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Re: Mathematica daily WTF

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115174] Re: Mathematica daily WTF
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 3 Jan 2011 03:58:01 -0500 (EST)

I don't want to get involved in what is likely to turn out a "linguistic" dispute, but I think your ideas about what constitutes "functional" and "procedural" are misconceived and do not correspond to what other's mean by these terms. While there is some difference between the meaning of "function" in mathematics and in programming, both concepts originate from the same source. To quote Thompson's "Haskel. The craft of functional programming": "A function is something that we can picture as a box with some inputs and an output:..." followed by a picture which is exactly the same that I used to draw in my lectures on introductory set theory and analysis for many years before I heard of functional programming. In this sense functions are ubiquitous in mathematics and science. "Procedural programming", on the other hand, is programming by "change of state" or "side-effects", and as the latter expression suggests, is less natural for the human mind even if it could be claimed to 
 c!
orrespond more closely to what goes on at "machine level". In any case, I cannot think of any scientific or mathematical problems that can be more naturally formulated in terms of "side-effects" than in terms of "functions". Perhaps they exist and I my bias is due to several decades of doing mathematics but I seriously can't think of a single example. Can you provide one?

Andrzej Kozlowski


On 2 Jan 2011, at 10:55, AES wrote:

> In article <ifmrvv$pim$1 at smc.vnet.net>,
> Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
>
>>
>> anyway, it does not matter as far as the point I was making is concerned,
>> which is that the C-like structure of Mathematica procedural programs is
>> helpful to people (somewhat) familiar with C or Fortran.
>>
>
> I'd argue it is also extremely helpful to people who _think_ physically,
> or if you like procedurally, and who are primarily focused on solving
> problems that have an inherently procedural character.
>
> The successive steps (lines, cells, expressions) in a procedural program
> will very often state or mimic or reproduce what happens as a function
> of time in a dynamic system, or as a function of distance as a wave
> propagates, or mimic the flow of control in a complex system, or . . .
>
> As such, they simplify the process of _coding_ these programs; they
> _document_ and make readable what the program is doing, step by step;
> they make it easy to _insert later refinements_ inside the procedure
> (e.g., tests for current values or for exceptional cases at points
> within the procedure).
>
> All of these things are much more valuable to some of us in our use of
> Mathematica than the speed at which the code executes, or the brevity
> with which it can be typed.  And none of this is to argue that many
> basic functions within the language (things like Fourier transforms,
> finding matrix eigensolutions, many others) should not be provided and
> used as pre-coded non-procedural routines within larger programs.
>
> I make a lot of use of self-programmed Modules[] in my own programming. 
> The active or working part of the completed program, where numerical
> results get asked fror and results displayed, can be quite briefly
> written, mostly just setting input variables, then calling these
> modules.  But these modules themselves are heavily procedurally coded
> internally, and I think that makes a lot of sense.
>


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