New Notions of Reduction and Non-Semantic Proofs of Strong β-Normalization in Typed λ-Calculi (1995)
| Venue: | PROCEEDINGS OF LOGIC IN COMPUTER SCIENCE |
| Citations: | 9 - 2 self |
BibTeX
@INPROCEEDINGS{Kfoury95newnotions,
author = {A.J. Kfoury and J. B. Wells},
title = {New Notions of Reduction and Non-Semantic Proofs of Strong β-Normalization in Typed λ-Calculi},
booktitle = {PROCEEDINGS OF LOGIC IN COMPUTER SCIENCE},
year = {1995},
publisher = {}
}
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Abstract
Two notions of reduction for terms of the λ-calculus are introduced and the question of whether a λ-term is β-strongly normalizing is reduced to the question of whether a λ-term is merely normalizing under one of the notions of reduction. This gives a method to prove strong β-normalization for typed λ-calculi. Instead of the usual semantic proof style based on Tait's realizability or Girard's "candidats de réductibilité", termination can be proved using a decreasing metric over a well-founded ordering. This proof method is applied to the simply-typed λ-calculus and the system of intersection types, giving the first non-semantic proof for a polymorphic extension of the λ-calculus.
