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Re: Rule-based programming: declare variables to be a number

• To: mathgroup at smc.vnet.net
• Subject: [mg80832] Re: Rule-based programming: declare variables to be a number
• From: Szabolcs <szhorvat at gmail.com>
• Date: Tue, 4 Sep 2007 03:35:04 -0400 (EDT)
• Organization: University of Bergen
• References: <fb83lf$82d$1@smc.twtelecom.net> <200709020651.CAA25850@smc.twtelecom.net> <fbgmuq$9d7$1@smc.vnet.net>

Andrzej Kozlowski wrote:
>   NumericQ has clearly been designed with this in mind. Note, for  
> example, that althou NumericQ is Protected, a definition like
> 
> NumericQ[a]=True
> 
> does not require unprotecting NumericQ. Moreover, it does not add a  
> DownValue to NumericQ.
> 
> NumericQ[g] = True;
> DownValues[NumericQ]
> {}
> 
> 
> There are plenty of other reasons to believe that all all  
> theseproperties of NumericQ are designed precisely for this type of  
> use. Besides, I have another reason to think that no probems of the  
> kind you are imagining would happen in this case: I have been using  
> NumericQ inprecisly this way for about 10 years in numerous notebooks  
> without any problems.
> 
> Note alo the post from Carl Woll which, I think, can be regarded as  
> an "offcial" WRI authorization for this kind of usage ;-)
> 
> (However, note also that using Carl's definition:
> 
> In[19]:= g /: NumericQ[g] = True;
> 
> Dos not actually add an UpValue to g:
> 
> UpValues[g]
> {}
> 
> and I don't think it has any advantage over the more straightforward
> 
> NumericQ[g] = True;
> 
> 
> I am sure all this is deliberate design, and even though it may not  
> be easy to explain, it is very convenient.
> 
> Andrzej Kozlowski
> 

Thanks for the explanation!

But this is very curious.  If neither the UpValues or Attributes of g, 
or the DownValues of NumericQ are changed, then where is this 
information about g stored?  Is this something that is implemented at a 
lower level than the Mathematica language?  Is it possible to create 
other custom properties, that can be set with a command as simple as 
someProperty[g] = True (without using g /: someProperty[g] = True)?

Perhaps NumericQ itself behaves similarly to DownValues, OwnValues, 
etc., where it is also possible to write OwnValues[a]={a->3} directly, 
but when 'a' is removed, its OwnValues are gone too.

(When 'g' is Removed, the information that NumericQ[g] === True is gone 
too.)

Szabolcs

• References:
  • Re: Rule-based programming: declare variables to be a number
    • From: David Bailey <dave@Remove_Thisdbailey.co.uk>