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Subtyping and intersection types revisited

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Frank PfenningAuthors Info & Claims

ICFP '07: Proceedings of the 12th ACM SIGPLAN international conference on Functional programming

Page 219

https://doi.org/10.1145/1291151.1291153

Published: 01 October 2007 Publication History

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Abstract

Church's system of simple types has proven to be remarkably robust: call-by-name, call-by-need, and call-by-value languages, with or without effects, and even logical frameworks can be based on the same typing rules. When type systems become more expressive, this unity fractures. An early example is the value restriction for parametric polymorphism which is necessary for ML but not Haskell; a later manifestation is the lack of distributivity of function types over intersections in call-by-value languages with effects.

In this talk we reexamine the logical justification for systems of subtyping and intersection types and then explore the consequences in two different settings: logical frameworks and functional programming.

In logical frameworks functions are pure and their definitions observable, but complications could arise from the presence of dependent types. We show that this is not the case, and that we can obtain soundness and completeness theorems for a certain axiomatization of subtyping. We also sketch a connection to the type-theoretic notion of proof irrelevance.

In functional programming we investigate how the encapsulation of effects in monads interacts with subtyping and intersection types, providing an updated analysis of the value restriction and related phenomena. While at present this study is far from complete, we believe that its origin in purely logical notions will give rise to a uniform theory that can easily be adapted to specific languages and their operational interpretations.

References

[1]

Rowan Davies and Frank Pfenning. Intersection types and computational effects. In P. Wadler, editor, Proceedings of the Fifth International Conference on Functional Programming (ICFP'00), pages 198--208, Montreal, Canada, September 2000. ACM Press.

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[2]

William Lovas and Frank Pfenning. A bidirectional refinement type system for LF. In B. Pientka and C. Schürmann, editors, Proceedings of the Second International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, pages 11--25, Bremen, Germany, July 2007.

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[3]

Frank Pfenning and Rowan Davies. A judgmental reconstruction of modal logic. Mathematical Structures in Computer Science, 11:511--540, 2001.

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[4]

Noam Zeilberger. On the unity of duality. Annals of Pure and Applied Logic, 2007. To appear in a special issue on "Classical Logic and Computation".

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Index Terms

Subtyping and intersection types revisited
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation

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Published In

ICFP '07: Proceedings of the 12th ACM SIGPLAN international conference on Functional programming

October 2007

346 pages

ISBN:9781595938152

DOI:10.1145/1291151

General Chair:
Ralf Hinze
Universität Bonn, Germany
,
Program Chair:
Norman Ramsey
Harvard University, USA

ACM SIGPLAN Notices Volume 42, Issue 9
Proceedings of the ICFP '07 conference
September 2007
331 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1291220
Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 2007

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ICFP07

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ICFP07: ACM SIGPLAN International Conference on Functional Programming

October 1 - 3, 2007

Freiburg, Germany

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Overall Acceptance Rate 272 of 887 submissions, 31%

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