A Decidable Subtyping Logic for Intersection and Union Types

  • Luigi LiquoriEmail author
  • Claude StolzeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10608)


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 \(\varXi \).


Logics and lambda-calculus Type Subtype systems 



We are grateful to Ugo de’Liguoro, Daniel Dougherty, and the anonymous referees for their useful comments and suggestions.


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Authors and Affiliations

  1. 1.Université Côte d’Azur, INRIASophia AntipolisFrance

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