Thanks for pointing out my impreciseness. I guess I meant “thanks to the fact that we can partially apply curried functions”. Or am I still misusing the word “curry” even there? I’m still working on getting all the jargon right.

As for your generalized fold, I’m sure I’ll be referring back to it for inspiration, even if I don’t fully understand it now.

I’ve posted another Haskell post already. On Monday, I start a new computer music class, so I’m not sure how many more of these I’ll have time to do in the near future. But I might still sneak one or two in. Keep the comments coming!

Evan

An open question on MY mind which you have brought up is this: What would a fold look like on church numerals?

Just for fun, here is a generalization of the fold function:
gfoldr :: (c -> Maybe a) -> (c -> c) -> (a -> b -> b) -> b -> c -> b
gfoldr first rest f z d
| isNothing $ first d = z
| otherwise = f (fromJust $ first d) (gfoldr first rest f z (rest d))

And it’s application to lists (equivalent to foldr in the Prelude):
foldrList = gfoldr safeHead tail where
safeHead [] = Nothing
safeHead (x:xs) = Just x

And it’s application to numbers (your definition):
foldrNumber = gfoldr (\x -> if x == 0 then Nothing else Just x) (+(-1))