Wolfgang Jeltsch protests (all this is about pathologies of the floating
point computations in Haskell, of course...):
Please don’t suggest that “illegalizing” some Ord instance is similar to
killing people out of religious motives.
Did I? Where?? This is silly...
I admit that I have over-reacted to Ketil, I didn't notice that he proposed
the "bombing reaction" as an *option*, not as the Only True way of dealing
with NaNs. I am sorry, although then Ketil seems saying that raising the
exception *is* the correct approach, while I think it is not, being too
brutal. OK, probably the best for people who learn the language. No good
for professionals, and impossible for some library procedures.
But *you* seem to have decided that all "weakness" in treating exceptional
values is absolutely wrong and sinful.
The analogy with religious issues is weak, there is simply a thought
pattern of "purists" who want to break the existing imperfections in name
of their visions. You demonstrate this kind of absolute thinking through
the usage of the clause "as a whole":
Even if I don’t use numerics, I do care about the Haskell language
as a whole.
Your name is Legion...
But I think that Lennart is right. *DO* something positive. In other terms,
instead of destroying an existing church, gather some followers, and make
your own. Seriously.
No type Double, but something possessing variants:
* Float2 (regular)
* UnderF (non-normalizable, underflow fl.p.)
* PositiveInfinity | NegativeInfinity
* NaN Mantissa [where Mantissa is a restricted numerical thingie, their
number is the no. of floats between 0.5 and 1]
etc. With appropriate arithmetic operators.
And if you are unhappy with: blah>blah = False, but: compare blah blah
giving GT, please tell what do you think SHOULD be the answer. I say that
those operators are being used outside their allowed domain. Any answer
is bad. Exception? Maybe... Better: leave it...
But anyway, I don't buy this:
if (==) yields false
when comparing a value with itself, this can break code (like a set
implementation) which relies on certain guarantees.
In pathological cases you are not allowed really to use the word "itself"
as casually as you would like to. I agree that
The fact that Haskell allows to define (==) rather arbitrarily doesn’t
mean that the use of arbitrary definitions of (==) is what we want.
The problem of equality/identity of things relies partially in the fact
that it is a human construction. The Nature does not "compare things for
equality". So, the arbitrariness is unavoidable.
My impression is that staying close to math is good from a software
technology point of view. And it has the advantage of less confusion
for the user.
What does it mean "close to math"?
How close? Does math raise exceptions upon the division by zero?
Does *MATH* answer the question what is: (0/0)==(0/0) ? Nope!
David Roundy says
...
Prelude> x/x
NaN
The "true" answer here is that x/x == 1.0 (not 0 or +Infinity),
but there's no way for the computer to know this, so it's NaN.
His comment uses not very legally the word "true", even in quotes.
Who is to say what the "truth" mean here? We cannot oblige the computer
to interpret the division operator as we think, in math terms!
Wherever you look, you will see some red lines not to neglect. If the
physical processes which implement real arithmetics are far from true
real math, trying to purify a programming language to make it more math-
oriented serves nobody. Or the Devil... We are discussing simple things,
but I have seen already a guy who claimed that all computer logic is
inherently wrong because of the Gödel's theorem... This is a neverending
discussion.
I don’t see what’s so extreme about suggesting that IEEE floating point
comparison should maybe be a seperate operator.
You were more picky than that. Here, I would only repeat that this - for
me - is not just a question of operators, but of the *type* of numbers.
And I think, it is really
inappropriate to compare this to horrible sects and doctrines.
Ugh... Again. Sorry if you took it personally. But a doctrine is just that,
a system which is meant to be autoritative, and if applied, then without
discussion. Usually based on personal visions of one or a few people. It
doesn't need to be negative nor horrible, although often is.
http://en.wikipedia.org/wiki/Doctrine
I mentioned a particular variant of doctrinal thinking: the *purification*
of existing. It doesn't need to be dangerous, but often is...
====
An anecdote.
At the time of Konrad Duden (Vater der deutschen Rechtschreibung,
1829–1911
as you probably know much better than I...) there was a tendency to "purify"
the German language, full of foreign words, roots, forms, etc.
There is a story of one of such words, the shortwriting: "stenography".
Stenografie.
Who needs Greek? And a good Germanic word has been proposed: Kurzschrift.
Yes!
Please - (if you are not German, they don't need to do that) - repeat a few
times: Kurzschrift, Kurzschrift, Kurzschrift, Kurzschrift ...
You will hear the Walkyrien galloping through the skies, the huge shadow of
Siegfried or some other Lohengrin will lie over the murky fields, etc.
*absolutely* Germanic!
But...
This word comes from "curtus", "short" in Latin, and the verb "scribere",
"scriptus", Latin again...
In such a way, German purists translated Greek into Latin. This is the
story, I hope nobody will shout that I have something against a particular
European nation; I know this story from a decent Berliner, who told me
it while eating a Hamburger. Or, perhaps it was vice-versa. Too much beer...
Jerzy Karczmarczuk
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