Thanks Daniel and Felipe.
To me it seems Daniel's foo doesn't break referential transparency
because we can always replace "foo (+3) (\x -> x+3)" with "Yay :)",
and "foo (+3) somethingWhichIsTheSameButCan'tBeProvedToBe" with "Nay
:(".
It just contradicts our expectation that "foo (+3) something....ToBe"
should return "Yay :)", which is another story.
On Mon, Dec 12, 2011 at 3:24 AM, Daniel Fischer
But it's not possible, so all you have is that for some pairs of functions equality can be proved, for some pairs it can be disproved and for some pairs, it cannot be decided.
This sounds like quite common function behavior as we can see in f n = if n > 0 then True else if n == 0 then f 0 else False Here, f 1 returns True, f (-1) returns False, and f 0 doesn't terminate. Still f is referentially transparent, isn't it? If so, why can we not say foo is referentially transparent? On the other hand, I agree that Felipe's obviouslyEqual is not referentially transparent as its behavior really depends on how Haskell runtime allocates functions (thunks) in memory. I understand that we cannot construct such a function that always terminates and decides functions' equality (equality defined as, say, "f1 equals f2 iff f1 x == f2 x for any argument x"). But again, does this have something to do with referential transparency? Isn't this just because it's undecidable problem?