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Re: Pure Functions in rules



Will,

This has to do with delayed versus immediate replacement.

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

Out[1]=
{1,2,3}

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

Out[2]=
{2,4,6}


For In[1] above, the right hand side or the replacement rule ((2*#& /@
m))
is evaluated before the rule is applied the result of evaluating (2*#&
/@ m) is
just m, so {1,2,3}/.(m_List->(2*#& /@ m)) is equivilant to
{1,2,3}/.(m_List-> m)
as long as m hasn't been defined previously in the Mathematica session.
These are the same issues as arise for "=" versus ":="

In In[2] I use RuleDelayed and the result that you expect is obtained
since the right hand side is not evaluated prior to the execution of the
rule.

Cheers,

David



Will Self wrote:

> 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
> this?
>
> Will Self





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