Abstract.
We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing terms of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 15 June 1998 / Revised version: 15 November 1999 / Published online: 15 June 2001
Rights and permissions
About this article
Cite this article
Valentini, S. An elementary proof of strong normalization for intersection types. Arch. Math. Logic 40, 475–488 (2001). https://doi.org/10.1007/s001530000070
Issue Date:
DOI: https://doi.org/10.1007/s001530000070