection
نویسنده
چکیده
In this paper, it is shown that induction is derivable in a type-assignment formulation of the second-order dependent type theory λP2, extended with the implicit product type of Miquel, dependent intersection type of Kopylov, and heterogeneous equality type of McBride. The crucial idea is to use dependent intersections to internalize a result of Leivant’s showing that Church-encoded data may be seen as realizing their own type correctness statements, under the Curry-Howard isomorphism.
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تاریخ انتشار 2016