On Tue, Dec 16, 2003 at 01:31:19PM +0100, Vincenzo aka Nick Name wrote:
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?
trace is one of many variants of fix; it's only interesting because this variant generalizes to arrows. You wouldn't normally use fix or its variants: you just use recursion. But a simple example is trace (\(b,d) -> (d,b:d)) which is another way of writing repeat. However in the arrow world, general recursion isn't available. The closest to it is loop (a generalization of trace) but not all arrows provide that. (This extends the situation for monads, which don't have recursion in general, but many of them have mfix.)