Open Access
VOL. 2 | 1998 Intersection Types, $\lambda$-models, and Böhm Trees
Mariangiola Dezani-Ciancaglini, Elio Giovannetti, Ugo de'Liguoro

Editor(s) Mariangiola Dezani-Ciancaglini, Mitsuhiro Okada, Masako Takahashi

MSJ Memoirs, 1998: 45-97 (1998) DOI: 10.2969/msjmemoirs/00201C020


This paper is an introduction to intersection type disciplines, with the aim of illustrating their theoretical relevance in the foundations of $\lambda$-calculus. We start by describing the well-known results showing the deep connection between intersection type systems and normalization properties, i.e., their power of naturally characterizing solvable, normalizing, and strongly normal- izing pure $\lambda$-terms. We then explain the importance of intersection types for the semantics of $\lambda$-calculus, through the construction of filter models and the representation of algebraic lattices. We end with an original result that shows how intersection types also allow to naturally characterize tree representations of unfoldings of $\lambda$-terms (Böohm trees).


Published: 1 January 1998
First available in Project Euclid: 17 January 2014

zbMATH: 0946.03016
MathSciNet: MR1728759

Digital Object Identifier: 10.2969/msjmemoirs/00201C020

Rights: Copyright © 1998, The Mathematical Society of Japan

Vol. 2 • 1 January 1998
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