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Re: Mathematica and Lisp
*To*: mathgroup at smc.vnet.net
*Subject*: [mg129570] Re: Mathematica and Lisp
*From*: Richard Fateman <fateman at cs.berkeley.edu>
*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
editors.
>
> 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 http://www.wolframalpha.com/termsofuse/)
>
> 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.
RJF
>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>
>
>
>
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