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