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Re: Re: General--Difficulties in Understanding Mathematica Syntax

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  • Subject: [mg69030] Re: [mg69006] Re: General--Difficulties in Understanding Mathematica Syntax
  • From: Andrzej Kozlowski <akoz at>
  • Date: Sun, 27 Aug 2006 01:23:59 -0400 (EDT)
  • References: <echdk4$oir$> <ecmgpr$9b3$> <>
  • Sender: owner-wri-mathgroup at

On 26 Aug 2006, at 08:04, AES wrote:

> In article <ecmgpr$9b3$1 at>,
>  Jean-Marc Gulliet <jeanmarc.gulliet at> wrote:
>> Now, it is utterly better to use high-level constructs such as Map,
>> Thread, Apply, ... when you code in Mathematica.
> I don't exactly quarrel with this -- but I sure don't fully accept it
> either.
> Concepts like Map[ ], Thread[ ], Apply[ ] are thoroughly understood by
> adepts, and marginally understood by some of the rest of us.  They're
> not concepts, or terms, commonly used in everyday speech.  And they  
> may
> have some hidden subtleties in their operation, even some  
> "gotchas", in
> how they apply to what's inside the [ ]s.
> Constructs like Do[] , If[ ], While[ ] are fairly likely to be
> understood not just by adepts, but by anyone who's ever done even very
> elementary programming in (horrors!) BASIC.  Their programming use
> matches up pretty well with the same terms in everyday speech.  They
> make the flow of the program logic more obviously visible (at least to
> us non-adepts).  And I suspect they have fewer hidden gotchas.
> Writing complex Mathematica expressions as dense, deeply nested,
> sometimes lengthy expressions full of arcane shorthands ("\\@",  
> etc) is
> akin to writing dense, arcane, possible lengthy prose sentences  
> full of
> arcane terminology.  Writing them as short, crisp, clear  
> constructs, one
> task at a time, is like writing short, crisp, clear prose sentences.
> The people who construct "readability indexes" for prose have some
> opinions about this.
> [We all, of course, fondly remember APL:  "Code once, read or modify
> never".]
> What is it that's actually **better** (for the "ordinaryt user") about
> these more sophisticated constructs?
> *  Readability? -- except for adepts, I don't think so.
> *  Faster, more efficient execution? -- perhaps so, but in the vast
> majority of cases, who cares?!?
> *  More accurate execution?  -- I sure hope not.
> *  Shorter code (fewer characters)? -- again, who cares?!?
> *  Bragging rights (I can accomplish the task with fewer characters  
> than
> anyone around)? -- Well, that was a very salable skill, in magnetic  
> core
> and assembly language days.
> Again, to each his own.  Part of the genius of Mathematica is that it
> serves the novice user and the sophisticated adept.  But "better"?

I don't really disagree with you but I also find your comments  
somewhat. I think the answer to the question: is it much better to  
use functional rather than procedural programing depends above all on  
what you are doing. I am doubtful that your view correctly reflects  
the "vast majority" of Mathematica users.
For some purposes, for example, when you want to implement quickly in  
Mathematica an algorithm written in some sort of pseudo code in some  
book on algorithms, and many other similar purposes, procedural code  
will generally be much more convenient. It indeed corresponds better  
to the way normal processors work and therefore it is use din almost  
all books on algorithms etc.

For purely numerical purposes, provided your program can be compiled,  
you can often achieve pretty satisfactory results with procedural  
code (but note that it is very hard to make use of Mathematica's  
ultra-efficient numerical methods like packed arrays or SparseArrays  
unless you have use functional programming. This may not be important  
to you but judging by the posts to this list people who do not care  
about the speed of execution of their numerical code are not "the  
vast majority of cases".)

Finally, the area that interests me most and where I have the most  
experience: symbolic algebra. Here I have no doubt that "algebraic"  
languages (which for the sake of argument we can identify with  
"functional") like Lisp, ML or Mathematica, etc., are vastly superior  
to procedural ones. Just remember that you can map a function not  
only onto a list but onto any algebraic expression. Here is a silly  
example I just made up on the spot and which is not supposed to have  
any significance besides showing the kind of thing that would be  
pretty hard do accomplish in a non-functional language:

(If[#1 >= 3 && PrimeQ[#1], #1^2, #1] & ) //@
   (7*x^2 + 3*y^4 + 2.5)

9*y^4 + 49*x^2 + 2.5

This may be of little interest to those users not interested in  
symbolic algebra, but if they are not interested in it than I am not  
exactly sure why they use a Computer Algebra System rather than an  
ordinary programming language, like, for example, Basic.

Andrzej Kozlowski

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