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Some stuff you just can't make up. From the
c-jump website:
Discover fundamentals of computer programming by playing a board game! c-jump helps children to learn basics of programming languages, such as C, C++ and Java.
While I believe that learning how to think algorithmically early on is a good idea, I would dispute that C and C-like languages are rewarding choices as first languages. Alan Kay and the SqueakLand folks have something to say about teaching programming to kids as well.
Knut Arild Erstad uses Common
Lisp to calculate some
pretty visualizations of Lindenmayer systems. With the site being
updated last in 2002 this is not exactly news, but still quite
interesting.
Walter Pelissero wrote some interesting Common Lisp software:
Andres implemented (product of) powerset functionality in Smalltalk:
allProductsTimes: aNumber do: aBlock self allProductsTimes: aNumber startingAt: 1 do: aBlock allProductsTimes: aNumber startingAt: anIndex do: aBlock anIndex > self size ifTrue: [aBlock value: aNumber] ifFalse: [self allProductsTimes: aNumber startingAt: anIndex + 1 do: aBlock. self allProductsTimes: aNumber * (self at: anIndex) startingAt: anIndex + 1 do: aBlock]Isn't that absolutely beautiful?
I would not know how to judge beauty of the above code, but on technical grounds I would have to remark that powerset and arithmetic set product functionality is intermingled.
On closer inspection, the code consists of a fold (or reduce) operation over the result of a powerset operation. Some better factored Haskell code might look like this:
powerset :: [a] -> [[a]]
-- returns powerset of given set
powerset [] = [[]]
powerset (x:xs) = concat [ [s, x:s] | s <- powerset xs ]
With lists as set representation, a powerset is constructed
recursively just like in the Smalltalk code: the powerset of the empty
set [] is the set containing the
emptyset [[]], otherwise the powerset is built by picking
an element x, then for each set s in the
powerset of the remaining elements xs, include it once
with and once without picked element x.
powerset works for any type of sets.
Trying it out for numbers:
Main> powerset [2 .. 4] [[],[2],[3],[2,3],[4],[2,4],[3,4],[2,3,4]]
Now, that was only half the work, we still need to calculate the
product. I mentioned already that it can be done with a folding
operation (we will choose a left fold foldl):
Main> :t foldl foldl :: (a -> b -> a) -> a -> [b] -> a
We fold the set with multiplication and initial
argument 1 (the same definition as builtin
function product):
Main> :t foldl (*) 1 foldl (*) 1 :: Num a => [a] -> a Main> :t product product :: Num a => [a] -> a
Note that so far, I have written three lines of code, and otherwise presented you a bunch of type signatures. So, putting it all together:
powerset :: [a] -> [[a]]
-- returns powerset of given set
powerset [] = [[]]
powerset (x:xs) = concat [ [s, x:s] | s <- powerset xs ]
allProducts :: Num a => [a] -> [a]
-- returns arithmetic product of each subset of given set
allProducts = map product . powerset
Main> allProducts [2 .. 4] [1,2,3,6,4,8,12,24]
Now, isn't that absolutely beautiful close
to the math underneath it?
For what it's worth, I believe the Smalltalk code could be factored similarly.
Notes:
Main> :t foldl1 (*) foldl1 (*) :: Num a => [a] -> a
[a] with Set a => a is left
as an exercise to the reader (it will look uglier).
Andres looked at my Haskell powerset code and asked some questions which I try to address here.
I had a hard time understanding the meaning behind the names a, b, x, s, and what seemed to me as operators of some sort: ->, =>, [a].
I am afraid that's how simple functions are written in idiomatic Haskell. It's not as bad as it might look on first glance, I can try to explain some of it. A more detailed overview of Haskell syntax can be found elsewhere.
powerset :: [a] -> [[a]]
This is a type signature (denoted by ::), declaring
function powerset to take list of
(a[a]) and returning some list of lists of a
(with a being an arbitrary type).
That is, the function is polymorphic.
Type variables in Haskell are commonly
named a, b, c,... because they
denote any type, it does not matter which.
powerset (x:xs) = concat [ [s, x:s] | s <- powerset xs ]
Here x, xs, s are old-fashioned
variables. x:xs is a pattern which the first parameter
of powerset is matched against.
It must be a list, with at least one element (which x
will be bound to), and a rest list (which xs will be bound to).
Patterns like x:xs or y:ys can be found all
over the place in Haskell, it's a naming convention akin
to aBlock in Smalltalk.
More complicated functions usually have more expressive variable
names, as you would expect.
The following is list comprehension syntax:
[ x | x <- gen ]
It roughly means:
collect all x where each x is generated
from gen.
Again, Haskell syntax tries to be close to math where you would write
something like { x | x in gen }.
Now to Andres' other questions:
Does the Haskell version need to be modified to accept the value of the empty product as an argument?
Not sure what you mean by empty product
exactly, but
powerset [] == [[]]
i.e. powerset applied to the empty set yields the set containing the empty set.
What would you need to write to iterate through the products with an arbitrary piece of code (the aBlocks in Smalltalk)?
Haskell supports anonymous functions (lambda's) just like blocks in Smalltalk. The moral equivalent of Smalltalk(ish)'s
1 to: 42 allProducts do: [ x | frob x ]
would perhaps be
mapM (\ x -> frob x) (allProducts [1 .. 42])
Would it work if the collection had stuff other than integers (such as modular integers, polynomials, functions or matrices)?
allProducts' type (Num a => [a] -> [a])
suggests that it works for any type a which is in
typeclass Num (class not quite in OO sense, though), i.e. the complete
numeric tower.
