[sorry about that, let's try again...] Ross Paterson wrote (in regards variations on factorial):
Another version:
fac = foldr (*) 1 . unfoldr (\n -> guard (n > 0) >> return (n, n-1))
Thanks for forwarding this; may I quote it on the web site? (with full attribution, of course) If so, you are welcome to give it a name and a pithy little "slogan" (also for the one below).
Also, the combinatory programmer would regard defining y by recursion as cheating, and would probably prefer one of these versions:
newtype SelfApp a = SA (SelfApp a -> a)
selfApply :: SelfApp a -> a selfApply (SA f) = f (SA f)
yCurry :: (a -> a) -> a yCurry f = selfApply (SA (\x -> f (selfApply x)))
yTuring :: (a -> a) -> a yTuring = selfApply (SA (\x f -> f (selfApply x f)))
Yes, this is definitely the right way to go here. I comment on the site about the fact that we should really *define* Y (and I felt a bit guilty about it :) ), but I didn't try hard enough to get around the typing issue. You have done so quite elegantly. Of course, there is also a trade-off at some point between the impact of the various examples and their sheer number (I added an environment-model based interpreter yesterday that started to push this boundary). Still, more monads (arrows, even?) are needed. -- Fritz Ruehr PS: for those who missed it, the site is at: http://www.willamette.edu/~fruehr/haskell/evolution.html