Re: Apply a rule to an expression only once

• To: mathgroup at smc.vnet.net
• Subject: [mg116330] Re: Apply a rule to an expression only once
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Fri, 11 Feb 2011 04:15:11 -0500 (EST)

```expr = f a + f b;
rule = f p_ :> f[p];
first = First@Cases[expr, First@rule]
where = First@Position[expr, first]
ReplacePart[expr, where -> (first /. rule)]

a f

{1}

b f + f[a]

Bobby

On Thu, 10 Feb 2011 04:22:37 -0600, Guido Walter Pettinari
<coccoinomane at gmail.com> wrote:

> Hello group!
>
> Does anybody know how to apply a rule to an expression only once?
> In other words, is it possible to tell ReplaceAll to stop after the
> first application of a rule?
>
> Simple example:
>
> expr = f a + f b;
> rule = f p_ :> f [p];
> ReplaceAll [ expr, rule ]
>
> The output, as expected, is:
> f [a] + f [b]
>
> However, what I want is something like:
>
> ReplaceAll [ expr, rule, OnlyFirst -> True ]
>
> that gives the output
>
> f [a] + f b.
>
> My simple example can be solved by using ReplacePart, but alas it is
> not the kind of solution I am looking for.
>
> Thank you for your consideration!
>
> Best regards,
>
> Guido W. Pettinari
>
> P.S. I found a temporary solution by using a pattern test at the time
> of rule definition, i.e.
>
> rule = f p_ /; matchFirst[] :> f [p],
>
> with
>
> matchFirst [] := Module [ { },
>   ],
>
> but this does not satisfy me since (i) I do not want to alter the rule
> definition, and (ii)  I have to update the global variable
> \$alreadyMatched every time I want to use the trick.
>
>

--
DrMajorBob at yahoo.com

```

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