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Strong normalization with non-structural subtyping

Published online by Cambridge University Press:  04 March 2009

Mitchell Wand
Affiliation:
College of Computer Science, Northeastern University, 360 Huntington Avenue, 161CN, Boston, MA 02115, USA. E-mail: wand@ccs.neu.edu
Patrick O'Keefe
Affiliation:
151 Coolidge Avenue #211, Watertown, MA 02172, USA. E-mail: pmo@world.std.com
Jens Palsberg
Affiliation:
Computer Science Department, Aarhus University, DK-8000 Aarhus C, Denmark. E-mail: palsberg@daimi.aau.dk

Abstract

We study a type system with a notion of subtyping that involves a largest type ⊤, a smallest type ⊥, atomic coercions between base types, and the usual ordering of function types. We prove that any λ-term typable in this system is strongly normalizing, which solves an open problem of Thatte. We also prove that the fragment without ⊥ types has strictly fewer terms. This demonstrates that ⊥ adds power to a type system.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1995

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References

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