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Strong normalisation for applied lambda calculi

Ulrich Berger
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Abstract

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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Ulrich Berger. 2005-07-04. Strong normalisation for applied lambda calculi. https://doi.org/10.2168/lmcs-1(2:3)2005

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