[Haskell-beginners] help on writing a typeclass

[Silent Leaf]

I got a function, named mdk (don't ask). It happens it's a method of a
class, as follows:

class C a where
 mdk :: C b => a -> b -> (a, b)

yet i got another function, called so far mdk'
 mdk' :: C b => b -> a -> (a, b)


Say there are the following instances:
instance C X where
 mdk x b = ... :: C b => (X, b)
 mdk' b x = ... :: C b => (X, b)
instance C Y where
 mdk y b = ... :: C b => (Y, b)
 mdk' b y = ... :: C b => (Y, b)

if you get what's happening, mdk and mdk' are basically the same method,
save for the final type-result, which is reversed, without data loss mind
you (aka (A, B) and (B, A) could be the same type, if only i knew of a way
to make a type in haskell without forcing the order (a kind of set or
something).
so, there are four cases:
input have types, in this order, X and Y, and expected output is (X, Y):
then mdk from X's instance of C is called/must be used;
input have types Y and X, output (X, Y): X's mdk'
input X and Y, output (Y, X): Y's mdk
input Y and X, output (Y, X): Y's mdk'

it might seem confusing, but all amounts to the issue that even though (Y,
X) is strictly equivalent, in my program, to (X, Y), in principle haskell
differentiate the types.
thus i have to write two versions of mdk for each type, even though the
methods "X's mdk" and "Y's mdk'" are identical, and same for the two other
methods.
indeed:
mdk :: C b => X -> b -> (X, b)
mdk' :: C b => b -> Y -> (Y, b)
are identical signatures, if in the first one you replace `b` with Y, and
in the latter you replace `b` with X, and ofc if you consider (X,Y) ==
(Y,X).

only one of those two methods should be enough to handle the job, and be
chosen by the compiler on the sole value of the type of the first variable;
but the fact both methods return tuples of "mirrored" types, crushes that.
if i only write `mdk` instances, as soon as the compiler will meet this
following signature:
 mdk :: a -> b -> (b, a)
it will crash an exception, because mdk's original signature has for output
value a tuple whose first type should here be `a`, because it's meant to be
the type of the first argument, not the second.

thus, at last my question: can i tell the compiler to consider (b, a) and
(a, b) as identical types (don't worry it's not really a tuple in my
program, but it's equivalent)?
if not, can i make an overloading of mdk so it accepts both a->b->(a,b) and
a->b->(b,a)?

hope i didn't lose anyone. if so, do tell me, i'll try to clarify.

thanks in advance of the time spent trying to understand my problem!
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