Type variables are not what you're thinking.

   add :: Int -> Int -> Int
   add a b = a + b

   add2 :: a -> a -> a
   add2 c d = c + d

1st function adds integers. 2nd function adds anything that can be added. For example: add2 [1,2,3] [4,5,6] evaluates to [1,2,3,4,5,6]

The 'a' in the second function is a type variable.