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From: P. Fonseca on 29 Jul 2010 06:44
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?

Regards,
P. Fonseca


From: Andy Ross on 30 Jul 2010 06:56
On 7/29/2010 5:44 AM, 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?
>
> Regards,
> P. Fonseca
>

I believe the following gives a clue...

test[x_] := Module[{u},
Which[x == 0, 0, True, u[t_] := t^2;u[x]]]

In[11]:= test[t]

Out[11]= Which[t == 0, 0, True, u$612[t_] := t^2; u$612[t]]

Since t == 0 doesn't explicitly evaluate to False, the entire Which
remains unevaluated. You could use either of the following to ensure
the first check always evaluates to either True or False.

SameQ:

In[12]:= test[x_] := Module[{u}, Which[x === 0, 0, True, u[t_] := t^2;
u[x]]]

In[13]:= test[t]

Out[13]= t^2

TrueQ:

In[14]:= test[x_] :=
Module[{u}, Which[TrueQ[x == 0], 0, True, u[t_] := t^2;
u[x]]]


In[15]:= test[t]

Out[15]= t^2

-Andy

From: Szabolcs Horvát on 31 Jul 2010 02:39
[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


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