[Haskell-beginners] Help using Type Families

[MAN]

I desperately need help with this little predicament I got myself into.
I thought It'd be nice to write a piece of code that would wrap around
an older function, which given a bunch of parameters produces a plot (a
file) in the working directory. This new code receives the parameters
first, and only if the plot is not already present in the directory,
should pass the parameters to (and run) the wrapped function.

With that in mind I've defined the following type class. The older
function is treated as an anonymous 'muscle', capable of taking its
parameters ordered in some structure unknown.

> class Show parType => MuscleCapable parType where
>   -- | This could be a list or a tuple, etc. Whatever way of
implementing it, it
>   --   contains all necessary parameters to make the muscle produce a
resource.
>   --   Notice that this definition forces the type of ALL the
parameters of
>   --   the wrapped up muscle to be the same.
>   data Parameters parType
>
>   -- | A way to obtain the values of a @Parameters a@, for printing
purposes
>   listOfParams :: Parameters parType -> [parType]
>
>   -- | This wrapper around the muscle function will allow me to
produce a
>   --   resource on demand.
>   muscle :: Parameters parType -> IO FilePath

But when trying to use that, I get different errors at compile time
related to my (mis)use of type families, most of which are above my
head.
I use this dummy code to test the mechanism:

> data ThreeTuple a = T3 a a a
>
> listFromThreeTuple :: ThreeTuple a -> [a]
> listFromThreeTuple (T3 x y z) = [x,y,z]
>
> fun (T3 x y z) = do
>   withFile "output.out" WriteMode $ flip hPutStrLn (concatMap show
[x,y,z])
>   return "output.out"
>
> instance MuscleCapable Int where
>   data Parameters Int = ThreeTuple Int
>   listOfParams = listFromThreeTuple
>   muscle = fun

This fires the following error in GHC (I do add the TypeFamilies
LANGUAGE pragma):
"""
    Couldn't match expected type `Parameters Int'
           against inferred type `ThreeTuple Int'
      NB: `Parameters' is a type function
"""

If I use a similar data type without type parameters:

> data ThreeTuple = T3 Int Int Int

And modify the above snippet accordingly, I get the same thing:
"""
    Couldn't match expected type `Parameters Int'
           against inferred type `ThreeTuple'
      NB: `Parameters' is a type function
    In the expression: listFromThreeTuple
    In the definition of `listOfParams':
"""

Whatever alternative I try (and I have gone far along the trial-error
path) inevitably yields those errors for both lines implementing
'listOfParams' and 'muscle'.

Could somebody help me understand what's going on? I'm really lost at
this point.


PS: My first attempt at the class used 'type' to define the associated
type. I had to switch to 'data' due to problems regarding the chosen
type not being _injective_. GHC error messages and the paper "Fun with
type functions" helped on that.