Strong normalisation for applied lambda calculi

Details Strong normalisation for applied lambda calculi Strong normalisation for applied lambda calculi

2005-07-04

arxiv.org/abs/cs/0507007v4

LMCS 1 (2:3) 2005

Computer Science

Computer Science and Game Theory

14 pages, paper acceptet at electronic journal LMCS

Scientific paper

10.2168/LMCS-1(2:3)2005

We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations' are. From this we derive a general normalisation theorem for applied typed lambda-calculi: If all constants have a total value, then all typeable terms are strongly normalising. We apply this result to extensions of G\"odel's system T and system F extended by various forms of bar recursion for which strong normalisation was hitherto unknown.

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