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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
Abstract
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.
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- Theoretical Pearls
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- 2005 Cambridge University Press
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