However there is nothing in the functions themselves that restricts their use to just T Double. Thus the functions can be compared for equality by supplying an argument of type T Double but used elsewhere in the program with args of type (plain) Double eg: .. Thus we can determine that f is implemented by different code from g (The example would be even more convincing if Int's were used instead of Double's) and so f and g are not interchangeable.
if you have two functions f and g, and an argument applied to which they deliver different results, then the functions can hardly be equal, can they? if they are not equal, what makes you think they should be interchangeable?
... nothing prevents us from defining that instance in such a way that we construct a representaton instead of doing any additions.
Thus referential transparency of polymorphic functions is foiled.
polymorphic functions (as in: parametrically polymorphic) do not allow such tricks. overloaded expressions are interpreted as functions from type information to non-overloaded expressions, so you have to take that type information into account when comparing or exchanging the expressions. in particular, an overloaded expression instantiated at a particular type is not the same as the overloaded expression itself. btw, you'll notice that I avoid the use of terms like rt - there are too many non-equivalent interpretations of such terms flying around, so it is better to define what it is you're talking about (try this for one study of the many definitions [scanned paper - >3MB]: http://www.dina.kvl.dk/~sestoft/papers/SondergaardSestoft1990.pdf ). cheers, claus