Earlier quoted context omitted.
> A much more foundational difference of opinion about purity arises from whether or not you allow termination. Termination or non-termination? One of the (many) things that annoy me about PFP is the special treatment of non-termination, which is nothing more than unbounded complexity. In particular, I once read a paper by D.A. Turner about Total Functional Programming that neglected to mention that every program eve…
Non-termination, my bad! And of course that's true! Trivially so, though, in that we could do the same by picking the counter to be 10 instead of 2^1000, since we don't appear to care about changing the meaning of the program. If we do, then we have to consider whether we want our equality to distinguish terminating and non-terminating programs. If it does distinguish, then non-terminating ones are impure. Now, what…
But this is what bugs me. As someone working on algorithms (and does not care as much about semantics and abstractions), the algorithm's correctness is only slightly more important than its complexity. While there are (pragmatic) reasons to care about proving partial correctness more than total correctness (or prioritizing safety over liveness in algorithmists' terms), it seems funny to me to almost completely sweep complexity -- the mother of all effects, and the one at the very core of computation -- under the rug. Speaking about total functions does us no favors: there is zero difference between a program that never terminates, and one that terminates one nanosecond "after" the end of the physical universe. Semantic proof of termination, then, cannot give us any more useful information than no such proof. Just restricting our computational model from TM to total-FP doesn't restrict it in any useful way at all! Moreover, in practical terms, there is also almost no difference (for nearly all programs) between a program that never terminates and one that terminates after a year.
Again, I fully understand that there are pragmatic reasons to do that (concentrate on safety rather than liveness), but pretending that there is a theoretical justification to ignore complexity -- possibly the most important concept in computation -- in the name of "mathematics" (rather than pragmatism) just boggles my mind. The entire notion of purity is the leakiest of all abstractions (hyperbole; there are other abstractions just as leaky or possibly leakier). But we've swayed waaaay off course of this discussion (entirely my fault), and I'm just venting :)