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MathGroup Archive 2002

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Re: Function vs. Procedure

  • To: mathgroup at smc.vnet.net
  • Subject: [mg37127] Re: [mg37114] Function vs. Procedure
  • From: Alexander Sauer-Budge <ambudge at MIT.EDU>
  • Date: Sat, 12 Oct 2002 05:04:51 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

There is indeed a logical and fundamental difference, but not in what 
can be done, as all "complete" languages are "equivalent" in terms of 
what can be done with them (it all has to become machine code 
eventually). But this nuts and bolts equivalency is hardly the whole 
story, as I don't think any of us would want to dig a tunnel with a 
spoon just because it is possible, and similarly, I am sure there is a 
reason why you are using Mathematica and not assembly language.

As some linguists have postulated in the context of human languages, 
languages might effect our ability understand the world and reason 
about the world (and thus solve problems).  This should be clear from 
your experience with mathematical notation-- a good notation can help 
you solve problems by revealing symmetry and structure (at least in the 
sense of patterns). In this way functional programming languages *tend* 
to represent computation at a much higher level than procedural 
programming. For example, adding the elements of a vector in a 
functional language style, "Fold[Add,0,vector]" , focuses on the 
conceptual fact that we are contracting a vector with an addition 
operator, while a procedural style, "sum=0; Do[sum = sum + vector[[i]], 
{i,1,Length[vector]}]" focuses on the mechanics of summing.  There are 
benefits to both styles and much much more to the story than I've 
indicated here (like issues of verifying that a program is correct, or 
at least won't crash the computer or run forever, as well as 
reusability, parallelization, memory management, and on and on, 
efficiency).

Although I am certainly not an expert in this area, I suggest a 
reasonable place to start would be what functional programming 
advocates consider their classic manifesto, which you can access by 
clicking on the title "Can Programming Be Liberated from the von 
Neumann Style?" of the following discussion:

http://lambda.weblogs.com/discuss/msgReader$4172

You can find much more information about functional programming and 
language design in general through this web log if your interested. I 
also found the article below to be very interesting

Paul Hudak, "Conception, Evolution, and Application of Functional 
Programming Languages," ACM Computing Surveys, September 1989, Volume 
21, Number 3, p.359-411.

As far as why, when and where to choose one approach over another: in 
general, you need to by informed of advantages and disadvantages of 
different styles, know how to program in different styles, and have 
good representative languages from different styles available to you so 
that you can choose, to the best of your ability, the best tool for the 
problem.  For any given language, you should use it as it was design to 
be used, since languages, like it seems for all engineered things, tend 
to be quite fragile when used in ways they weren't design to be used 
(if you've programmed in C, think about how much trouble you can get 
into with the preprocessor macro facility if you are not careful).

As far as Mathematica is concerned, you can choose either style in many 
cases, but I feel that Mathematica in many ways is a naturally 
functional programming environment, with its use of first-class 
functions and its basic building blocks being constructs like Fold, 
Map, etc., so I approach it as such. I am actually still learning 
Mathematica, but I think the book supports my feeling because it says: 
"Functional operations provide one of the most conceptually and 
practically efficient ways to use Mathematica. "

Alex


On Thursday, October 10, 2002, at 03:20  AM, Steven wrote:

> Is there a logically fundamental difference between functional and
> procedural programming?  What I mean to ask is, can we do exactly the 
> same
> thing with purely functional approaches as we can with purely 
> procedural
> approaches?
>
> Is this basically the recursive verses iterative distinction?
>
> Why would one chose one approach over the other?
>
> STH



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