Trace and loop examples?

[Vincenzo aka Nick Name]

Hi all, I am trying to lear more about arrows in haskell, so I am 
reading the paper at:

http://www.soi.city.ac.uk/~ross/papers/fop.html

However, I can't understand how to produce a working and meaningful 
example of the trace function, or the loop arrow (I am using the 
"automata" example).

The trace function is defined like:

trace f b = let (c,d) = f (b,d) in c

Can someone show an example function f to pass to trace and what the 
purpose is? 

Thanks

Vincenzo