what is the type signature for “return Nothing”?

Question

In the chapter 14 of Real World Haskell (Monads) , the type signature of the inject function return is return :: a -> ma , where ma is a type constructor, so under ghci I can specify a type signature for a return arg1 , such as:

*Main> return 1 :: Maybe Integer
Just 1

*Main> return "ok" :: Maybe String
Just "ok"   

Because Nothing is the value of the type Maybe a , Nothing 's type is Maybe Integer or Maybe String , so I think I can specify the type as follows:

*Main> return Nothing :: Maybe String

But I got an error:

    Couldn't match type `Maybe a0' with `[Char]'
Expected type: String
  Actual type: Maybe a0
In the first argument of `return', namely `Nothing'
In the expression: return Nothing :: Maybe String
In an equation for `it': it = return Nothing :: Maybe String

I am confused about what is the type signature for that.

Answer 1

In the lines

return 1
return "ok"

the return works inside the Maybe monad, so return = Just here.

In the line

return Nothing :: Maybe String

the compiler spots that your code is of the form

return ... :: Maybe ...

so, once again, return = Just . Your code is equivalent to

Just Nothing :: Maybe String

which is the same as

Just (Nothing :: String)

but Nothing is not a string, it is a Maybe a for any a -- hence the type error.

You probably are looking for

Nothing :: Maybe String -- no return here

which works fine.

By the way, you can ask GHCi to give the type for an expression with the :t command:

> :t return Nothing
Monad m => m (Maybe a)

Answer 2

The difference between:

*Main> return 1 :: Maybe Integer

And

*Main> return Nothing :: Maybe String

Is that 1 has type Integer , but Nothing has type Maybe a . If you want to wrap Nothing into another Maybe value, you should specify the type for Nothing like this:

*Main> return Nothing :: Maybe (Maybe String)
Just Nothing