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THEORETICAL PEARLS: A bargain for intersection types: a simple strong normalization proof

Published online by Cambridge University Press:  17 June 2005

PETER MØLLER NEERGAARD
Affiliation:
Michtom School of Computer Science, Brandeis University, Waltham, MA 02454, USA (e-mail: turtle@achilles.linearity.org)
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Abstract

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This pearl gives a discount proof of the folklore theorem that every strongly $\beta$-normalizing $\lambda$-term is typable with an intersection type. (We consider typings that do not use the empty intersection $\omega$ which can type any term.) The proof uses the perpetual reduction strategy which finds a longest path. This is a simplification over existing proofs that consider any longest reduction path. The choice of reduction strategy avoids the need for weakening or strengthening of type derivations. The proof becomes a bargain because it works for more intersection type systems, while being simpler than existing proofs.

Type
Theoretical Pearls
Copyright
2005 Cambridge University Press
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