On 22/08/2008, at 3:34 PM, William Stein wrote:
>
> On Thu, Aug 21, 2008 at 9:41 PM, Arnaud Bergeron
> <[EMAIL PROTECTED]> wrote:
>>
>>>>> data /. x_?(# < 0 &) -> 0 (this is perhaps not the killer example)
>>>>
>>>> What does that do?
>>>
>>> /. is the pattern replacement operator, _ is a placeholder pattern
>>> that matches anything, x_ gives this placeholder a name so you can
>>> use
>>> it later, ? filters the matches (in this case, everything matches)
>>> with the pure function # < 0&, which takes one argument and returns
>>> true if the argument is less than 0, and the -> 0 part says anything
>>> that made it through the filter gets set to 0. So
>>>
>>> In[40]:= data = {-1, 2, 3};
>>> In[41]:= data /. x_?(# < 0 &) -> 0
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> Just out of curiosity, what words do you say in your head
> when you read In[41]?
Keep in mind that it is a Lisp-like expression. That means there has
to be some intracranial translation into lisp-like nested
expressions. If there is a flamewar to be had, it is probably about
the relative merits of Lisp-like languages. I am not at all
interested in proving that Mathematica is better than language X, I am
only pointing out features that I think are worth studying.
Start small:
data /. x->y
means "data, replacing all occurrences of x with y".
x_?( # < 0&) is a pattern somewhat like in ocaml. It reads like this
"any item x, such that when the test 'argument is less than zero' is
applied, returns True"
So line 41 reads:
data, replacing all (/.) items (x_) that are less than zero (?(#<0&) )
with (->) zero.
More strictly, though, the -> indicates a rule, whose full form is:
Rule[ x_?(#<0&), 0]
The "x" is strictly unnecessary, but it is simpler to understand.
If you had more than one rule, you would read it differently:
data /. { a -> 2, b -> 3}
"data, transformed by replacing a with 2 and b with 3"
Can one do the same with Arnaud's python version?
> I would like to understand what
> people are thinking when they find an expression like that
> easy to read and appealing.
It is neat because I can write it from left to right, and I think
about the object to be manipulated before the operations.
> When I look at Arnaud's python version:
>
>> sage: data = [-1, 2, 3]
>> sage: [(0 if d < 0 else d) for d in data]
>
> I read "the list got from data where the negative
> entries are replaced by 0", or maybe more literally
> "the list made by taking each entry d of data and
> putting 0 if it is negative else putting d."
The unappealing thing is the emphasis on "the list". No such
requirement in Mathematica: "data" could just as well be Cos[8 x].
snip.
> I could certainly see a place in sage for something
> like this:
>
> sage: data = [-1, 2, 3]
> sage: data = ma_eval('data /. x_?(# < 0 &) -> 0')
> sage: data
> [0, 2, 3]
>
> where ma_eval is a function that evaluates a mathematica-style
> expression in the scope of the current Sage
> session, and returns the result as a Python object.
> It's something that could be totally ignored by most users,
> but something people who understand the power of
> Mathematica might find very useful. Anyway, that's why
> this thread is I think potentially interesting.
I would be scared of getting sued into oblivion. I would have a
lawyer look at the Mathematica EULA before even thinking about it.
"WRI is the holder of ... including without limitation... structure,
sequence, organization, "look and feel", programming language and
compilation of command names." I hope one can't own such things but I
don't want a legal fight.
Otherwise, I agree. A mathematica-like parser would be useful.
Though I'd be surprised if the concepts map across well enough for it
to be anything other than an ugly hack.
D
==================================
David J Philp
Postdoctoral Fellow
National Centre for Epidemiology and Population Health
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