type checking fails with a correct type

[Daniel Fischer]

Am Donnerstag 30 April 2009 15:52:12 schrieb Jan Jakubuv:
> Hi,
>
> I have the following problem. Below is the smallest program I have found
> that shows the problem. That is why the program makes no sense (I have also
> meaningful but more complicated program). When I run this program in ghci:
>
>     class SUBST s where
>         empty :: s
>
>     --nonsense :: SUBST s => t -> Maybe s
>     nonsense t = case nonsense t of
>         Nothing -> Just empty
>
> then everything is fine and I can see the type signature of `nonsense`
> inferred by ghci:
>
>     *Main> :t nonsense
>     nonsense :: (SUBST s) => t -> Maybe s
>
> But, when I put this signature into the code (that is, when the commented
> line above is uncommented) then type checking fails with the following
> error:
>
>     Ambiguous type variable `s' in the constraint:
>       `SUBST s'
>         arising from a use of `nonsense' at problem-type.hs:6:18-27
>     Probable fix: add a type signature that fixes these type variable(s)
>
> Now, what is the problem here? Why does type checking fail with the
> signature that the type inference itself inferred?
>
In

nonsense t = case nonsense t of
                Nothing -> Just empty

, which type has the Nothing? 
It can have the type Maybe s1 for all s1 belonging to SUBST, that is the ambiguous type 
variable.

>
> BTW, I don't understand why but everything works fine with the following
> addition:
>
>     nonsense' :: SUBST s => t -> Maybe s
>     nonsense' t = case nonsense' t of
>         Nothing -> Just empty
>         x       -> x
>

Here, Nothing must have the same type as x. Since x may be returned, x must have type 
Maybe s, for the type variable s of the signature, so the types are completely determined.

> I am developing kind of generic interface and I don't want to fix the type
> `s`. I want `nonsense` to work possibly for any instance of SUBST and the
> concrete instance to be determined by the context where `nonsense` is used.
>
> In my original, meaningful but more complicated example I had the following
> error:
>
>     Couldn't match expected type `STerm s'
>            against inferred type `STerm s1'
>     When generalising the type(s) for `refute'
>
> (this message does not provide any information where `s1` comes from)

Probably something like the above.
To fix the error, you could use asTypeOf:

nonsense :: SUBST s => t -> Maybe s
nonsense t = res
      where
        res = case nonsense t `asTypeOf` res of
                Nothing -> Just empty

or 

{-# LANGUAGE ScopedTypeVariables #-}

nonsense :: forall s. SUBST s => t -> Maybe s
nonsense t = case nonsense t :: Maybe s of
                Nothing -> Just empty

>
> The original example shares with the above one the property that the type
> `s` is not mentioned in types of arguments, just in the type of a result
> (although, in the original example, some relation between types `t` and `s`
> is expressed in the type context via equality constrains on associated
> types (STerm from the error message) ).
>
> I tested this with ghc-6.6.1, ghc-6.10.1, ghc-6.10.2 obtaining the same
> result.

> I'll be grateful for any explanation of this issue.
>
> Sincerely,
>   Jan.