If you object to notions of purity, why did you bring it up in the first place?
The first place it was used in this thread was your citing a paper entitled "Pure versus Impure Lisp".
In that paper, it was used to mean prohibiting "set-car!" and "set-cdr!". ST provides the equivalent of "set-car!" and "set-cdr!", so in the presence of ST the result you were citing in the paper doesn't even apply to a strict version of Haskell.
Please just stop making claims about Haskell until you have some sense of what you're talking about (or at least add a caveat warning others that you might not).
I don't object to purity, I want to know what it means. I didn't
realise that this is not a well-understood concept. (I mentioned
Sabry's definition of purity which I found surprising.)
The original discussion started because somebody complained that
Haskell programmers often appear unable to transliterate imperative
algorithms. I assume that this complaint was about transliteration
into pure Haskell (whatever that may mean exactly). Clearly
transliteration into full Haskell with actual mutability is
possible. I mentioned Pippenger's article to bring to the debate the
idea that the question whether such transliteration is always possible
is an open research problem.
"I assume that this complaint was about transliteration into pure Haskell (whatever that may mean exactly). Clearly transliteration into full Haskell with actual mutability is possible."
Ah, if you'd made that assumption explicit I would not have objected.
I don't see anywhere the querent suggesting that his translation demand invoked any notion of purity. If it did, then certainly he was asking a harder question than he presented, although even in that case a naive translation could have trivially produced an O(m n lg(n)) solution and O(m^n) should quite reasonably be considered failure.
I think the issue in the main is that relatively novice Haskell developers are likely to be the most eager to try and translate arbitrary code on demand in #haskell.
I don't think anyone knows a solid definition of purity. It certainly refers to at least two things (1. independence of order of evaluation, 2. no side effects) and informally speaking we often "know" what it is in a particular context, but writing down a formal definition is very hard. I'm certainly not satisfied with Sabry's definition. I don't like the idea that you have to have both a strict and a non-strict evaluation for your language.
If nobody knows what purity means, then what are all those tortured discussions on whether Haskell is pure or not about? ...
Anyway, I'm a bit unhappy about the requirement of full evaluation order
independence, because even the purest of pure languages (e.g. the
untyped lambda-calculus or PCF) don't have full evaluation order
independence. I guess you mean evaluation order independence modulo
termination?
My intuition is that pure means that all language expressions M can always be
evaluated locally by just looking at the meaning of all subterms of
M. In terms of Hoare logic (for total correctness) that would mean
that the pre-condition speaks only about the termination of the free
variables of M (sorry for being so terse, I think this can be made
formal).
Usually this is the way words work - we notice a regularity in the environment we wish to refer to; we build a sense of it, usually motivated by some examples and counterexamples; we give it a handle; and we then try to find a definition that matches our intuition. There certainly seem to be regularities that "pure" is intended to point at in this context, but it definitely seems that we've not settled on a definition, and we may not even agree on examples.
The notions of purity I was pointing at was any that entailed the restrictions in the paper you'd linked. There are restrictions of Haskell that are pure in those senses, but Haskell taken as a whole is not, even without invoking anything unsafe.
If you object to notions of purity, why did you bring it up in the first place?
The first place it was used in this thread was your citing a paper entitled "Pure versus Impure Lisp".
In that paper, it was used to mean prohibiting "set-car!" and "set-cdr!". ST provides the equivalent of "set-car!" and "set-cdr!", so in the presence of ST the result you were citing in the paper doesn't even apply to a strict version of Haskell.
Please just stop making claims about Haskell until you have some sense of what you're talking about (or at least add a caveat warning others that you might not).