# A pecular algebraic data structure

**Jan Skibinski
**
jans@numeric-quest.com

*Tue, 5 Jun 2001 09:38:48 -0400 (EDT)*

I've been working with one pecular algebraic data structure,
named Register, which is described in currently upgraded
http://www.numeric-quest.com/haskell/QuantumComputer.html.
or in gzipped version of the same document
http://www.numeric-quest.com/haskell/QuantumComputer.html.gz.
Section 13 of that document outlines the background for
the topic of this message. But the section is just way too
long to quote it in here.
But to summarize it: data Register is pecular because
it is indexable but not observable in a standard way,
and because two different representations can describe the same
state. In theory there should be well defined transformation
from one representation to another. This seems to me as a good
subject for some research work.
Granted that there are many experts on functional data
structures out there (I do not want to pressure any
of you gurus, so I am not naming anyone :-)), could you please
look at the write-up and help me with the following questions?
+ Is the Register data structure strangely unique,
or does it fit somewhere into a hierarchy of known
functional data structures? I would be happy to learn
that the latter is the case, since I could then start
looking at it at a more formal, well known and tested way.
+ Is a non-uniqness of representation amenable to formal
treatment, such as deforestation?
Jan