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Re: Best practice passing expressions to functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85303] Re: Best practice passing expressions to functions
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 5 Feb 2008 19:40:35 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fo9gvu$t1l$1@smc.vnet.net>

Remo Aschwanden wrote:

> I want to write procedures that accept expressions as parameters and be 
> able define functions based on these expressions, i.e.
> 
> f[exp_]:=Module[
>    "g[x_] := exp "
> ]
> 
> The code between the " " should clarify what I intend to do. Calling 
>    f[x^2-2x+4] 
> should lead to the definition of a function (or pattern)
>    g[x_]:=x^2-2x+4;
> 
> What's the best way to do this? How can I do this without being 
> dependent on the variables used in the expressions ("x")?

One possible way, though I do not know whether it qualifies as best 
practice, is as follows.

The first argument of f, exp_, is the expression that is going to be 
transformed into a function definition, function definition that depends 
on the variable var_, which is passed as second argument and as default 
value, say, x.

The transformation rule applied to the pattern p_ looks for a pattern 
named p$ rather than p since Mathematica renames p_ as p$_ (you can see 
that by using the command *Trace*).

In[1]:= f[exp_, var_: x] := g[p_ /. p$ -> var] := exp

In[2]:= f[x^2 - 2 x y + 4 y]
g[3]

Out[3]= 9 - 2 y

In[4]:= f[x^2 - 2 x y + 4 y, x]
g[3]

Out[5]= 9 - 2 y

In[6]:= f[x^2 - 2 x y + 4 y, y]
g[3]

Out[7]= 12 - 6 x + x^2


Regards,
-- 
Jean-Marc


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