"<-" and associated values

Question

Say I've written the following amazin piece of code:

func = do
  a <- Just 5
  return a

It's pretty pointless, I know. Here, a is 5, and func returns Just 5.

Now I rewrite my awesome (yet pointless) function:

func' = do
  a <- Nothing
  return a

This function returns Nothing, but what the heck is a? There's nothing to extract from a Nothing value, yet the program doesn't whine when I do something like this:

func'' = do
  a <- Nothing
  b <- Just 5
  return $ a+b

I just have a hard time seeing what actually happens. What is a? In other words: What does <- actually do? Saying it "extracts the value from right-side and binds it to the left-side" is obviously over-simplifying it. What is it I'm not getting?

Thanks :)

Answer 1

Let's try and desugar the do-notation of that last example.

func'' = Nothing >>= (\a -> Just 5 >>= (\b -> return $ a+b))

Now, let's see how >>= is defined for Maybe. It's in the Prelude:

instance  Monad Maybe  where
    (Just x) >>= k   =  k x
    Nothing  >>= k   =  Nothing
    return           =  Just
    fail s           =  Nothing

So Nothing >>= foo is simply Nothing

Answer 2

The answer lies in the definition of the Monad instance of Maybe:

instance Monad Maybe where
   (Just x) >>= k      = k x
   Nothing  >>= _      = Nothing
   (Just _) >>  k      = k
   Nothing  >>  _      = Nothing
   return              = Just

Your func'' translates to:

Nothing >>= (\a -> (Just 5 >>= (\b -> return (a+b))))

From the definition of (>>=) you can see that the first Nothing is just threaded through to the result.