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!