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MathGroup Archive 1999

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Standard Evaluation with UpValues

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19355] Standard Evaluation with UpValues
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Fri, 20 Aug 1999 23:09:35 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Section 7.1.3 of the excellent book "Power Programming With Mathematica The
Kernel" by David B. Wagner explains the main evaluation loop.  In that
Section it indicates UpValues for a symbol are applied before DownValues for
the symbol are applied.

OK then consider the case below where (f) has both an UpValue and a
DownValue defined by the user.

At Out[4] the UpValue for (f) was used.  In that case the DownValue couldn't
be used to evaluate f[t].  
Then at Out[5] the DownValue for (f) is used to evaluate  f[E] --> 1+E
before the kernel checked to see if the UpValue would apply (and it would
have).  I get the same result using Versions 3 and 4.

When the kernel evaluates g[f[E]] it must figure out that the Head is (g)
before it evaluates f[E].  After determining that the Head is (g) it checks
to see if (g) has any Hold* attributes, and continues with evaluation as
required.  So by the time the kernel evaluates f[E] it has all the
information it needs to know that the UpValue for (f) can be used.  However,
the DownValue is used instead.  Wait a minute, aren't UpValues applied
before DownValues are applied?

Can someone convince me that the main evaluation loop performs as explained
by David Wagner when evaluating In[5] below?  Also can someone give a
different example that more clearly shows that UpValues are used first?
------------------------------
 
In[1]:=
ClearAll[f,g,t];
f[x_?NumericQ]:=1+x;
f/:g[f[x_]]:=x+4;
 
 
In[4]:=
g[f[t]]

Ou[4]=
4+t
 
 
In[5]:=
g[f[E]]

Out[5]=
g[1+E]

--------------------
Regards,
Ted Ersek

For Mathematica tips, tricks see 
http://www.dot.net.au/~elisha/ersek/Tricks.html



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