## Notre Dame Journal of Formal Logic

### The "Relevance" of Intersection and Union Types

#### Abstract

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 --typed combinatory logic terms are proved to completely codify the associated logical proofs.

#### Article information

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

Dates
First available in Project Euclid: 12 December 2002

http://projecteuclid.org/euclid.ndjfl/1039724889

Digital Object Identifier
doi:10.1305/ndjfl/1039724889

Mathematical Reviews number (MathSciNet)
MR1489412

Zentralblatt MATH identifier
0918.03008

#### Citation

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

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