# Weak normalization implies strong normalization in a class of non-dependent pure type systems

```@article{Barthe2001WeakNI,
title={Weak normalization implies strong normalization in a class of non-dependent pure type systems},
author={Gilles Barthe and John Hatcliff and Morten Heine S\orensen},
journal={Theor. Comput. Sci.},
year={2001},
volume={269},
pages={317-361}
}```
The Barendregt–Geuvers–Klop conjecture states that every weakly normalizing pure type system is also strongly normalizing. We show that this is true for a uniform class of systems which includes, e.g., the left-hand side of Barendregt’s -cube as well as the system U . This seems to be the 7rst result giving a positive answer to the conjecture not merely for some concrete systems for which strong normalization is known to hold, but for a uniform class of systems in which not all systems are… CONTINUE READING