 
Summary: Continuous Normalization for the
LambdaCalculus and Godel's T
Klaus Aehlig ? and Felix Joachimski
faehligjjoachskig@mathematik.unimuenchen.de
Mathematisches Institut, LudwigMaximiliansUniversitat Munchen
Theresienstrasse 39, 80333 Munchen, Germany
Abstract. Building on previous work by Mints, Buchholz and Schwicht
enberg, a simplied version of continuous normalization for the untyped
calculus and Godel's T is presented and analyzed in the coalgebraic
framework of nonwellfounded terms with socalled repetition construc
tors.
The primitive recursive normalization function is uniformly continuous
w.r.t. the natural metric on nonwellfounded terms. Furthermore, the
number of necessary repetition constructors is locally related to the num
ber of reduction steps needed to reach and the size of the normal form
(as represented by the Bohm tree).
It is also shown how continuous normal forms relate to derivations of
strong normalizability in the typed calculus and how this leads to new
bounds for the sum of the height of the reduction tree and the size of
the normal form.
