Errata to the PhD thesis of Ralph Matthes
Since May 1998 there has been the version
I submitted (also available as
DVI file) to the Faculty
of Mathematics and Computer Science of the
Ludwig-Maximilians-Universität München. It moreover
contained the following errors:
Page 56, third paragraph (in section 4.1.2): "There is no hope
for...". I did hope there were no such types! Unfortunately,
we may set tau:=(not alpha)->alpha and easily get closed terms s and
t with s:rho->tau (use elimination for type 0) and t:tau->rho
(only using minimal propositional logic). Nevertheless one
would not call rho and tau isomorphic because the compositions
of s with t are far
from being identities.
Thanks to Thorsten
Altenkirch who showed a similar example to me concerning the
streamlined version involving the Peirce type (August 12, 1999).
If someone still has the old version it may be worthwile keeping it
since I have only done the following changes in order to produce
the final version:
Footnote 8 in chapter 9 (on Page 115 in the original version) concerning
the proof of normalization in
[Sce89] is quite misleading: Proving that weakly normalizing terms are
closed under beta reduction is very easy when using confluence. If one
tries to avoid the reference to confluence then the problems mentioned
in the footnote arise. However, one should bear in mind that
René David has shown how to prove confluence from
standardization. Therefore it is best to cancel the footnote
Typo in the first line of chapter 9: is strongly normalizing
There have been no changes concerning content.
- Titlepage adjusted to the formal requirements. Formalities on
- Renumbering of the pages before p. 1.
- Reformulation in a part of the acknowledgements better reflecting
- New footnote on p.8 to acknowledge Thorsten Altenkirch's
contribution more visible (not only on p. 145 and in the
- An even better streamlined proof that the Peirce type is not
inhabited (Lemma 2.42 and Corollary 2.43).
- Removal of footnote 8 in chapter 9 (p. 115) because it was
- A new footnote 7 on p.114 discussing the relation to the work of
Breazu-Tannen and Gallier.
- Therefore, the old footnote 7 becomes footnote 8.
- Reference to Brian Howard's PhD thesis in footnote 1 on p. 74.
- Updates of information on years of appearance of cited works.
- Removal of typos, correction of punctuation (for i. e. and e. g.)
Last modified: Tue Nov 30 10:52:26 CET 1999