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Pure Functions in rules

It appears that I cannot depend on using a pure function
in a pattern-matching rule.

Here I am trying to convince reluctant students that they're
better off learning to use Mathematica than doing things
by hand, and we run across something like this, and in a
much more complicated situation where the trouble was
hard to isolate.

I am quite frankly incensed by the behavior shown in
In/Out 80, below.  Look at these examples:

In[73]:=     {1,2,3}/.(m_List->7)
Out[73]=    7

In[74]:=     {1,2,3}/.(m_List->(2*m))
Out[74]=    {2,4,6}

In[75]:=     2*#& /@ {1,2,3}
Out[75]=    {2,4,6}

In[77]:=     f[m_List]:=2*#& /@ m

In[78]:=     f[{1,2,3}]
Out[78]=    {2,4,6}

In[79]:=     {1,2,3}/.m_List->f[m]
Out[79]=    {2,4,6}

Now try this:

In[80]:=     {1,2,3}/.(m_List->(2*#& /@ m))
Out[80]=    {1,2,3}

Does anyone (say, at WRI for example) care to comment on

Will Self

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