Notre Dame Journal of Formal Logic

The "Relevance" of Intersection and Union Types

Mariangiola Dezani-Ciancaglini,Silvia Ghilezan, and Betti Venneri


The aim of this paper is to investigate a Curry-Howard interpretation of the intersection and union type inference system for Combinatory Logic. Types are interpreted as formulas of a Hilbert-style logic L, which turns out to be an extension of the intuitionistic logic with respect to provable disjunctive formulas (because of new equivalence relations on formulas), while the implicational-conjunctive fragment of L is still a fragment of intuitionistic logic. Moreover, typable terms are translated in a typed version, so that $\vee$-$\wedge$-typed combinatory logic terms are proved to completely codify the associated logical proofs.

Article information

Notre Dame J. Formal Logic Volume 38, Number 2 (1997), 246-269.

First available: 12 December 2002

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Zentralblatt MATH identifier

Primary: 03B40: Combinatory logic and lambda-calculus [See also 68N18]
Secondary: 03B46 03B55: Intermediate logics 68N15: Programming languages


Dezani-Ciancaglini, Mariangiola; Ghilezan, Silvia; Venneri, Betti. The "Relevance" of Intersection and Union Types. Notre Dame Journal of Formal Logic 38 (1997), no. 2, 246--269. doi:10.1305/ndjfl/1039724889.

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