On 30 Nov 2004, at 13:22, Adam Zachary Wyner wrote:
Question -- is this all there is to the issue, or is there something more? Apologies in advance for not understanding the math better here.
From the point of view of a programmer, that's all there is to it: there is no way of proving two functions are the same except by exhaustively checking every input.
Question -- though Haskell, as a lazy language, does not otherwise have problems with infinite lists, why does it here?
Try [1..]==[1..] You'll find it runs forever. (Aside: [1..]==[2..] returns False straightaway, though) In the same sense, you could try (map f [1..]) == (map g [1..]) and it will return False quickly if they are different, but it will run forever if they are the same.
Question -- is there some way around this problem? It is very handy to be able to have a variable over functions and then compare the value to a designated function. This would let me say things like:
You don't need records to pair functions with strings, but yes, one way to do this is to make your functions more structured types and compare them some other way. If you happen to know all your functions are 2nd order polynomials, then it suffices to check them at three points (or, check f, f', and f'' at 0, say): you could implement equality checks this way. In other function domains there may be other effective equality tests. The general situation is: there is no effective way to check the equality of functions on infinite domains. However, for most particular classes of functions you would actually want to compare, there are specific effective procedures. Jules