As Michael suggests using zipWith (+) is the simplest solution.
If you really want to be able to write [1,2,3] + [4,5,6], you can define
"Jonathan Grochowski"
instance (Num a) => Num [a] where xs + ys = zipWith (+) xs ys
You can do this in the sense that it's legal Haskell... but it is a bad idea to make lists an instance of Num, because there are situations where the result doesn't act as you would like (if you've had abstract algebra, the problem is that it isn't a ring). More concretely, it's not hard to see that the additive identity is [0,0,0...], the infinite list of zeros. But if you have a finite list x, then x - x is NOT equal to that additive identity! Instead, you'd only get a finite list of zeros, and if you try to do math with that later, you're going to accidentally truncate some answers now and then and wonder what went wrong. In general, most type classes in Haskell are like this... the compiler only cares that you provide operations with certain types, but the type class also carries around additional "laws" that you should obey when writing instances. Here there's no good way to write an instance that obeys the laws, so it's better to write no instance at all. -- Chris Smith