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From realizability to induction via dependent intersection
Journal article   Open access   Peer reviewed

From realizability to induction via dependent intersection

Aaron Stump
Annals of pure and applied logic, Vol.169(7), pp.637-655
07/2018
DOI: 10.1016/j.apal.2018.03.002
url
https://doi.org/10.1016/j.apal.2018.03.002View
Published (Version of record) Open Access

Abstract

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 a built-in equality type. 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.
Derivable induction Extrinsic typing Internalized realizability Lambda encodings

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