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Re: Confused about contexts ...
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg570] Re: [mg523] Confused about contexts ...
*From*: villegas (Robert Villegas)
*Date*: Sun, 19 Mar 1995 05:22:09 -0600
Hello Paul,
> I think I'm getting my contexts in a muddle. Can you help me with the
> following please?
>
> Consider the following simple package:
>
> BeginPackage["Example`"]
> test::usage = "Test function"
> Begin["`Private`"]
> test[a_] := Module[{}, z=Sin[x];Function[x,z]]
> End[]
> EndPackage[]
>
> I'm trying to code a function "test" that returns a function as its
> argument.
> Thus, _what_I'd_like_to_happen_ is this:
>
> In[1] :=
> <<Package.m
> In[2] :=
> f = test[a]
> Out[2] :=
> Function[x,Sin[x]]
> In[3] :=
> f[theta]
> Out[3] :=
> Sin[theta]
>
> However, what actually happens is this:
>
> In[1] :=
> <<Package.m
> In[2] :=
> f = test[a]
> Out[2] :=
> Function[Example`Private`x, Example`Private`z]
> In[3] :=
> f[theta]
> Out[3] :=
> Sin[Example`Private`x]
The reason the z in Function[x, z] didn't expand to a formula is that
Function is one of those things that doesn't evaluate its arguments.
If you want to override this behavior, use Evaluate. Here's a simplified
example to show what I mean:
In[64]:= z = Sin[x]
Out[64]= Sin[x]
(* The formula ends up being 'z', literally: *)
In[65]:= Function[x, z]
Out[65]= Function[x, z]
(* But we can make the formula be the _value_ of z instead: *)
In[66]:= Function[x, Evaluate[z]]
Out[66]= Function[x, Sin[x]]
There could be another complication to deal with in your usage,
because you've got a Function inside of a Module, which is a
situation of nested scoping constructs. This is no problem, except
that I suspect you might use 'z' as a local variable of the
Module (in your real, bigger example, I mean), and also within the
body of the Function. This would cause renaming of the Function's
variable. A quick example:
In[61]:= test[a_] := Module[{z}, z = Sin[x/a]; Function[x, Evaluate[z]] ]
In[62]:= test[5]
x
Out[62]= Function[x$, Sin[-]]
5
One standard way to circumvent this is to disguise the Function by
constructing it during the evaluation of the Module. Here's a way
to do that:
In[68]:= test[a_] := Module[{z}, z = Sin[x/a]; Function @@ {x, z}]
In[69]:= test[5]
x
Out[69]= Function[x, Sin[-]]
5
Hopefully, this will do what you want.
Best regards,
Robby Villegas
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