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Re: About Condition and HoldAll

• To: mathgroup at smc.vnet.net
• Subject: [mg76088] Re: [mg76030] About Condition and HoldAll
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 16 May 2007 05:25:19 -0400 (EDT)
• References: <200705150848.EAA16743@smc.vnet.net>

On 15 May 2007, at 17:48, solidifire wrote:

> In[1]:= {f[1 + 1, 2 + 3], g[1 + 1, 2 + 3], h[1 + 1, 2 + 3]}
> Out[1]= {f[2, 5], g[2, 5], h[2, 5]}
>
> In[2]:= SetAttributes[f, HoldAll]
>
> In[3]:= SetAttributes[g, HoldRest]
>
> In[4]:= {f[1 + 1, 2 + 3], g[1 + 1, 2 + 3], h[1 + 1, 2 + 3]}
> Out[4]= {f[1 + 1, 2 + 3], g[2, 2 + 3], h[2, 5]}
>
> In[5]:= Attributes[Condition]
> Out[5]= {HoldAll, Protected}
>
> In[6]:= Condition[1 + 1, 2 + 3]
> Out[6]= 2 /; 2 + 3
>
> The version of Mathematica is 5.0 for Microsoft Windows.
>
> My question is that why does Condition behave as having HoldRest
> as attribute although the attribute is HoldAll actually?
>
>

The "evaluation" of 1+1 that you see is not "pre-evaluation" but  
"post-evaluation". The difference between pre-evaluatio nand post- 
evlaution can be seen on this simple example:

In[1]:= SetAttributes[f, HoldAll]
In[2]:= f[x_] := x
In[3]:= f[1 + 1]
Out[3]= 2

Since f has a HoldAll attribute 1+1 was not pre-evaluated by it was  
still post-evaluated.

You can see the working of the HodlAll attribute here:

g[t_] := Condition[Print["evaluated"], t]

Note that:

g[True]
"evaluated"

  g[False]
g(False)

Clearly, if Condition pre-evaluated the first argument it would have  
printed "evalauted" no matter what the value of t was.
By contrast, If has attribute HoldRest so, if we define:

h[t_] := If[Print["evaluated"]; t, Print[1], Print[0]]

h[True]
"evaluated"
1
h[False]
"evaluated"
0

"evaluated" always gets printed, but 1 or 0 are printed depending on  
the value of t.

ALso, note that the behaviour of Condition seems hard coded and can't  
be changed by changing its attributes.

Andrzej Kozlowski

• References:
  • About Condition and HoldAll
    • From: solidifire <barabbasgospel@yahoo.com.tw>