Trace and loop examples?

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