[mrkeen]

> If a :: Num would mean a is a value of type Num

`a` is the type. Num is a `class`.

Here's an example. x is an Int32 and y is an Int64. If they had type Num, then this would be valid:

  add :: Num -> Num -> Num           -- Not valid Haskell
  add x y = x + y

However it's not valid, because you can't add an Int32 and an Int64:

  add :: Int32 -> Int64 -> ?     -- Doesn't compile
  add x y = x + y

But you can add Nums together, as long as they're the same type. You indicate they're the same type by using the same type variable 'a':

  add :: a -> a -> a      -- Doesn't compile
  add x y = x + y

But now the above complains because you used (+) which belongs to Num, so you have to declare that these `a`s can (+) because they're Nums.

  add :: Num a => a -> a -> a
  add x y = x + y

And it comes out shorter than your suggestion of putting the constraints afterward:

  add :: (a :: Num) -> (a :: Num) -> (a :: Num)       -- Not valid Haskell
  add x y = x + y