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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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