If you define multiplication for matrices or polynomials, the code
would work unchanged for them, too.
With a collection of size 20, it would create (I am no Haskell expert!) 2^20 collections. Is that so?
Let's try it out:
Main> take 10 (powerset [1 .. 1000]) [[],[1],[2],[2,1],[3],[3,1],[3,2],[3,2,1],[4],[4,1]] Main>
The output is instantaneous. Clearly, Haskell does not create the full powerset (of size 21000). Instead, it relies on lazy evalutation to only evaluate as much as is needed to produce the result. In the above case I requested only the first 10 elements of the powerset, so that's what is generated.
Actually, we can do even better (trading some of the presentational
points). With a modified, even lazier version
of powerset, we could generate the powerset of e.g. the
natural numbers, i.e. an infinite set:
powerset :: [a] -> [[a]]
powerset xs = []:(powerset' xs [[]])
where
powerset' :: [a] -> [[a]] -> [[a]]
powerset' [] _ = []
powerset' (x:xs) ps = let ps' = [ x:s | s <- ps ]
in ps' ++ powerset' xs (ps ++ ps')
The idea behind this approach is to generate the
powerset ps of all elements before x, then
add element x to all subsets s
of ps, emit those (ps') and continue for
the remaining elements xs in the same way.
Main> take 10 (powerset [1 ..]) [[],[1],[2],[2,1],[3],[3,1],[3,2],[3,2,1],[4],[4,1]]
I believe the same can be done in Smalltalk with the standard OO trick to emulate infinite lists: a generator/iterator object (which can be queried for the next element). Actually, I would love to see such a solution to compare to.
Regarding the lines of code, I would suggest that overall we're pretty close.
Yes, I did not mean to imply that the Haskell version is shorter in
terms of LOC (which is a poor
metric anyway), apologies if it came across like this. My main point
is how close Haskell code is to math: if we
exchange concat and (++) for set union and
curlies for brackets we are almost there.
A minor point (and this is really with my code police hat on) which I
made: the original Smalltalk code could have been factored
some more, and the question I have is now would that increase
code readability/reuse/beauty even more?
.
I think the following well-known quote from the Wizard Book says it all:
Programs should be written for people to read, and only incidentally for machines to execute.
Interestingly, but not entirely surprisingly, there has already been
a Haskell
Cafe discussion about different versions of powerset.
I encourage the reader to try these versions out with
Main> take 10 (powerset [1 ..])
Gah. Why do email clients suck so much? Let me explain what I am looking for.
From the top of my head, here's a list of features I would like to see in a MUA (yes, I am blue-skying here):
Must support
IMAP,
including advanced features like server-side searching, partial
message download, etc.
Nevermind that IMAP is
actually a pretty involved protocol and not very easy to get
right, this is what I am currently stuck with.
Maybe SMAP will be better
(under some metric), but that remains to be seen.
Must support external editors.
A MUA should handle the
network protocol part of email handling and message display,
everything else (and in particular editing) is somebody else's
problem.
For various reasons I like to edit text in GNU/Emacs, so why should I be satisfied with some simplish, less configurable editor?
Must be able to handle large amounts of email fast.
I would like to be able to access at least the current year's
worth of email without much hassle, without long periods of
waiting. Access
includes searching (by sender,
recipient, date, keywords, etc.) and sorting.
Must support Unicode and various charsets correctly.
This affects message display and searching, mostly.
Must support encrypted email.
This includes PGP/MIME and
S/MIME.
Must support various means of sending mails.
I do not want to run an SMTP server on my laptop, if I can hand
off email to some MSA
like /usr/sbin/sendmail instead. If not the sendmail
interface, at least RFC 2476 should
be supported.
Must support offline reading capabilities.
Already downloaded emails should be cached, so that I can read,
manage and answer them while disconnected. Upon reconnect, the
offline state is synchronized.
Must be lightweight.
Writing emails is not a main task, at least for me, so the client
should be unobtrusive and not take up all the resources by itself.
sensiblemeans to decode and print attachments if I desire so, instead of dumping base64 encodings or worse onto the printer.
Already tested email clients:
trash file, I installed a new version and
then it started working. It seemed fast, but does not support an
external editor. Mail submission only via SMTP.
[321]% sudo apt-get install kmail
Reading Package Lists... Done
Building Dependency Tree... Done
The following extra packages will be installed:
[...]
Need to get 21.8MB/21.9MB of archives.
After unpacking 69.2MB of additional disk space will be used.
Do you want to continue? [Y/n] n
Abort.
Thanks, but no thanks.
So, dear reader, which email client are you using, and where do you compromise? Write me!
Apparently, Brian Nelson seems to agree with me on this one. Others have similar griefs about email clients.
I am seeing a lot of Google referers coming in to this article. Perhaps I should point out that some of the information is outdated. I am using Apple's Mail.app at the moment. It works decently in most everyday situations and has decent (off-line) IMAP capabilities. However, it sucks in other exciting ways.
Having said that, why not add some more possibly outdated information. I came across a description of the BikINI protocol, a proposed replacement for IMAP. The project appears to be on hold at the moment, but might be resurrected in the future.