Re: Pure Functions in rules

• To: mathgroup at smc.vnet.net
• Subject: [mg16010] Re: Pure Functions in rules
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 20 Feb 1999 02:52:03 -0500
• Organization: University of Western Australia
• References: <7ag34l\$aie@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Will Self wrote:

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

Pure functions are not the problem in your example. (Sometimes you do
need to take care with parens because of the precedence of # and &).

> I am quite frankly incensed by the behavior shown in
> In/Out 80, below.
>
> In[80]:=     {1,2,3}/.(m_List->(2*#& /@ m))
> Out[80]=    {1,2,3}

See what happens when you replace -> with :>

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

I think you might now work out what is going on.  The distinction
between -> and :> can be very important but somwhat difficult to
explain. My favorite example to explain the difference between immediate
and delayed replacement is to get the student to compare

{x,x,x} /. x -> Random[]

with

{x,x,x} /. x :> Random[]

Analogously, to explain the difference between Set and SetDelayed,
compare

r = Random[];
Table[r,{3}];

with

r := Random[];
Table[r,{3}];

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                        http://www.physics.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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