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Re: Function vs. Procedure

• To: mathgroup at smc.vnet.net
• Subject: [mg37128] Re: [mg37114] Function vs. Procedure
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Sat, 12 Oct 2002 05:04:53 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

 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?
>

 There is a fundamental difference, a strictly functional language does 
 not allow destructive assignments to be performed.  From this 
 statement alone then it is obvious that there are some things that can 
 be done in a procedural (nowadays people prefer to call them 
 imperative) language that cannot be done in a functional language.  On 
 the other hand in imperative languages without pointers to procedures 
 on cannot define a function which takes another function as an 
 argument which functional languages allow.  What you are probably 
 really interested in is whether there exist a class of programs in the 
 sense of a transformation on some input set into an output set which 
 can be expressed in only one paradigm.  Because nearly all major 
 programming languages (SQL being the glaring exception) can implement 
 a Turing Machine any algorithm which can be performed by a Turing 
 Machine can be performed by any programming language, imperative or 
 functional.  So in principle functional and imperative languages are 
 equivalently powerful although in practice it is easier to express 
 some concepts in one paradigm or another.

> Is this basically the recursive verses iterative distinction?
>

 No.

> Why would one chose one approach over the other?
>

 In software engineering circles there is some evidence that the 
 functional programming paradigm allows for efficient implementation of 
 large programming projects, see 
 http://www.math.chalmers.se/~rjmh/Papers/whyfp.html.  Also it is 
 possible to prove a strictly functional program correct because it 
 cannot have side effects (no destructive updates of global states) 
 which caused some excitement in academia but has not been a big 
 selling point in industry.

 That said, by now you must realize that Mathematica is not a strictly 
 functional language although you can use it as such.  Actually 
 Mathematica has a lot in common with LISP which is sometimes lumped 
 together with the functional languages since it admits that 
 programming style but both Mathematica and LISP are not pure (the 
 desirability of purity being left to personal preference).  One last 
 advantage of functional programs though (which is related to the fact 
 that they admit correctness proofs) is that it is relatively easy for 
 a compiler/interpreter to optimize a functional program.  This is why 
 implicit iteration (Map in Mathematica) tends to outperform imperative 
 style loops (Do, For, While etc.), which have to do a destructive 
 update of the loop counter variable and therefore cannot reorganize a 
 loop since statements in the loop may also destructively update the 
 loop counter.  C et al. get around this problem by being closely 
 matched to the hardware.

 Regards,

 Ssezi