Open Access
Spring 1997 The "Relevance" of Intersection and Union Types
Mariangiola Dezani-Ciancaglini, Silvia Ghilezan, Betti Venneri
Notre Dame J. Formal Logic 38(2): 246-269 (Spring 1997). DOI: 10.1305/ndjfl/1039724889


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.


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Mariangiola Dezani-Ciancaglini. Silvia Ghilezan. Betti Venneri. "The "Relevance" of Intersection and Union Types." Notre Dame J. Formal Logic 38 (2) 246 - 269, Spring 1997.


Published: Spring 1997
First available in Project Euclid: 12 December 2002

zbMATH: 0918.03008
MathSciNet: MR1489412
Digital Object Identifier: 10.1305/ndjfl/1039724889

Primary: 03B40
Secondary: 03B46 , 03B55 , 68N15

Rights: Copyright © 1997 University of Notre Dame

Vol.38 • No. 2 • Spring 1997
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