Re: pure function

*To*: mathgroup at smc.vnet.net*Subject*: [mg113745] Re: pure function*From*: Stephan <stschiff80 at googlemail.com>*Date*: Wed, 10 Nov 2010 06:28:36 -0500 (EST)

Cool, thanks for the hint about using "With", everyone. Best, Stephan Am 09.11.2010 um 08:52 schrieb Ray Koopman: > 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 y= our 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 t= o With: >>> parameters are textually substituted to the body before the body starts= to evaluate. >>> There are a few subtle differences (related to name collision resolutio= n 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> wr= ote: >>>> 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 th= e >>>> 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 t= he >>>> value instead of digging out the local variable a$57... >>>> >>>> >>>> >>>> Thanks, >>>> >>>> Stephan >