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Re: Lisp Macros in Mathematica (Re: If Scheme is so good

• To: mathgroup at smc.vnet.net
• Subject: [mg102545] Re: Lisp Macros in Mathematica (Re: If Scheme is so good
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Thu, 13 Aug 2009 03:20:59 -0400 (EDT)
• References: <b0g665llur83sj9dnumktjvnipacj7bgrt@4ax.com> <h5r8ek$l71$1@smc.vnet.net>

David Bakin wrote:
> It is very easy to make what Lisp calls "special forms". You use HoldAll or
> related attributes to create your own "special forms", then manipulate the
> arguments in their full form (aka S-expressions), evaluating things when you
> wish.
> 
> As far as I am aware you do not get reader syntax like quotes and
> quasiquotes that make Lisp macros easy to write.  But depending on what
> you're trying to do you may not need them.  With Mathematica you get full
> pattern matching on arguments (not just destructuring) and rule-based
> programming, and everything else that Mathematica provides.  You may find
> these features are even more effective than quoting and quasiquoting in
> writing macros.
> 
> BTW, Mathematica does not need a separate defmacro call that basically means
> "define this function such that you don't evaluate any arguments, but when I
> return the result, you evaluate it".  That is because 1) To get the first
> part you add the HoldAll attribute to your function name, and 2) Mathematica
> automatically evaluates the result returned by any/all functions, until
> there's nothing more to evaluate (which is an important difference between
> the Lisp REPL and the Mathematica REPL).
> 

If I understand what you mean, then surely this is missing the point.

Let's take a specific example. Suppose you have a vector of data 
representing conditions in a reaction vessel, and you define functions 
such as:

pH[x_]:=x[[17]];

This is a function, and could be used to access the relevant component 
of a vector, but not to change that value. However, if you code in that 
style, you will sacrifice a lot of performance for the sake of clarity.

One way to solve that problem, is to define another operator for use in 
defining functions instead of SetDelayed (:=). This lets you make 
substitutions on the held form of the RHS before the DownValue is 
created - so you code pH[vec] but execute vec[[17]] .

Alternatively, you could use $Pre or $PreRead, but since these do not 
work on code loaded by Get or Needs, I don't find this approach general 
enough.

As I said before, I think a built-in macro mechanism would be a valuable 
addition to Mathematica.

David Bailey
http://www.dbaileyconsultancy.co.uk