On 9/9/10 1:04 AM, David Menendez wrote:
Fascinating. I figured there might be a counter-example involving seq, but this is pretty subtle.
In particular, would it be fair to say that in Haskell-without-seq, "E (f a) a" and "E (f a) (f a)" are indistinguishable?
Yes, I think that without polymorphic seq (or within a strict language) they are observationally equivalent. But, observational equivalence is not the same as equality. And the category theoretic laws really do mean equality. To pick an example: consider the case where 'a' is an enormous data structure and (f a) returns some small value. Even though (E (f a) a) and (E (f a) (f a)) are observationally equivalent within Haskell, they're still observationally distinct from outside of the language because they have very different memory profiles. (We may need to make E strict in the second argument, or NOINLINE impure, in order to guarantee this behavior.) Thus, the equality still fails, though this may go undetected for a long time until someone notices the memory leak. -- Live well, ~wren