On 15 Oct 2007, at 5:41 am, [EMAIL PROTECTED] wrote:
But, when J. Vimal "threateneds us" to throw away Haskell,
complained about
monads, and most people confirmed that the underlying theory is
difficult,
ugly, and useless, I began to read those postings with attention,
since
I disagree with spreading such atmosphere. And A.C. additionally
wrote that
all this theory has nothing to do with Haskell, and submitted three
more
postings, one more dubious than the other, I found that a warning
seems
suitable, not for him, but for his readers!
I hope we can agree on several things here:
(1) The mathematical background of Haskell is one of the things that
makes Haskell a beautiful and useful programming language. It
may even be one of the most important factors.
(2) The mathematical background of Haskell is extremely important
for implementations. Some important data structures and
techniques are practical in large part because of the kinds of
optimisations that are only straightforward in a language that
has such foundations.
(3) Beginners do not need to understand all the mathematics behind
Haskell to use it.
I really really hope we can agree on the next two points:
(4) It is not unfair to describe "Category Theory" as "The mathematical
study of sound analogies between mathematical structures"; it leads
to concepts of great generality and power, and encourages a
consistent
use of terminology which makes it easier to transfer ideas and
techniques from one area of mathematics to another. It's about
*consistently* pushing generality rather hard.
(5) Precisely because it seeks generality, category theory seems
difficult to "concrete thinkers". And books on category theory
tend to be extremely fast-paced, so ideas which are not in
themselves
particularly esoteric (which may in fact be eminently practical)
tend to be presented in a way which people trying to study by
themselves have trouble with. So people can be scared off by
what _ought_ to be a big help to them.
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