On Sun, Dec 06, 2009 at 10:57:58PM -0600, Zachary Turner wrote:

GHCi, version 6.10.4: http://www.haskell.org/ghc/ :? for help Loading package ghc-prim ... linking ... done. Loading package integer ... linking ... done. Loading package base ... linking ... done. Prelude> let f x = x*x Prelude> let g x y = x+y Prelude> let q x y = (f . g) x y Prelude> :t q q :: (Num (a -> a), Num a) => a -> a -> a

I'm somewhat of a beginner so the error could definitely be my own, but it seems to me like the third line should be rejected by GHCi. As for the 4th line, the type of q seems nonsensical to me. I can't figure out any possible valid meaning of 'Num (a -> a) '.

The last line is the key: all this code is perfectly valid, *as long as* there is an instance of Num for the type a -> a. (If you want more careful explanation of how this works, let me know.) There is no such instance in the standard libraries, but type classes are open, so you could always add such an instance yourself (although you are right that this probably wouldn't make much sense); hence GHC cannot reject the code. GHC isn't perfect, but it's fairly polished and you're not likely to stumble across a bug so easily. =) In the future you'll probably have more luck sending questions to beginners@haskell.org or haskell-cafe@haskell.org; or come by the #haskell IRC channel on freenode.net. -Brent