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New Notions of Reduction and Non-Semantic Proofs of Strong β-Normalization in Typed λ-Calculi
- PROCEEDINGS OF LOGIC IN COMPUTER SCIENCE
, 1995
"... 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 typ ..."
Abstract
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Cited by 9 (2 self)
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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.
