# A Decidable Subtyping Logic for Intersection and Union Types

1 KAIROS - Logical Time for Formal Embedded System Design
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : Using Curry-Howard isomorphism, we extend the typed lambda-calculus with intersection and union types, and its corresponding proof-functional logic, previously defined by the authors, with subtyping and explicit coercions.We show the extension of the lambda-calculus to be isomorphic to the Barbanera-Dezani-de’Liguoro type assignment system and we provide a sound interpretation of the proof-functional logic with the $\mathsf {NJ}(\beta )$ logic, using Mints’ realizers.We finally present a sound and complete algorithm for subtyping in presence of intersection and union types. The algorithm is conceived to work for the (sub)type theory $\varXi$ .
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Cited literature [27 references]

https://hal.inria.fr/hal-01760641
Contributor : Hal Ifip <>
Submitted on : Friday, April 6, 2018 - 3:08:02 PM
Last modification on : Thursday, March 5, 2020 - 12:20:51 PM

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440117_1_En_7_Chapter.pdf
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### Citation

Luigi Liquori, Claude Stolze. A Decidable Subtyping Logic for Intersection and Union Types. TTCS 2017 - 2nd International Conference on Topics in Theoretical Computer Science, Sep 2017, Tehran, Iran. pp.74-90, ⟨10.1007/978-3-319-68953-1_7⟩. ⟨hal-01760641⟩

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