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On isomorphisms of intersection types

On isomorphisms of intersection types The study of type isomorphisms for different λ-calculi started over twenty years ago, and a very wide body of knowledge has been established, both in terms of results and in terms of techniques. A notable missing piece of the puzzle was the characterization of type isomorphisms in the presence of intersection types. While, at first thought, this may seem to be a simple exercise, it turns out that not only finding the right characterization is not simple, but that the very notion of isomorphism in intersection types is an unexpectedly original element in the previously known landscape, breaking most of the known properties of isomorphisms of the typed λ-calculus. In particular, isomorphism is not a congruence and types that are equal in the standard models of intersection types may be nonisomorphic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

On isomorphisms of intersection types

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References (23)

Publisher
Association for Computing Machinery
Copyright
The ACM Portal is published by the Association for Computing Machinery. Copyright © 2010 ACM, Inc.
Subject
Lambda calculus and related systems
ISSN
1529-3785
DOI
10.1145/1805950.1805955
Publisher site
See Article on Publisher Site

Abstract

The study of type isomorphisms for different λ-calculi started over twenty years ago, and a very wide body of knowledge has been established, both in terms of results and in terms of techniques. A notable missing piece of the puzzle was the characterization of type isomorphisms in the presence of intersection types. While, at first thought, this may seem to be a simple exercise, it turns out that not only finding the right characterization is not simple, but that the very notion of isomorphism in intersection types is an unexpectedly original element in the previously known landscape, breaking most of the known properties of isomorphisms of the typed λ-calculus. In particular, isomorphism is not a congruence and types that are equal in the standard models of intersection types may be nonisomorphic.

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Jul 1, 2010

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