       Re: Re: Types in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg62205] Re: [mg62203] Re: Types in Mathematica
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 15 Nov 2005 04:16:04 -0500 (EST)
• References: <200511120833.DAA19252@smc.vnet.net> <43762529.7060603@math.umass.edu> <dl8s4g\$n41\$1@smc.vnet.net> <dl980q\$r2a\$1@smc.vnet.net> <200511140805.DAA00041@smc.vnet.net>
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```>
>> a=1;
>>
>> simply means whenever you see "a", replace it with "1". That's
>> all. No
>> type.
>
> But there is IntegerQ.

Yes, but

f[(x_)?IntegerQ] := x^2

a /: IntegerQ[a] = True;

f[a]

a^2

>
> One can view all symbols in Mathematica as variables in the sense of
> computer science.

All symbols? In what sense of symbol? How about:

Symbol

Is Table a "variable in the sense of computer science"?

>>
>> FORGET C++.
>
> Why?  Just because Mathematica doesn't behave like C++, doesn't
> mean there
> is no value in comparing the two languages.

Undoubtedly, when you are beginner in Mathematica, knowing some other
programming language can be of help. I remember that early versions
of the Mathematica Book included several paragraphs in the
introduction, each comparing Mathematica to a (then) better known
programming language: I still recall that among these languages were
C, Pascal, Lisp, and even Basic. However, once you get to a more
of a hindrance than help.
The reason is that people coming form other programming languages
tend to identify language with syntax. If they find that they can use
familiar syntax they often believe they now know the language. But in
the case of Mathematica the equation language = syntax does not hold.
Users notice this eventually when they discover that two Mathematica
programs, both written using perfectly valid syntax, and both
seemingly implementing the same algorithm (note the word "seemingly")
can differ in performance by several orders of magnitude (if you want
to see this really convincingly demonstrated just search for some
past postings by Carl Woll). If then one understands by "knowing the
Mathematica language" simply knowing how write programs that run,
then it is true that anyone who knows C or LISP already knows quite a
bit about Mathematica programming. But if by "knowing the Mathematica
language" one means "knowing how to write efficient programs" than
the advice "FORGET C++." needs to be only supplemented by the advice
"FORGET LISP".
In spite of some deliberate similarities in syntax internally
Mathematica is neither like C nor like Lisp (which I am sure RJF, who
certainly knows about LISP, will be happy to confirm ;-)) In fact
Mathematica isn't even a really functional language (the only real
functional aspect of Mathematica are pure functions like Function
[x,x^2] or #^2&). the language is obviously a hybrid, with certain
unique characteristics. For me this "hybrid" nature is one of the
best things about the language but I am aware that there are some who
have the opposite view on this. But I think everybody who has been
following this list for a few month would would agree that to write
an efficient Mathematica program knowing other languages is of very
little help.

Andrzej Kozlowski

```

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