Berger, Ulrich - Strong normalisation for applied lambda calculi

lmcs:2267 - Logical Methods in Computer Science, October 5, 2005, Volume 1, Issue 2
Strong normalisation for applied lambda calculi

Authors: Berger, Ulrich

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.

Source :
DOI : 10.2168/LMCS-1(2:3)2005
Volume: Volume 1, Issue 2
Published on: October 5, 2005
Submitted on: January 25, 2005
Keywords: Computer Science - Computer Science and Game Theory,D.1.1,F.3.2,F.3.3,F.4.1


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