Re: HoldPattern question

• To: mathgroup at smc.vnet.net
• Subject: [mg70076] Re: HoldPattern question
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Mon, 2 Oct 2006 00:33:54 -0400 (EDT)
• References: <eflejf\$dh6\$1@smc.vnet.net>

```Hi,

look what happens when you enter

{Integrate[y_, x_] -> f, Log[x] -> Exp[x]}

and you see that Integrate[y_, x_] is not evaluated
Only
{Integrate[y, x] -> f, Log[x] -> Exp[x]}

will try to evaluate the integral, while

{Integrate[y_, x] -> f, Log[x] -> Exp[x]}
{Integrate[y, x_] -> f, Log[x] -> Exp[x]}
and
{Integrate[y_, x_] -> f, Log[x] -> Exp[x]}

stay unevaluated.

Regards
Jens

dimmechan at yahoo.com wrote:
> Hello to all.
>
> I copied from the Help Browser.
>
> HoldPattern[expr] is equivalent to expr for pattern matching,
> but maintains expr in an unevaluated form.
> (...)
> Example: expr /. HoldPattern[Integrate[y_, x_]] -> rhs transforms
> any subexpression of the form Integrate[y_, x_] in expr. Without
> the HoldPattern, the Integrate[y_, x_] in the rule would immediately
> be evaluated to give x_ y_, and the replacement would not work."
>
> So based on this notes the folowing rule seems normal and well
> justified.
>
> Hold[Integrate[a, x]] + Log[x] /. {HoldPattern[Integrate[y_, x_]] -> f,
> Log[x] -> Exp[x]}
> E^x + Hold[f]
>
> However why the following rule (that is without HoldPattern) gives the
> same output?
>
> Hold[Integrate[a, x]] + Log[x] /. {Integrate[y_, x_] -> f, Log[x] ->
> Exp[x]}
> E^x + Hold[f]
>
> Using Trace I notice that even without HoldPattern surrounded
> Integrate[y_,x_] the latter is not evaluated to x_y_.
>
> Trace[Hold[Integrate[a, x]] + Log[x] /. {Integrate[y_, x_] -> f, Log[x]
> -> Exp[x]}]
> {{{HoldForm[Integrate[y_, x_] -> f], HoldForm[Integrate[y_, x_] -> f]},
>  {{HoldForm[E^x], HoldForm[E^x]},  HoldForm[Log[x] -> E^x],
> HoldForm[Log[x] -> E^x]},
> HoldForm[{Integrate[y_, x_] -> f, Log[x] -> E^x}]},
> HoldForm[Hold[Integrate[a, x]] + Log[x] /. {Integrate[y_, x_] -> f,
> Log[x] -> E^x}], HoldForm[Hold[f] + E^x], HoldForm[E^x + Hold[f]]}
>
> Based on the Help Browser it is very curious that this worked.
> Otherwise something I am missing.
>
> I really appreciate some guidance.
>
> Thanks.
>

```

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