Re: pure function

*To*: mathgroup at smc.vnet.net*Subject*: [mg113721] Re: pure function*From*: Ray Koopman <koopman at sfu.ca>*Date*: Tue, 9 Nov 2010 03:52:22 -0500 (EST)*References*: <ib8k3m$659$1@smc.vnet.net>

On Nov 8, 2:40 am, Stephan <stschif... at googlemail.com> wrote: > Ah, I forgot a follow up: > > What if I don't want to use a constant like in the example I stated? > What if I want to compute the local value of a in the module and > return the computed value instead of the symbol? I am kind of > looking for a general way to evaluate a part of an expression > within the delayed evaluation of the function body. > > Thanks, > > Stephan In[1]:= getFunk := Module[{a=2}, With[{b=a^2}, Function[{x}, b * x]]] In[2]:= g = getFunk Out[2]= Function[{x$},4 x$] > > Am 08.11.2010 um 09:20 schrieb Leonid Shifrin: > >> Stephan, >> >> Yes, sure, use With instead of Module: >> >> In[2]:== getFunc:==With[{a==2},Function[{x},a*x]] >> >> In[3]:== f==getFunc >> >> Out[3]== Function[{x$},2 x$] >> >> So, by using Module, you can create a closure whose state (variable <a> >> in this case) comes from surrounding context but can be modified by it >> at a later time. Using With gets you a textual substitution of a value that >> a given expression had, at the moment when With was invoked. >> >> You can also accomplish your goal somewhat differently, by redefining your getFunc: >> >> In[4]:== >> Clear[getFunc]; >> getFunc[y_] :== Function[{x}, y*x] >> >> In[6]:== getFunc[2] >> >> Out[6]== Function[{x$}, 2 x$] >> >> The semantics of parameter-passing in Mathematica is somewhat similar to With: >> parameters are textually substituted to the body before the body starts to evaluate. >> There are a few subtle differences (related to name collision resolution in nested >> scoping constructs), but they do not show up in this particular case. >> >> Regards, >> Leonid >> >> On Mon, Nov 8, 2010 at 11:37 AM, Stephan <stschif... at googlemail.com> wrote: >>> Hi, >>> >>> I have a function that returns a pure function: >>> >>> In[1]:== getFunc :== Module[{a==2}, Function[{x}, a * x]] >>> >>> In[2]:== f == getFunc >>> >>> Out[2]== Function[{x$}, a$57 x$] >>> >>> Is there any way, to have the body of the returned function contain the >>> actual _value_ of the local variable a, instead of the _symbol_ ? >>> So I would like the returned function to be written as >>> >>> Function[{x$}, 2 x$] >>> >>> The reason is, that I would like to have a quick way to actually see the >>> value instead of digging out the local variable a$57... >>> >>> >>> >>> Thanks, >>> >>> Stephan