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Topic: Mathematica and Lisp
Replies: 83   Last Post: Mar 5, 2013 10:12 PM

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Richard Fateman

Posts: 1,404
Registered: 12/7/04
Re: Mathematica and Lisp
Posted: Jan 16, 2013 11:15 PM
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On 1/15/2013 10:38 PM, John Doty wrote:
> On Friday, January 11, 2013 8:23:16 PM UTC-7, amzoti wrote:
>

>> It is clear the Mathematica uses Lisp as one of the example programming paradigms

it pulls from and I have a general question regarding this.
>
> Perhaps not as much as you think. Mathematica is fundamentally a term rewriting system,



a more general concept than the lambda calculus behind Lisp.

....
If you want a term rewriting system, several of them (free, open source)
have been written in Lisp. Anything that Mathematica can
do computationally can be done, in principle, with any "Turing equivalent"
programming language, and that includes Lisp.

Lisp is not an implementation of the lambda calculus as some people
seem to think. McCarthy used the word "lambda" the way Mathematica
uses the word "Function".
Other than that use to introduce formal parameters, nothing much was
taken from Church's writings, as McCarthy has explained in some
historical articles.


To be sure, the easiest thing to express as term rewriting

is the replacement of a function invocation by its body

(as in the lambda calculus), but Mathematica can do more

complex things, some rather strange from the lambda calculus point of
view. Consider
>
> f_[whoCalled]^:=f
> Sin[whoCalled]


Certainly such a feature could be implemented in a pattern-matching
system written in Lisp. Since most lisp implementations provide
many "introspective" features including examining the run-time call
stack, I think it would be possible to extract "who called me" from
this information of the (complete) call stack. Lisp systems also tend
to provide tools that answer questions like "where are all the calls to
the function f in the source code.

>
> which yields
>
> Sin
>
> Very alien to Lisp!


Not really.

>





Date Subject Author
1/11/13
Read Mathematica and Lisp
amzoti
1/12/13
Read Re: Mathematica and Lisp
Richard Fateman
1/12/13
Read Re: Mathematica and Lisp
David Bailey
1/14/13
Read Re: Mathematica and Lisp
Richard Fateman
1/14/13
Read Re: Mathematica and Lisp
David Bailey
1/16/13
Read Re: Mathematica and Lisp
Richard Fateman
1/18/13
Read Re: Mathematica and Lisp
David Bailey
1/22/13
Read Re: Mathematica and Lisp
Richard Fateman
1/22/13
Read Re: Mathematica and Lisp
David Bailey
1/24/13
Read Re: Mathematica and Lisp
Richard Fateman
1/25/13
Read Re: Mathematica and Lisp
Richard Fateman
1/26/13
Read Re: Mathematica and Lisp
Murray Eisenberg
1/26/13
Read Re: Mathematica and Lisp
Murray Eisenberg
1/26/13
Read Re: Mathematica and Lisp
W. Craig Carter
1/16/13
Read Re: Mathematica and Lisp
Murray Eisenberg
1/16/13
Read Re: Mathematica and Lisp
Richard Fateman
1/16/13
Read Re: Mathematica and Lisp
David Bailey
1/18/13
Read Re: Mathematica and Lisp
Murray Eisenberg
1/31/13
Read Re: Mathematica and Lisp
Noqsi
2/2/13
Read Re: Mathematica and Lisp
Daniel Lichtblau
2/3/13
Read Re: Mathematica and Lisp
Richard Fateman
2/2/13
Read Re: Mathematica and Lisp
Richard Fateman
2/3/13
Read Re: Mathematica and Lisp
David Bailey
2/5/13
Read Re: Mathematica and Lisp
Richard Fateman
2/6/13
Read Re: Mathematica and Lisp
David Bailey
2/6/13
Read Re: Mathematica and Lisp
Richard Fateman
2/3/13
Read Re: Mathematica and Lisp
Andrzej Kozlowski
2/5/13
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Richard Fateman
2/6/13
Read Re: Mathematica and Lisp
David Bailey
2/8/13
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2/5/13
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2/6/13
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Joseph Gwinn
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Matthias Bode
2/3/13
Read Re: Mathematica and Lisp
Noqsi
2/6/13
Read Re: Mathematica and Lisp
Richard Fateman
2/6/13
Read Re: Mathematica and Lisp
David Bailey
2/6/13
Read Re: Mathematica and Lisp
mathgroup
2/4/13
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Alex Krasnov
2/6/13
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Noqsi
2/8/13
Read Re: Mathematica and Lisp
Richard Fateman
2/9/13
Read Re: Mathematica and Lisp
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2/9/13
Read Re: Mathematica and Lisp
Richard Fateman
2/10/13
Read Re: Mathematica and Lisp
michael
2/10/13
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2/8/13
Read Re: Mathematica and Lisp
Andrzej Kozlowski
2/8/13
Read Re: Mathematica and Lisp
Noqsi
2/9/13
Read Re: Mathematica and Lisp
Richard Fateman
2/10/13
Read Re: Mathematica and Lisp
David Bailey
2/9/13
Read Re: Mathematica and Lisp
Matthias Bode
2/15/13
Read Re: Mathematica and Lisp
Noqsi
2/17/13
Read Re: Mathematica and Lisp
David Bailey
2/18/13
Read Re: Mathematica and Lisp
Joseph Gwinn
2/18/13
Read Re: Mathematica and Lisp
David Park
2/22/13
Read Re: Mathematica and Lisp
Richard Fateman
2/23/13
Read Re: Mathematica and Lisp
David Bailey
2/23/13
Read Re: Mathematica and Lisp
Richard Fateman
2/25/13
Read Re: Mathematica and Lisp
David Bailey
2/26/13
Read Re: Mathematica and Lisp
Richard Fateman
2/27/13
Read Re: Mathematica and Lisp
Bill Rowe
2/27/13
Read Re: Mathematica and Lisp
Richard Fateman
3/2/13
Read Re: Mathematica and Lisp
Bill Rowe
3/3/13
Read Re: Mathematica and Lisp
Richard Fateman
3/3/13
Read Re: Mathematica and Lisp
Noqsi
3/5/13
Read Re: Mathematica and Lisp
Richard Fateman
3/5/13
Read Re: Mathematica and Lisp
Vince Virgilio
3/3/13
Read Re: Mathematica and Lisp
Bob Hanlon
1/16/13
Read Re: Mathematica and Lisp
Noqsi
1/16/13
Read Re: Mathematica and Lisp
Richard Fateman
1/18/13
Read Re: Mathematica and Lisp
Noqsi
2/23/13
Read Re: Mathematica and Lisp
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2/25/13
Read Re: Mathematica and Lisp
Richard Fateman
2/26/13
Read Re: Mathematica and Lisp
Noqsi

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