       Re: Re-evaluation of Conditional expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg3474] Re: [mg3460] Re-evaluation of Conditional expressions
• From: Richard Mercer <richard at seuss.math.wright.edu>
• Date: Sat, 16 Mar 1996 22:37:43 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```Patrice,

This is a good one!
To my surprise, "If" turns out the have the HoldAll attribute,
which seems to be the cause of the behavior you describe.
If you first execute

Unprotect[If];
ClearAttributes[If,HoldAll]

Then your example works as one would expect.
The problem then is: why does the first example work with the
HoldAll attribute in place?
SetAttributes[If,HoldAll]
x = True; y
1

Apparently "If" is willing to evaluate one step in search of a True or
False result in spite of the HoldAll attribute. Indeed "If" would be
pretty useless without such a capability. This *appears* to be a
special exception to HoldAll.

I don't have an explanation for why the HoldAll attribute is there
in the first place. Probably it is like "Plot": it works well in some
cases and not well in others (like yours). It would be interesting to
hear a good case for the use of HoldAll for "If".

Richard Mercer

>  While teaching Mathematica, I found the following quite
>  strange behaviour of Conditional expressions in
>  Mathematica. Define symbol y as follows:
>

>  y = If[x,1,2]
>

>  (* Then set x to True and revaluate y *)
>  x=True;y
>

>  (* as expected, the answer is 1 *)
>  (* Now, set x to z, a fresh symbol, and evaluate y *)
>  Clear[x,z];x=z;y
>

>  (* The result is If[x,1,2] *)
>

>  (* Finally, set z to True, and evaluate y *)
>  z=True;y
>

>  The result is still If[x,1,2], although a re-evaluation
>  of x gives True, as expected.
>

>  The only way to get a re-evaluation of y is to use the
>  function Update:
>

>  Update[];y
>

>  which gives the result 1. In summary, it seems that If
>  is re-evaluated only if the expression that assigned to
>  x has changed, and not when the value of x has changed.
>

>  Is there a special reason for this? Any way to circumvent
>  this problem?
>

>  Thanks.
>

>  Patrice Quinton

==== [MESSAGE SEPARATOR] ====

```

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