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Re: Pure Functions in rules

  • To: mathgroup at
  • Subject: [mg15975] Re: Pure Functions in rules
  • From: gaylord at (richard j. gaylord)
  • Date: Fri, 19 Feb 1999 03:26:59 -0500
  • Organization: university of illinois
  • References: <7ag34l$>
  • Sender: owner-wri-mathgroup at

In article <7ag34l$aie at>, wself at (Will Self) wrote:

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

> 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?

i'll comment:

i think you have a problem with premature evaluation [not with the use of
anonymous functions in a rule per se ].look at this

Map[(2*#)&, m]


Trace[Map[ (2*#)&, m]]

{(2 #1&)/@m,m}

the problem is that in use lhs -> rhs, the rhs of the rule is evaluated
before its used for substition[and it evaluates to the global variable m
which you introduced in the rule

look at 

Trace[{1,2,3} /. m_List -> Map[ (2*#)&, m] ]

and at

m = 5;
Trace[{1,2,3} /. m_List -> Map[ (2*#)&, m] ]

[i'd put the output here but i'm having a problem copy-pasting from Mma
to  my newswatcher app]

if you use :> instead of -> so that the rhs of the rule is not evaluated
before its applied to the evaluated expression [in this case {1,2, 3} it
works fine.

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

note: - i suppose there's some reason you mapping an anonymous function
for doubling the elements of a list onto a list rather than just
multiplying the list by two.
"I would say life is pretty pointless, wouldn't you, without the movies?"
Vincent Gallo as Johnny Tempi in The Funeral (1996)

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