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Continuous Normalization for the Lambda-Calculus and Godel's T
 

Summary: Continuous Normalization for the
Lambda-Calculus and Godel's T
Klaus Aehlig ? and Felix Joachimski
faehligjjoachskig@mathematik.uni-muenchen.de
Mathematisches Institut, Ludwig-Maximilians-Universitat Munchen
Theresienstrasse 39, 80333 Munchen, Germany
Abstract. Building on previous work by Mints, Buchholz and Schwicht-
enberg, a simpli ed version of continuous normalization for the untyped
-calculus and Godel's T is presented and analyzed in the coalgebraic
framework of non-wellfounded terms with so-called repetition construc-
tors.
The primitive recursive normalization function is uniformly continuous
w.r.t. the natural metric on non-wellfounded 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.

  

Source: Aehlig, Klaus T. - Institut für Informatik, Ludwig-Maximilians-Universität München

 

Collections: Mathematics; Computer Technologies and Information Sciences