A Decidable Subtyping Logic for Intersection and Union Types

Luigi Liquori (1) , Claude Stolze (1)

1 KAIROS - Logical Time for Formal Embedded System Design

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 $ .

Mots clés: Subtype systems; Type; Logics and lambda-calculus

Domaines: Informatique [cs]

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⟩