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. >