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Typing streams in the Λμ-calculus

Typing streams in the Λμ-calculus Λμ-calculus is a Böhm-complete extension of Parigot's Λμ-calculus closely related with delimited control in functional programming. In this article, we investigate the meta-theory of untyped Λμ-calculus by proving confluence of the calculus and characterizing the basic observables for the Separation theorem, canonical normal forms . Then, we define Λ s , a new type system for Λμ-calculus that contains a special type construction for streams, and prove that strong normalization and type preservation hold. Thanks to the new typing discipline of Λ s , new computational behaviors can be observed, which were forbidden in previous type systems for λμ-calculi. Those new typed computational behaviors witness the stream interpretation of Λμ-calculus. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Typing streams in the Λμ-calculus

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References (31)

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
10.1145/1805950.1805958
Publisher site
See Article on Publisher Site

Abstract

Λμ-calculus is a Böhm-complete extension of Parigot's Λμ-calculus closely related with delimited control in functional programming. In this article, we investigate the meta-theory of untyped Λμ-calculus by proving confluence of the calculus and characterizing the basic observables for the Separation theorem, canonical normal forms . Then, we define Λ s , a new type system for Λμ-calculus that contains a special type construction for streams, and prove that strong normalization and type preservation hold. Thanks to the new typing discipline of Λ s , new computational behaviors can be observed, which were forbidden in previous type systems for λμ-calculi. Those new typed computational behaviors witness the stream interpretation of Λμ-calculus.

Journal

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

Published: Jul 1, 2010

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