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Re: mathematica's syntax is very like lisp language

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95944] Re: mathematica's syntax is very like lisp language
  • From: John Doty <jpd at whispertel.LoseTheH.net>
  • Date: Fri, 30 Jan 2009 05:45:39 -0500 (EST)
  • References: <glj85j$dds$1@smc.vnet.net>

water wrote:
> mathematica's syntax is very like lisp language.
> 
> is there any relation between mathematica and lisp ?

Wolfram was surely aware of Lisp and its application to computer algebra 
when he invented Mathematica. In terms of expression structure, they are 
very similar. One can certainly identify the "head" of a Mathematica 
expression with the "car" of a Lisp expression.

The big difference is in evaluation. The Mathematica evaluator is driven 
by patterns in the expression, while the Lisp evaluator is driven by the 
car of the expression. Of course, in Mathematica it is common to make 
definitions that drive the evaluator to mimic the behavior of the Lisp 
evaluator. On the other hand, you can do other things, and "upvalues" 
are there to facilitate them, e.g.:

f_[loki]^="Haha"

for a silly example (try Sin[loki] after making this definition if you 
don't understand it).

The Lisp evaluator does a single evaluation. The Mathematica evaluator 
continues to evaluate the results until the expression stops changing. 
And, related to this, the Mathematica evaluator simply leaves alone an 
expression that fails to match any definition, while an undefined 
function is an error in Lisp.

-- 
John Doty, Noqsi Aerospace, Ltd.
http://www.noqsi.com/
--
The axiomatic method of mathematics is one of the great achievements of 
our culture. However, it is only a method. Whereas the facts of 
mathematics once discovered will never change, the method by which these 
facts are verified has changed many times in the past, and it would be 
foolhardy to expect that changes will not occur again at some future 
date. - Gian-Carlo Rota


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