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Re: Do we need a When function?

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  • Subject: [mg132554] Re: Do we need a When function?
  • From: Szabolcs HorvÃt <szhorvat at>
  • Date: Fri, 11 Apr 2014 02:09:49 -0400 (EDT)
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On 2014-3-8, 2:42 , David Bailey wrote:
> Dear All,
> Recently I wanted to create an expression that only evaluated when x was
> a number. Obviously, one way to do that is to write something like:
>    If[x<1000000000000,f[x]]
> This will stay unevaluated until x is assigned to a number - as required
> - but it is very ugly because it makes it hard to understand what is
> going on.
> More generally, it would be nice to write an expression that will only
> evaluate when an expression is true. I solved that by writing a function
> When:
> SetAttributes[When, HoldAll];
> When[cond_, val_] := val /; cond
> However, my point is that this construction is sufficiently useful that
> it should be built in to Mathematica, and my solution might not be
> obvious to all users.
> Am I missing a simpler solution?
> Do others agree that this is an omission in the language?

Putting aside the question whether this should be a part of the core 
language, I got quite convinced that this is a pretty useful function. 
I am saying this one month after David's original post, so this opinion 
is based on some practical experience.  During this month I found myself 
remembering and using this function on a number of occasions.  (Not very 
often, but it does keep coming back.)

Admittedly, in all cases I used it with NumericQ, so I might as well 
have hard-coded NumericQ into it ...

SetAttributes[whenNumeric, HoldRest]
whenNumeric[x_?NumericQ, val_] := val

My point is that it seems that this is going to stay in my personal 
toolbox permanently, it is indeed a useful function.

To show an example, most recently I used it while experimenting with 
this piecewise function:

NIntegrate[when[NumericQ[x], First@test[x]], {x, -2, 2}]

test[] is a function that returns a vector here.  Its implementation 
details are irrelevant for my argument.

Using When here was much easier than defining a separate function only 
to allow NIntegrate to be used on the first component of the vector.

This When[] function doesn't allow me to do anything I couldn't do 
without it.  I wouldn't miss it at all when writing a package.  But it 
is very useful for quick-and-dirty or "improvisational" programming, 
i.e. what I do 90% of the time when I use Mathematica interactively.  It 
saves me time and effort.


P.S. One thing that bothers me slightly is that I do not yet see clearly 
whether Condition caching might interact badly with this function.

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