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MathGroup Archive 2006

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HoldPattern question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70026] HoldPattern question
  • From: dimmechan at yahoo.com
  • Date: Sat, 30 Sep 2006 05:13:17 -0400 (EDT)

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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