Re: Which inside Module causes problems with ReplaceAll
- To: mathgroup at smc.vnet.net
- Subject: [mg111398] Re: Which inside Module causes problems with ReplaceAll
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Sat, 31 Jul 2010 02:39:08 -0400 (EDT)
- References: <i2rm29$r6b$1@smc.vnet.net>
[note: message sent to comp.soft-sys.math.mathematica as well]
On 2010.07.29. 12:44, P. Fonseca wrote:
> Hi,
>
> Version 7.0.1
>
> This works:
>
> In[7]:= test[x_]:=Module[{u},
> u[t_]:=t^2;
> u[x]]
>
> In[8]:= test[t]/.t->3
>
> Out[8]= 9
>
>
>
>
> This doesn't:
>
> In[9]:= test[x_]:=Module[{u},
>
> Which[
> x==0,0,
>
> True,
> u[t_]:=t^2;
> u[x]
> ]
> ]
>
> In[10]:= test[t]/.t->3
>
> During evaluation of In[10]:= Pattern::patvar: First element in
> pattern Pattern[3,_] is not a valid pattern name.>>
> Out[10]= u$670[3]
>
>
>
> What's going on?
>
The key to understanding what happens in cases like this is breaking
down your expressions and looking at what each part evaluates to. If
you evaluate test[t], you get something similar to
Which[t == 0, 0, True, u$743[t_] := t^2; u$743[t]]
This is because Which will only evaluate if the test inside it evaluates
to either True or False, not something else.
If you replace t in this expression, it gets replaced in t_ (full form:
Pattern[t, _]) as well, leading to the nonsensical Pattern[3, _].
Hope this explains it,
Szabolcs