Re: Pure Functions in rules

• To: mathgroup at smc.vnet.net
• Subject: [mg15965] Re: Pure Functions in rules
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Fri, 19 Feb 1999 03:26:53 -0500
• References: <7ag34l\$aie@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Will Self wrote in message <7ag34l\$aie at smc.vnet.net>...
>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
>

Will.
In[80 evaluates thus:

{1,2,3}/.(m_List->(2*#& /@ m))  (*right side of -> evauates before
replacement*)

{1,2,3}/.(m_List->(m))

{1,2,3}

Using :> instead of -> gives

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

2*#& /@ {1,2,3}

{2,4,6}

You don't get the same sort of problem with

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

because f only evauates on lists.

Allan

---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

```

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