processing tuples in SML

Question

I have an assignment where I need to take a tuple and return another tuple, of the same size, with certain elements changed. The problem is I don't know how to process a tuple of an undefined size. The function needs to be able to process tuples of any size. My idea was to make the tuple into a list that i could process much more easily, by making a recursive helper function to take element #1 of the tuple and cons it to a call to the same function which would give element #2 consed onto the recursion again until there are no elements left, but this just gives an error when i get to #n+1 where n is the total number of items in the tuple. Am I going about this the wrong way? is there a way to find the size of a tuple? is there a way to handle this error? I know about exception handling, but I'm not sure how to apply it to his case, if even possible.

the question is create a function named subst, such that subst (e',x) e = [e'/x]e ie the function subst will replace any free occurrence of the variable x in the expression e' by the expression e. Add the appropriate case for tuples.

Answer 1

The function needs to be able to process tuples of any size.

This cannot be done. Tuples of different sizes are completely different and unrelated types; there is no type of function that is polymorphic enough to be both 'a * 'b -> ... and 'a * 'b * 'c -> ... , unless it's simply of type 'a -> ... (ie, it accepts any argument at all, with no special understanding of tuples).

(The built-in notations # 1 , # 2 , etc. are overloaded functions that work for any tuple type, but this is magic that you can't duplicate. You can't even write something like val f = # 1 without giving the compiler enough information to infer f 's exact type; you'd have to write eg val f : 'a * 'b -> 'a = # 1 to specify that f returns the first field of a pair .)