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Re: Mathematica and Lisp

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  • Subject: [mg129570] Re: Mathematica and Lisp
  • From: Richard Fateman <fateman at>
  • Date: Fri, 25 Jan 2013 01:34:53 -0500 (EST)
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On 1/22/2013 8:18 PM, David Bailey wrote:
(regarding Lisp)

> Having 3 types of brackets, definitely helps to discern the structure,
> even with indentation.
Some lisp implementations allowed for the use of ]  to terminate all
open parentheses up to the prior [.  It is possible to alter the meaning
of characters in ANSI Common Lisp, so almost anything can be implemented.

  Perhaps LISP could have been improved by
> permitting all three, to be used interchangeably so long as they paired
> correctly.
I expect that this can be done, and maybe already exists. Mathematica
does not allow the nesting of ([{}]) except for special uses, so
building up a big expression as you type is probably about as error 
prone as Lisp, if not quite as unfamiliar.  Note that f(a,g(b),c) has
as many parens as the Lisp  (f a (g b) c)   and that using square 
brackets as f[a,g[b],c] is not much different.  Also note that
the highlighting of the matching left parenthesis is done in 
Mathematica's current front end.  A similar feature is available in Lisp
> Unless the infix front end distinguished reliably between code and data
> (which I don't think it could, in general),

This is generally considered a benefit for advanced programming.  On the
other hand, most programmers spend their time composing programs for 
which it is pretty clear what is a program.   Of the  various types of
data (array, vector, string, hash table, file descriptor, integer, 
float, complex, rational, ..., list ...)  only one could possibly be
a program, namely list.  So it is perhaps not such a big problem as
you might think.

  you would still have a
> problem - ideally you want to see
> sin(a)
> but
> (apples oranges pears)
> Also, if you print out an expression, you want the first format, and if
> you print a list, you want the second.

Actually, the notation  (sin a)    instead of  Sin[a] is pretty much of 
a wash.
If you print a fragment of code,
> you may want to see a mixture of both styles. Extra types of brackets
> make all that simple.
Or you may prefer uniformity.  E.g. compare:

Mathematica Input,  Mathematica FullForm    Lisp

a+b+c                   Plus[a,b,c]     (+ a b c)
a^2                     Power[a,2]      (expt a 2)
Sin[x]                  Sin[x]          (sin x)

Also note that Mathematica has abandoned infix for such well known syntax as
the "do" loop.  This would ordinarily look like

for i=1 to 10 by 2 do f(i)....  but is instead Do[f[i],{i,1,10,2}]. 
That's pretty close to (dotimes (f i) i 1 10 2).
Incidentally, common lisp allows
(loop for i from 1 to 10 step 2 do (f i))  or some such thing.
[I don't use it much myself :)

>> I rarely write programs of any length in Mathematica, because (as I've
>> said) I hold the programming language in generally low regard.
>> On the other hand I am pretty much familiar with the language because
>> I wrote a parser for it (in Lisp) some time ago, and in my experience
>> one of the best ways to really learn a language is to "implement" it.
> Did you implement it, or just parse it?

Certainly not all the application.  Parser + pattern matcher + some 
simple application programs like differentiation, integration. numerical
evaluation done differently; display.  See my web page for free download.
> I do agree about learning a language by implementing it. Two of us once
> wrote a Fortran compiler in Fortran (!!), and bootstrapped it. It was
> widely used on Prime computers. One of the things I discovered, was that
> the old issue about Fortran's context sensitive grammar, was an utterly
> trivial problem!

I think there is a standard hack to recognize a "DO" statement by the
fact that there is a comma not enclosed in parentheses. Check for this 
and handle the card differently. There are Fortran compilers written in
Lisp;  in fact most compiler implementations depend upon an intermediate
expression tree language which requires that they include internally
a subset of what some people would recognize as Lisp -- for building
and traversing trees.
>> If I were using a computer to do something that required correct answers
>> for, say, life safety, like building a bridge, I would follow WRI's
>> advice and not use Mathematica.
>> (see
> So have you found the perfect language - one in which none of the
> functions contain imperfections, and yet which offers anything
> approaching the computational sophistication of Mathematica?

I think that perfection depends on the context. Though they are
not my areas of primary interest, I suspect the Mathematica is pretty
good for some kinds of graphics (though I find it clumsy sometimes,
that is probably my unfamiliarity with the nuances of Graphics objects),
and maybe linear cellular automata.
There seems to be a fairly strong consensus that for numerical
programming there are other competitors favored in engineering schools.

> BTW, I wouldn't be surprised if a lot of safety critical code isn't
> written in Fortran!

I expect that is true. It would be a LOT easier to formally prove the
correctness of a FORTRAN program than a Mathematica program.  And there
is even a history of proving FORTRAN compilers correct.  I daresay no
proof that Mathematica is correct is likely to appear any time soon.


> David Bailey

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