Re: Mathematica vs. Lisp

From: Richard Fateman (rfateman_at_sbcglobal.net)
Date: 06/21/04 

Date: Sun, 20 Jun 2004 23:54:32 GMT

I agree with the comments by Albert Reiner.

Wolfram wrote SMP because he felt that Macsyma, which he used
extensively, was too slow. Wolfram thought that he was
cleverer than anyone else and could read Knuth's books and
then write a better computer algebra system. He wrote it
with
S. Cole, Geoffrey C. Fox, Jeffrey M. Greif, Eric D. Mjolsness, Larry J.
Romans, Timothy Shaw, and Anthony E. Terrano.

SMP was terrible.
It had some bad designs, naive and buggy.

  For example, Wolfram thought he could use
double precision to approximate rational numbers, and no one
would notice.

Comments on its successor, Mathematica:

Since the fundamental paradigm for the user-level programming
language is pattern matching, what you usually get is a simulation
of functional programming using patterns and replacements. If you
look at this too closely, the analogy breaks. Wolfram would
like to claim that Mathematica combines (the best?) ideas from
many languages, including Lisp.

At least in the past, the time to add an element to the front
of a list, or the back of the list, was the same, but it depended
on the length of the list. How would you like "cons" to depend
on the size of the inputs? I haven't timed this Mathematica feature
recently.

Also, the evaluation model is quite bizarre. A value of a variable V
is re-evaluated whenever it is touched, iff something that V depends
upon has been changed since V was last touched. This is approximated
by keeping a collection of pages of items which have values on which
V depends.
  Since side effects are possible, you can have values change
non-deterministically. Sorry I can't give you a reproducible example:)
Note also, that if one value in an array a[n,m] is changed, then the
time to access any other value of that array increases, because they
have to be re-evaluated. This makes some algorithms that one would
think were (say) quadratic, into cubic or even exponential time.

Mathematica is interesting, but the programming language provided
to the user violates many rules of good behavior. But then, this
is true of other systems catering to scientific applications programmers
who are just fiddling around, whose answers probably don't matter,
or can be checked by physical experiment, whose programs are either
single commands or short programs, and never heard of big-Oh notation,
or floating-point error analysis.

I wrote a Mathematica parser and cut-down pattern matcher/evaluator in
Common Lisp. Wolfram made noises about copyright infringement, but
eventually stopped. Search on google for "mockmma" to find a copy
to download.

Of course another difference is that Mathematica is proprietary
and definitely not free.

RJF

ps. for the source of the "runic" comment, see

http://www.cs.berkeley.edu/~fateman/papers/mma.review.pdf

David Golden wrote:
> Sashank Varma wrote:
>
>
>>There are stories somewhere on the net that when Wolfram was
>>a wunderkind at Caltech, he used Macsyma -- the original
>>mathematical software package, written in Mac Lisp -- and
>>talked to some of the programmers about it.
>
>
> Worth noting that Common Lisp Maxima is a descendant
> of Macsyma, still around thanks to William Schelter
> getting it open sourced before he died. Pretty cool,
> and in debian with the rather understated package description
> "A fairly complete computer algebra system".
>
> http://maxima.sourceforge.net/
>

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