nothing - Using Haskell's "Maybe", type declarations [beginner's question]

Question

I've started experimenting with Haskell and have a problem. qqq is a function that should print one string if called with "Nothing" and print other things if called with "Just something".

The first attempt seems like working:

qqq Nothing = print "There isn't anything to be printed."
qqq (Just x) = print "There is something to be printed." >> print x

main :: IO ()
main = qqq (Just 43)

But:

• when I try to make main = qqq (Nothing) it fails ("Ambiguous type variable `a0' in the constraint: (Show a0) arising from a use of 'qqq'")
• When I want to add type signature if fails:
• • qqq :: Maybe x => x -> IO () -> Type constructor 'Maybe' used as a class -> But isn't it?
• • qqq :: (Maybe x) -> IO (). Now the signature itself looks like succeed. But main = qqq (Just 43) starts failing with that mysterious (Show a0) error like in main = qqq (Nothing) case.

Questions:

1. Why calling qqq with Nothing is so different than calling with Just 43?
2. What is (Show a0)? It is mentioned only in error messages. Any attempts to use it lead to something like "Show not in the scope".
3. What is correct type signature for this? How to make Haskell print type signature it deduced? Expecting something like:

f 0 = 2
f x = (f (x-1)) + 3

main = print get_type_as_string(f)
-- prints "Number -> Number"

Answer 1

The type of qqq is:

qqq :: Show a => Maybe a -> IO ()

That means that qqq takes one parameter of type Maybe a and returns an IO action without a value, with the constraint that a implements the Show typeclass. To find out what Show is, you can use :i Show in ghci.

Show is a typeclass which requires that a value of the type can be converted to a string. qqq has the constraint because print wants to print out the value (print has type Show a => a -> IO ()). Maybe is not a typeclass but a data type. You can read more about typeclasses here.

You can let GHC deduce the type signature either by typing the function in a .hs file, then loading the file with ghci (ghci Myfile.hs), and then typing :t qqq for displaying the type. You can also define the function in the interactive session with let qqq n = case n of { Nothing -> print "abc"; Just x -> print "def" >> print x } (it looks a bit different because the function definition has to be on one line in ghci, but the meaning is the same).

When main calls qqq with qqq (Just 43), it is clear the concrete type of Maybe a is a numeric type (ghci defaults to Integer), so qqq has the concrete type of Maybe Integer -> IO (). However, main calls qqq with qqq Nothing, a could be anything (it is ambiguous) and ghci reports an error.